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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Sherman-Morrison-Woodbury</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org87c8640">1. Headers</a></li>
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<li><a href="#org62d1526">2. Naïve Sherman-Morrison</a>
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<ul>
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<li><a href="#org1fb16c0">2.1. <code>qmckl_sm_naive</code></a>
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<ul>
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<li><a href="#orgbd1c14f">2.1.1. Introduction</a></li>
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<li><a href="#org7a9eb6d">2.1.2. API</a></li>
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<li><a href="#orgd733796">2.1.3. Requirements</a></li>
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<li><a href="#org6ae9dcb">2.1.4. Pedagogical kernel source (in Fortran)</a>
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<ul>
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<li><a href="#org784d42d">2.1.4.1. C interface (not directly exposed)</a></li>
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</ul>
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</li>
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<li><a href="#org542d316">2.1.5. C headers (exposed in qmckl.h)</a></li>
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<li><a href="#org96e46e0">2.1.6. C sources</a></li>
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<li><a href="#org278fc7e">2.1.7. Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</a></li>
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<li><a href="#orgce2507a">2.1.8. Performance</a></li>
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<li><a href="#org94ff75b">2.1.9. Tests</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#orgeecc8f0">3. Sherman-Morrison with Slagel Splitting (core)</a>
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<ul>
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<li><a href="#org94dfcbc">3.1. <code>qmckl_sm_splitting_core</code></a>
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<ul>
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<li><a href="#orga449ee2">3.1.1. Introduction</a></li>
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<li><a href="#org13b1557">3.1.2. API</a></li>
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<li><a href="#orgaae415d">3.1.3. Requirements</a></li>
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<li><a href="#orgf2c08ec">3.1.4. Pedagogical kernel source (in Fortran)</a>
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<ul>
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<li><a href="#org14ecc87">3.1.4.1. C interface to the pedagogical kernel (not directly exposed)</a></li>
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</ul>
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</li>
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<li><a href="#org476c4c1">3.1.5. C headers (exposed in qmckl.h)</a></li>
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<li><a href="#orgacc8e05">3.1.6. C sources</a></li>
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<li><a href="#orgcb39007">3.1.7. Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</a></li>
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<li><a href="#orga519336">3.1.8. Performance</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#org5966f29">4. Woodbury 2x2</a>
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<ul>
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<li><a href="#orgd214ab8">4.1. <code>qmckl_woodbury_2x2</code></a>
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<ul>
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<li><a href="#org47cf931">4.1.1. Introduction</a></li>
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<li><a href="#org9f51aa5">4.1.2. API</a></li>
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<li><a href="#org62cfa70">4.1.3. Requirements</a></li>
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<li><a href="#org5e27e71">4.1.4. Pedagogical kernel source (in Fortran)</a>
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<ul>
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<li><a href="#org2493bf0">4.1.4.1. C interface (not directly exposed)</a></li>
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</ul>
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</li>
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<li><a href="#orgeedd6dc">4.1.5. C headers (exposed in qmckl.h)</a></li>
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<li><a href="#org1366ddc">4.1.6. C sources</a></li>
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<li><a href="#org9360748">4.1.7. Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</a></li>
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<li><a href="#org4fea646">4.1.8. Performance</a></li>
|
|
<li><a href="#org5defcbf">4.1.9. Tests</a></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgcbc617b">5. Woodbury 3x3</a>
|
|
<ul>
|
|
<li><a href="#org1c111ec">5.1. <code>qmckl_woodbury_3x3</code></a>
|
|
<ul>
|
|
<li><a href="#org8896d6f">5.1.1. Introduction</a></li>
|
|
<li><a href="#orgd817e2a">5.1.2. API</a></li>
|
|
<li><a href="#org79e256f">5.1.3. Requirements</a></li>
|
|
<li><a href="#org4cf6603">5.1.4. Pedagogical kernel source (in Fortran)</a>
|
|
<ul>
|
|
<li><a href="#org743b142">5.1.4.1. C interface (not directly exposed)</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgd16448f">5.1.5. C headers (exposed in qmckl.h)</a></li>
|
|
<li><a href="#org75c9b2f">5.1.6. C sources</a></li>
|
|
<li><a href="#org8208ea2">5.1.7. Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</a></li>
|
|
<li><a href="#org9ecbdf0">5.1.8. Performance</a></li>
|
|
<li><a href="#org5272284">5.1.9. Tests</a></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgedd101f">6. Sherman-Morrison with Slagel Splitting</a>
|
|
<ul>
|
|
<li><a href="#orgb5b525b">6.1. <code>qmckl_sm_splitting</code></a>
|
|
<ul>
|
|
<li><a href="#org2ae2358">6.1.1. Introduction</a></li>
|
|
<li><a href="#org876c69a">6.1.2. API</a></li>
|
|
<li><a href="#org514f002">6.1.3. Requirements</a></li>
|
|
<li><a href="#orgf81577e">6.1.4. Pedagogical kernel source (in Fortran)</a>
|
|
<ul>
|
|
<li><a href="#org2442936">6.1.4.1. C interface to the pedagogical kernel (not directly exposed)</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org85f3506">6.1.5. C headers (exposed in qmckl.h)</a></li>
|
|
<li><a href="#org42d9709">6.1.6. C source</a></li>
|
|
<li><a href="#org39ce850">6.1.7. Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</a></li>
|
|
<li><a href="#orgf37d972">6.1.8. Performance…</a></li>
|
|
<li><a href="#org5a86004">6.1.9. Test</a></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org00488f9">7. End of files</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org87c8640" class="outline-2">
|
|
<h2 id="org87c8640"><span class="section-number-2">1</span> Headers</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"qmckl.h"</span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"assert.h"</span>
|
|
<span style="color: #483d8b;">#ifdef</span> HAVE_CONFIG_H
|
|
<span style="color: #483d8b;"> #include</span> <span style="color: #8b2252;">"config.h"</span>
|
|
<span style="color: #483d8b;">#endif</span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><math.h></span>
|
|
|
|
<span style="color: #228b22;">int</span> <span style="color: #0000ff;">main</span>() {
|
|
<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>;
|
|
context = qmckl_context_create();
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">rc</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
This is the range that determines the how many high performance kernel instantces will be generated, using the C-function templates defined in the sections below. If the name of the C-function template is called <code>qmckl_kernel_{Dim}</code>, then <code>range(K, L+1)</code> will results in kernel instances from <code>qmckl_kernel_K</code> to <code>qmckl_kernel_L</code>.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org62d1526" class="outline-2">
|
|
<h2 id="org62d1526"><span class="section-number-2">2</span> Naïve Sherman-Morrison</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
<div id="outline-container-org1fb16c0" class="outline-3">
|
|
<h3 id="org1fb16c0"><span class="section-number-3">2.1</span> <code>qmckl_sm_naive</code></h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
</div>
|
|
|
|
<div id="outline-container-orgbd1c14f" class="outline-4">
|
|
<h4 id="orgbd1c14f"><span class="section-number-4">2.1.1</span> Introduction</h4>
|
|
<div class="outline-text-4" id="text-2-1-1">
|
|
<p>
|
|
This is the simplest of the available Sherman-Morrison-Woodbury kernels. It applies rank-1 updates one by one in
|
|
the order that is given. It only checks if the denominator in the Sherman-Morrison formula is not too close to
|
|
zero when an update is evaluated. It will exit with an error code of the denominator is too close to zero.
|
|
</p>
|
|
|
|
<p>
|
|
#+TODO
|
|
Change the math notation so that the update vectors appear as row in the math
|
|
so that it is consistent with the representation in C (memory)
|
|
</p>
|
|
|
|
<p>
|
|
The formula for any update \(u_j\) (index \(j\) is suppresed for clarity) that is applied is
|
|
\[
|
|
(S + uv^T)^{-1} = S^{-1} - \frac{S^{-1} uv^T S^{-1}}{1 + v^T S^{-1} u}
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
where
|
|
\(S\) is the Slater-matrix,
|
|
\(u\) and \(v^T\) are the column and row vectors containing the updates,
|
|
\(S^{-1}\) is the inverse of the Slater-matrix.
|
|
</p>
|
|
|
|
<p>
|
|
Even though the Slater-matrix \(S\) with all updates applied at once is invertable, during the course of applying
|
|
updates to the inverse Slater-matrix \(S^{-1}\) one-by-one it can happen that one of the intermediate inverse
|
|
matrices \(S^{-1}\) becomes singular. Therefore a global threshold value \(\epsilon\) is defined that is used to
|
|
evaluate each individual update \(u_j\) when it is applied.
|
|
</p>
|
|
|
|
<p>
|
|
This value sets the lower bound for which the
|
|
denominator \(1+v_j^TS^{-1}u_j\) is considered to be too small and will most probably result in a singular matrix
|
|
\(S\), or at least in an inverse of \(S\) of very poor numerical quality. Therefore, when \(1+v_j^TS^{-1}u_j \geq \epsilon\),
|
|
the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
|
|
If \(1+v_j^TS^{-1}u_j \leq \epsilon\) the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
|
|
</p>
|
|
|
|
<p>
|
|
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
|
|
from applying the updates to the original matrix.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7a9eb6d" class="outline-4">
|
|
<h4 id="org7a9eb6d"><span class="section-number-4">2.1.2</span> API</h4>
|
|
<div class="outline-text-4" id="text-2-1-2">
|
|
<table id="orgd1dbbb7" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Variable</th>
|
|
<th scope="col" class="org-left">Type</th>
|
|
<th scope="col" class="org-left">In/Out</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left"><code>qmckl_context</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>LDS</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Dim</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>N_updates</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of rank-1 updates to be applied to Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates</code></td>
|
|
<td class="org-left"><code>double[N_updates*LDS]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates_index</code></td>
|
|
<td class="org-left"><code>uint64_t[N_updates]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the rank-1 updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>breakdown</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Break-down parameter on which to fail or not</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Slater_inv</code></td>
|
|
<td class="org-left"><code>double[Dim*LDS]</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the inverse of a Slater-matrix</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>determinant</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Determinant of the Slater-matrix</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd733796" class="outline-4">
|
|
<h4 id="orgd733796"><span class="section-number-4">2.1.3</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-2-1-3">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>LDS >= 2</code></li>
|
|
<li><code>Dim >= 2</code></li>
|
|
<li><code>N_updates >= 1</code></li>
|
|
<li><code>Updates</code> is allocated with \(N_updates \times Dim\) elements</li>
|
|
<li><code>Updates_index</code> is allocated with \(N_updates\) elements</li>
|
|
<li><code>breakdown</code> is a small number such that \(0 < breakdown << 1\)</li>
|
|
<li><code>Slater_inv</code> is allocated with \(Dim \times Dim\) elements</li>
|
|
<li><code>determinant > 0</code></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6ae9dcb" class="outline-4">
|
|
<h4 id="org6ae9dcb"><span class="section-number-4">2.1.4</span> Pedagogical kernel source (in Fortran)</h4>
|
|
<div class="outline-text-4" id="text-2-1-4">
|
|
<p>
|
|
The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
|
|
able to do numerically correct computations, it does not do it in the most efficient way possible. It should therefore
|
|
not be used in real workloads.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_sm_naive_doc_f(context, </span><span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
nupdates, <span style="color: #a020f0;">&</span>
|
|
upds, <span style="color: #a020f0;">&</span>
|
|
updates_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
determinant) <span style="color: #a020f0;">result</span>(info)
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lds, dim</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nupdates</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> updates_index(nupdates)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> upds(nupdates * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> breakdown</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> s_inv(dim * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> determinant</span>
|
|
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, nupdates) ::<span style="color: #a0522d;"> Updates</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, dim) ::<span style="color: #a0522d;"> Inverse</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim) ::<span style="color: #a0522d;"> C</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim) ::<span style="color: #a0522d;"> D</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> denominator, idenominator, update</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i, j, l, row</span>
|
|
|
|
info = QMCKL_FAILURE
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">Convert 'upds' and 's_inv' into the more easily readable Fortran</span>
|
|
! <span style="color: #b22222;">matrices 'Updates' and 'Inverse'.</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">convert</span>(upds, s_inv, Updates, Inverse, nupdates, lds, dim)
|
|
|
|
l = 1;
|
|
! <span style="color: #b22222;">For each update do...</span>
|
|
<span style="color: #a020f0;">do while</span> (l < nupdates + 1)
|
|
|
|
! <span style="color: #b22222;">Compute C = S^{-1}U(l)</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
C(i) = 0
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
C(i) = C(i) + Inverse(i, j) * Updates(j, l)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Compute denominator = 1 + V(l)^TC</span>
|
|
row = updates_index(l)
|
|
denominator = 1 + C(row)
|
|
|
|
! <span style="color: #b22222;">Return early if denominator is too small</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">abs</span>(denominator) < breakdown) <span style="color: #a020f0;">return</span>
|
|
idenominator = 1 / denominator
|
|
|
|
! <span style="color: #b22222;">Update det(S)</span>
|
|
determinant = determinant * denominator
|
|
|
|
! <span style="color: #b22222;">selecting column: v_l^T * S_inv</span>
|
|
D = Inverse(row, :)
|
|
|
|
! <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / denominator</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
update = C(i) * D(j) * idenominator
|
|
Inverse(i, j) = Inverse(i, j) - update
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
l = l + 1
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Copy updated inverse back to s_inv</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">copy_back_inv</span>(Inverse, s_inv, lds, dim)
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_sm_naive_doc_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org784d42d" class="outline-5">
|
|
<h5 id="org784d42d"><span class="section-number-5">2.1.4.1</span> C interface (not directly exposed)</h5>
|
|
<div class="outline-text-5" id="text-2-1-4-1">
|
|
<p>
|
|
The following Fortran function <code>qmckl_sm_naive_doc</code> makes sure
|
|
that the pedagogical kernel <code>qmckl_sm_naive_doc_f</code>, written in
|
|
Fortran, can be called from C using the <code>ISO_C_BINDING</code>. The Fortran function <code>qmckl_sm_naive_doc</code> will be exposed in the header file 'qmckl.h'
|
|
for C users and in the module file 'qmckl<sub>f.F90</sub>' for Fortran users.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org542d316" class="outline-4">
|
|
<h4 id="org542d316"><span class="section-number-4">2.1.5</span> C headers (exposed in qmckl.h)</h4>
|
|
<div class="outline-text-4" id="text-2-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_hpc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_doc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org96e46e0" class="outline-4">
|
|
<h4 id="org96e46e0"><span class="section-number-4">2.1.6</span> C sources</h4>
|
|
<div class="outline-text-4" id="text-2-1-6">
|
|
<p>
|
|
Common includes and macros used by all the Sherman-Morrison-Woodbury kernels.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><stdbool.h></span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><math.h></span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"qmckl.h"</span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"config.h"</span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"assert.h"</span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"stdio.h"</span>
|
|
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
<code>qmckl_sm_naive_hpc</code> is a high performance variation of
|
|
<code>qmckl_sm_naive</code> written in C. It is used in cases when <code>Dim</code> is
|
|
smaller than the leading dimension <code>LDS</code>, irrespective of whetether <code>LDS</code>
|
|
includes zero padding to benefit from SIMD instructions or not. Cases like this
|
|
include situations where one wants to apply updates to a square submatrix of the
|
|
full matrix.
|
|
It takes advantage of memory aligned data and assumes no data dependencies
|
|
inside the loops. The loops are fully vectorised whenever <code>Dim</code> is an integer
|
|
multiple of <code>SIMD_LENGTH</code>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_hpc</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith( context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_hpc"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[Dim];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[LDS];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x u_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator: v_l^T * C</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown)
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
D[j] = Slater_inv[cui * LDS + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * LDS + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
<code>qmckl_exit_code qmckl_sm_naive_{Dim}</code> is a C function-template that is used to genereate instances of C fucntions based on the range given above. The advantage of this method is that for each of these instances all the dimensions and loop-bounds are known at compile time, allowing the compiler to optimize more aggressively.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-c" id="org833ee5b"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">qmckl_sm_naive_</span>{Dim}(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_{Dim}"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D</span>{Dim}_P ((1+({Dim}-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[{Dim}];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D{Dim}_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
C[i] += Slater_inv[i * D{Dim}_P + j] * Updates[l * D{Dim}_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
D[j] = Slater_inv[cui * D{Dim}_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D{Dim}_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
This is the kernel generator written in Python. It uses the kernel generator range and templates defined above to generate the C kernel instances.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-python" id="org7333bcc"><span style="color: #a0522d;">text</span>=<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #8b2252;">static inline qmckl_exit_code qmckl_sm_naive_{Dim}(</span>
|
|
<span style="color: #8b2252;"> const qmckl_context context,</span>
|
|
<span style="color: #8b2252;"> const uint64_t N_updates,</span>
|
|
<span style="color: #8b2252;"> const double* restrict Updates,</span>
|
|
<span style="color: #8b2252;"> const uint64_t* restrict Updates_index,</span>
|
|
<span style="color: #8b2252;"> const double breakdown,</span>
|
|
<span style="color: #8b2252;"> double* restrict Slater_inv,</span>
|
|
<span style="color: #8b2252;"> double* restrict determinant) {</span>
|
|
|
|
<span style="color: #8b2252;"> if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {</span>
|
|
<span style="color: #8b2252;"> return qmckl_failwith(context,</span>
|
|
<span style="color: #8b2252;"> QMCKL_NULL_CONTEXT,</span>
|
|
<span style="color: #8b2252;"> "qmckl_sm_naive_{Dim}",</span>
|
|
<span style="color: #8b2252;"> NULL);</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> #define D{Dim}_P ((1+({Dim}-1)/SIMD_LENGTH)*SIMD_LENGTH)</span>
|
|
|
|
<span style="color: #8b2252;"> double __attribute__((aligned(8))) C[{Dim}];</span>
|
|
<span style="color: #8b2252;"> double __attribute__((aligned(8))) D[D{Dim}_P];</span>
|
|
|
|
<span style="color: #8b2252;"> uint64_t l = 0;</span>
|
|
<span style="color: #8b2252;"> // For each update</span>
|
|
<span style="color: #8b2252;"> while (l < N_updates) {</span>
|
|
<span style="color: #8b2252;"> // C = A^{-1} x U_l</span>
|
|
<span style="color: #8b2252;"> for (uint64_t i = 0; i < {Dim}; i++) {</span>
|
|
<span style="color: #8b2252;"> C[i] = 0;</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t j = 0; j < D{Dim}_P; j++) {</span>
|
|
<span style="color: #8b2252;"> C[i] += Slater_inv[i * D{Dim}_P + j] * Updates[l * D{Dim}_P + j];</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> // Denominator</span>
|
|
<span style="color: #8b2252;"> const int cui = Updates_index[l] - 1;</span>
|
|
<span style="color: #8b2252;"> double den = 1.0f + C[cui];</span>
|
|
|
|
<span style="color: #8b2252;"> if (fabs(den) < breakdown) {</span>
|
|
<span style="color: #8b2252;"> return QMCKL_FAILURE;</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> double iden = 1.0f / den;</span>
|
|
|
|
<span style="color: #8b2252;"> // Update det(A)</span>
|
|
<span style="color: #8b2252;"> if (determinant)</span>
|
|
<span style="color: #8b2252;"> *determinant *= den;</span>
|
|
|
|
<span style="color: #8b2252;"> // selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t j = 0; j < D{Dim}_P; j++) {</span>
|
|
<span style="color: #8b2252;"> D[j] = Slater_inv[cui * D{Dim}_P + j];</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> // A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #8b2252;"> for (uint64_t i = 0; i < {Dim}; i++) {</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t j = 0; j < D{Dim}_P; j++) {</span>
|
|
<span style="color: #8b2252;"> double update = C[i] * D[j] * iden;</span>
|
|
<span style="color: #8b2252;"> Slater_inv[i * D{Dim}_P + j] -= update;</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> l += 1;</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> return QMCKL_SUCCESS;</span>
|
|
<span style="color: #8b2252;">}</span>
|
|
<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #a0522d;">result</span> = []
|
|
<span style="color: #a020f0;">for</span> Dim <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(2, 22):
|
|
<span style="color: #a0522d;">Dim</span>=<span style="color: #483d8b;">str</span>(Dim)
|
|
result.append(text.replace(<span style="color: #8b2252;">"{Dim}"</span>,Dim))
|
|
|
|
<span style="color: #a020f0;">return</span> <span style="color: #8b2252;">''</span>.join(result)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Python script that generated C switch cases that call individual kernel instances.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-python" id="orgb22a053"><span style="color: #a0522d;">text</span>=<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #8b2252;">case {Dim}: </span>
|
|
<span style="color: #8b2252;"> return qmckl_sm_naive_{Dim}(context,</span>
|
|
<span style="color: #8b2252;"> N_updates,</span>
|
|
<span style="color: #8b2252;"> Updates,</span>
|
|
<span style="color: #8b2252;"> Updates_index,</span>
|
|
<span style="color: #8b2252;"> breakdown,</span>
|
|
<span style="color: #8b2252;"> Slater_inv,</span>
|
|
<span style="color: #8b2252;"> determinant);"""</span>
|
|
<span style="color: #a0522d;">result</span> = []
|
|
<span style="color: #a020f0;">for</span> Dim <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(2, 22):
|
|
<span style="color: #a0522d;">Dim</span>=<span style="color: #483d8b;">str</span>(Dim)
|
|
result.append(text.replace(<span style="color: #8b2252;">"{Dim}"</span>,Dim))
|
|
|
|
<span style="color: #a020f0;">return</span> <span style="color: #8b2252;">''</span>.join(result)
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_2</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_2"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D2_P</span> ((1+(2-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D2_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
C[i] += Slater_inv[i * D2_P + j] * Updates[l * D2_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
D[j] = Slater_inv[cui * D2_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D2_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_3</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_3"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D3_P</span> ((1+(3-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D3_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
C[i] += Slater_inv[i * D3_P + j] * Updates[l * D3_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
D[j] = Slater_inv[cui * D3_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D3_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_4</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_4"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D4_P</span> ((1+(4-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[4];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D4_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
C[i] += Slater_inv[i * D4_P + j] * Updates[l * D4_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
D[j] = Slater_inv[cui * D4_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D4_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_5</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_5"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D5_P</span> ((1+(5-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[5];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D5_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
C[i] += Slater_inv[i * D5_P + j] * Updates[l * D5_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
D[j] = Slater_inv[cui * D5_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D5_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_6</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_6"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D6_P</span> ((1+(6-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[6];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D6_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
C[i] += Slater_inv[i * D6_P + j] * Updates[l * D6_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
D[j] = Slater_inv[cui * D6_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D6_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_7</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_7"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D7_P</span> ((1+(7-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[7];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D7_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
C[i] += Slater_inv[i * D7_P + j] * Updates[l * D7_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
D[j] = Slater_inv[cui * D7_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D7_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_8</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_8"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D8_P</span> ((1+(8-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[8];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D8_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
C[i] += Slater_inv[i * D8_P + j] * Updates[l * D8_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
D[j] = Slater_inv[cui * D8_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D8_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_9</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_9"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D9_P</span> ((1+(9-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[9];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D9_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
C[i] += Slater_inv[i * D9_P + j] * Updates[l * D9_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
D[j] = Slater_inv[cui * D9_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D9_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_10</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_10"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D10_P</span> ((1+(10-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[10];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D10_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
C[i] += Slater_inv[i * D10_P + j] * Updates[l * D10_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
D[j] = Slater_inv[cui * D10_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D10_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_11</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_11"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D11_P</span> ((1+(11-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[11];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D11_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
C[i] += Slater_inv[i * D11_P + j] * Updates[l * D11_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
D[j] = Slater_inv[cui * D11_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D11_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_12</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_12"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D12_P</span> ((1+(12-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[12];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D12_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
C[i] += Slater_inv[i * D12_P + j] * Updates[l * D12_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
D[j] = Slater_inv[cui * D12_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D12_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_13</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_13"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D13_P</span> ((1+(13-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[13];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D13_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
C[i] += Slater_inv[i * D13_P + j] * Updates[l * D13_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
D[j] = Slater_inv[cui * D13_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D13_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_14</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_14"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D14_P</span> ((1+(14-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[14];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D14_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
C[i] += Slater_inv[i * D14_P + j] * Updates[l * D14_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
D[j] = Slater_inv[cui * D14_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D14_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_15</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_15"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D15_P</span> ((1+(15-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[15];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D15_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
C[i] += Slater_inv[i * D15_P + j] * Updates[l * D15_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
D[j] = Slater_inv[cui * D15_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D15_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_16</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_16"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D16_P</span> ((1+(16-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[16];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D16_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
C[i] += Slater_inv[i * D16_P + j] * Updates[l * D16_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
D[j] = Slater_inv[cui * D16_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D16_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_17</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_17"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D17_P</span> ((1+(17-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[17];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D17_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
C[i] += Slater_inv[i * D17_P + j] * Updates[l * D17_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
D[j] = Slater_inv[cui * D17_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D17_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_18</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_18"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D18_P</span> ((1+(18-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[18];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D18_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
C[i] += Slater_inv[i * D18_P + j] * Updates[l * D18_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
D[j] = Slater_inv[cui * D18_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D18_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_19</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_19"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D19_P</span> ((1+(19-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[19];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D19_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
C[i] += Slater_inv[i * D19_P + j] * Updates[l * D19_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
D[j] = Slater_inv[cui * D19_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D19_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_20</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_20"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D20_P</span> ((1+(20-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[20];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D20_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
C[i] += Slater_inv[i * D20_P + j] * Updates[l * D20_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
D[j] = Slater_inv[cui * D20_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D20_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive_21</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive_21"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #define</span> <span style="color: #a0522d;">D21_P</span> ((1+(21-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[21];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D21_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = A^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
C[i] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
C[i] += Slater_inv[i * D21_P + j] * Updates[l * D21_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
// <span style="color: #b22222;">Update det(A)</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">selecting column: D = v_l^T * S_inv</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
D[j] = Slater_inv[cui * D21_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D21_P + j] -= update;
|
|
}
|
|
}
|
|
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
<code>qmckl_sm_naive</code> is a generic function that contains decision making logic that calls the proper kernel based on the used library configuration (<code>--enable-doc</code> and <code>--enable-hpc</code>) and the passed array dimensions <code>LDS</code> and <code>Dim</code>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_naive</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_naive"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #ifdef</span> HAVE_HPC__BROKEN_WITH_CRAY
|
|
<span style="color: #a020f0;">if</span> (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // <span style="color: #b22222;">Most cases</span>
|
|
<span style="color: #a020f0;">switch</span> (Dim) {
|
|
<span style="color: #a020f0;">case</span> 2:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_2(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 3:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_3(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 4:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_4(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 5:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_5(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 6:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_6(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 7:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_7(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 8:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_8(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 9:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_9(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 10:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_10(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 11:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_11(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 12:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_12(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 13:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_13(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 14:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_14(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 15:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_15(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 16:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_16(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 17:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_17(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 18:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_18(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 19:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_19(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 20:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_20(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 21:
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_21(context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
}
|
|
}
|
|
<span style="color: #a020f0;">else</span>
|
|
{ // <span style="color: #b22222;">Updating smaller sub-matrix</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_hpc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
}
|
|
<span style="color: #483d8b;"> #else</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_naive_doc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #483d8b;"> #endif</span>
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org278fc7e" class="outline-4">
|
|
<h4 id="org278fc7e"><span class="section-number-4">2.1.7</span> Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</h4>
|
|
<div class="outline-text-4" id="text-2-1-7">
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgce2507a" class="outline-4">
|
|
<h4 id="orgce2507a"><span class="section-number-4">2.1.8</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-2-1-8">
|
|
<p>
|
|
This function performs best when there is only 1 rank-1 update in the update cycle. It is
|
|
not useful to use Sherman-Morrison with update splitting for these cycles since splitting
|
|
can never resolve a situation where applying the update causes singular behaviour.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org94ff75b" class="outline-4">
|
|
<h4 id="org94ff75b"><span class="section-number-4">2.1.9</span> Tests</h4>
|
|
<div class="outline-text-4" id="text-2-1-9">
|
|
<p>
|
|
The tests for the kernels are executed on datasets that are extracted from a run of
|
|
QMC=Chem on Benzene (21 spin-up/21 spin down electrons) using 329 unique alpha determinants.
|
|
The tests are run such that the kernels reject the computed inverse whenever the computed
|
|
intermediate determinants or denominators are smaller than 1e-3. This is the default value in
|
|
QMC=Chem. The tests will return QMCKL<sub>SUCCESS</sub> whenever all the elements of the final matrix
|
|
\(R=S.S^-1 - 1\) are smaller than the given tolerance value of 1e-3, and will return
|
|
QMCKL<sub>FAILURE</sub> if the values are larger than this tolerance value.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span> = 21;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span> = (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span> = 1e-3;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">tolerance</span> = 1e-3;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">res</span>[441];
|
|
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;">"sm_test.h"</span>
|
|
|
|
<span style="color: #0000ff;">assert</span>(Updates1 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Updates_index1 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Slater_inv1 != <span style="color: #008b8b;">NULL</span>);
|
|
|
|
// <span style="color: #b22222;">original determinant of Slater1 (before applying updates)</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = 3.407025646103221e-10;
|
|
rc = qmckl_sm_naive(context,
|
|
LDS,
|
|
Dim,
|
|
N_updates1,
|
|
Updates1,
|
|
Updates_index1,
|
|
breakdown,
|
|
Slater_inv1,
|
|
&det);
|
|
|
|
// <span style="color: #b22222;">Check that the determinant is updated properly</span>
|
|
<span style="color: #0000ff;">assert</span>(fabs(det + 4.120398385068217e-10) < 1e-15);
|
|
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
res[i * Dim + j] = 0;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">k</span> = 0; k < Dim; k++) {
|
|
res[i * Dim + j] += Slater1[i * Dim + k] * Slater_inv1[k * LDS + j];
|
|
}
|
|
}
|
|
}
|
|
rc = QMCKL_SUCCESS;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
<span style="color: #a020f0;">if</span> (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #a020f0;">if</span> (i != j && fabs(res[i * Dim + j]) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
}
|
|
}
|
|
<span style="color: #0000ff;">assert</span>(rc == QMCKL_SUCCESS);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgeecc8f0" class="outline-2">
|
|
<h2 id="orgeecc8f0"><span class="section-number-2">3</span> Sherman-Morrison with Slagel Splitting (core)</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
</div>
|
|
<div id="outline-container-org94dfcbc" class="outline-3">
|
|
<h3 id="org94dfcbc"><span class="section-number-3">3.1</span> <code>qmckl_sm_splitting_core</code></h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
</div>
|
|
|
|
<div id="outline-container-orga449ee2" class="outline-4">
|
|
<h4 id="orga449ee2"><span class="section-number-4">3.1.1</span> Introduction</h4>
|
|
<div class="outline-text-4" id="text-3-1-1">
|
|
<p>
|
|
<code>qmckl_sm_splitting_core</code> is the inner core part of 'Sherman-Morrison with update splitting' in the next section.
|
|
It is not normally used by itself but it is possible to use it nonetheless.
|
|
</p>
|
|
|
|
<p>
|
|
It has three extra parameters in its API:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li><code>later_updates</code> initially empty array that will contain the second halves of updates that were split during kernel execution</li>
|
|
<li><code>later_index</code> initially empty array that will contain the row/column numbers of the updates that were split during execution</li>
|
|
<li><code>later</code> initially zero integer that records the number of updates that were split during exection.</li>
|
|
</ul>
|
|
|
|
<p>
|
|
It is up to the user to decide what to do with these updates once the kernel returns. Normally <code>qmckl_sm_splitting_core</code> is
|
|
used as the core part of a recursive function, as is done in <code>qmckl_sm_splitting</code> or as part of a more complex
|
|
kernel like <code>qmckl_sherman_morrison_smw32s</code>.
|
|
</p>
|
|
|
|
<p>
|
|
If the determinant is passed it will only be partially updated if there were any update splits.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org13b1557" class="outline-4">
|
|
<h4 id="org13b1557"><span class="section-number-4">3.1.2</span> API</h4>
|
|
<div class="outline-text-4" id="text-3-1-2">
|
|
<table id="org26b046b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Variable</th>
|
|
<th scope="col" class="org-left">Type</th>
|
|
<th scope="col" class="org-left">In/Out</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left"><code>qmckl_context</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>LDS</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Dim</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>N_updates</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of rank-1 updates to be applied to Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates</code></td>
|
|
<td class="org-left"><code>double[LDS*N_updates]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the rank-1 updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates_index</code></td>
|
|
<td class="org-left"><code>uint64_t[N_updates]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing positions of the rank-1 updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>breakdown</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Break-down parameter on which to fail or not</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Slater_inv</code></td>
|
|
<td class="org-left"><code>double[Dim*LDS]</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the inverse Slater-matrix</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>later_updates</code></td>
|
|
<td class="org-left"><code>double[LDS*N_updates]</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the split updates for later</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>later_index</code></td>
|
|
<td class="org-left"><code>uint64_t[N_updates]</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the positions of the split updates for later</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>later</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Number of split updates for later</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>determinant</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Determinant of the Slater-matrix</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaae415d" class="outline-4">
|
|
<h4 id="orgaae415d"><span class="section-number-4">3.1.3</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-3-1-3">
|
|
<ul class="org-ul">
|
|
<li><code>LDS >= 2</code></li>
|
|
<li><code>Dim >= 2</code></li>
|
|
<li><code>N_updates >= 1</code></li>
|
|
<li><code>Updates</code> is allocated with \(N_updates \times Dim\) elements</li>
|
|
<li><code>Updates_index</code> is allocated with \(N_updates\) elements</li>
|
|
<li><code>breakdown</code> is a small number such that \(0 < breakdown << 1\)</li>
|
|
<li><code>Slater_inv</code> is allocated with \(Dim \times Dim\) elements</li>
|
|
<li><code>later_updates</code> is allocated with \(later \times Dim\) elements</li>
|
|
<li><code>later_index</code> is allocated with \(N_updates\) elements</li>
|
|
<li><code>later >= 0</code></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf2c08ec" class="outline-4">
|
|
<h4 id="orgf2c08ec"><span class="section-number-4">3.1.4</span> Pedagogical kernel source (in Fortran)</h4>
|
|
<div class="outline-text-4" id="text-3-1-4">
|
|
<p>
|
|
The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
|
|
able to do numerically correct computations, it does not do it in the most efficient way possible. It should therefore
|
|
not be used in real workloads.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_sm_splitting_core_doc_f( </span><span style="color: #a020f0;">&</span>
|
|
context, <span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
nupdates, <span style="color: #a020f0;">&</span>
|
|
upds, <span style="color: #a020f0;">&</span>
|
|
updates_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
later_upds, <span style="color: #a020f0;">&</span>
|
|
Later_index, <span style="color: #a020f0;">&</span>
|
|
Later, <span style="color: #a020f0;">&</span>
|
|
determinant) <span style="color: #a020f0;">result</span>(info)
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lds, dim</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nupdates</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> updates_index(nupdates)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> upds(lds * nupdates)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> breakdown</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> s_inv(dim * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> determinant</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> Later</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> Later_index(nupdates)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> later_upds(lds * nupdates)</span>
|
|
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, nupdates) ::<span style="color: #a0522d;"> Updates</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, nupdates) ::<span style="color: #a0522d;"> Later_updates</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, dim) ::<span style="color: #a0522d;"> Inverse</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim) ::<span style="color: #a0522d;"> C</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim) ::<span style="color: #a0522d;"> D</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> denominator, idenominator, update</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i, j, l, row</span>
|
|
|
|
info = QMCKL_FAILURE
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">Convert 'upds' and 's_inv' into the more easily readable Fortran</span>
|
|
! <span style="color: #b22222;">matrices 'Updates' and 'Inverse'.</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">convert</span>(upds, s_inv, Updates, Inverse, nupdates, lds, dim)
|
|
|
|
l = 1;
|
|
! <span style="color: #b22222;">For each update do...</span>
|
|
<span style="color: #a020f0;">do while</span> (l < nupdates + 1)
|
|
|
|
! <span style="color: #b22222;">Compute C = S^{-1}U(l)</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
C(i) = 0
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
C(i) = C(i) + Inverse(i, j) * Updates(j, l)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Compute denominator = 1 + V(l)^TC</span>
|
|
row = updates_index(l)
|
|
denominator = 1 + C(row)
|
|
|
|
! <span style="color: #b22222;">If denominator is too close to zero:</span>
|
|
! <span style="color: #b22222;">- Split update in 2 before storing in Later_updates</span>
|
|
! <span style="color: #b22222;">- Split previously computed vector C in 2</span>
|
|
! <span style="color: #b22222;">- Recompute the denominator</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">abs</span>(denominator) < breakdown) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
Later_updates(i, l) = Updates(i, l) / 2
|
|
C(i) = C(i) / 2
|
|
<span style="color: #a020f0;">end do</span>
|
|
Later_index(Later + 1) = updates_index(l)
|
|
Later = Later + 1
|
|
denominator = 1 + C(row)
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
idenominator = 1 / denominator
|
|
|
|
! <span style="color: #b22222;">Update det(S)</span>
|
|
determinant = determinant * denominator
|
|
|
|
! <span style="color: #b22222;">selecting column: v_l^T * S_inv</span>
|
|
D = Inverse(row, :)
|
|
|
|
! <span style="color: #b22222;">A^{-1} = A^{-1} - C x D / denominator</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
update = C(i) * D(j) * idenominator
|
|
Inverse(i, j) = Inverse(i, j) - update
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
l = l + 1
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Copy updated inverse and later updates</span>
|
|
! <span style="color: #b22222;">back to s_inv and later_upds</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">copy_back_inv</span>(Inverse, s_inv, lds, dim)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">copy_back_lu</span>(Later_Updates, later_upds, lds, dim, nupdates)
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_doc_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org14ecc87" class="outline-5">
|
|
<h5 id="org14ecc87"><span class="section-number-5">3.1.4.1</span> C interface to the pedagogical kernel (not directly exposed)</h5>
|
|
<div class="outline-text-5" id="text-3-1-4-1">
|
|
<p>
|
|
The function <code>qmckl_sm_splitting_core_doc</code> makes sure that
|
|
<code>qmckl_sm_splitting_core_doc_f</code> can be called from C using the
|
|
<code>ISO_C_BINDING</code>. Function <code>qmckl_sm_splitting_core_doc</code> will be
|
|
exposed in <code>qmckl.h</code> and <code>qmckl_f.F90</code>, but
|
|
<code>qmckl_sm_splitting_core_doc_f</code> will not.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org476c4c1" class="outline-4">
|
|
<h4 id="org476c4c1"><span class="section-number-4">3.1.5</span> C headers (exposed in qmckl.h)</h4>
|
|
<div class="outline-text-4" id="text-3-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_hpc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_doc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgacc8e05" class="outline-4">
|
|
<h4 id="orgacc8e05"><span class="section-number-4">3.1.6</span> C sources</h4>
|
|
<div class="outline-text-4" id="text-3-1-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_hpc</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_hpc"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[LDS];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[LDS];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < LDS; i++) {
|
|
later_updates[*later * LDS + i] = Updates[l * LDS + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x LDS</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
D[j] = Slater_inv[cui * LDS + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * LDS + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c" id="org99a6ae6"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">qmckl_sm_splitting_core_</span>{Dim}(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_{Dim}"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D{Dim}_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D{Dim}_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
C[i] += Slater_inv[i * D{Dim}_P + j] * Updates[l * D{Dim}_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D{Dim}_P; i++) {
|
|
later_updates[*later * D{Dim}_P + i] = Updates[l * D{Dim}_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D{Dim}_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
D[j] = Slater_inv[cui * D{Dim}_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D{Dim}_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python" id="org111fe86"><span style="color: #a0522d;">text</span>=<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #8b2252;">static inline qmckl_exit_code qmckl_sm_splitting_core_{Dim}(</span>
|
|
<span style="color: #8b2252;"> const qmckl_context context,</span>
|
|
<span style="color: #8b2252;"> uint64_t N_updates,</span>
|
|
<span style="color: #8b2252;"> const double* restrict Updates,</span>
|
|
<span style="color: #8b2252;"> const uint64_t* restrict Updates_index,</span>
|
|
<span style="color: #8b2252;"> const double breakdown,</span>
|
|
<span style="color: #8b2252;"> double* restrict Slater_inv,</span>
|
|
<span style="color: #8b2252;"> double* restrict later_updates,</span>
|
|
<span style="color: #8b2252;"> uint64_t* restrict later_index,</span>
|
|
<span style="color: #8b2252;"> uint64_t* restrict later,</span>
|
|
<span style="color: #8b2252;"> double* restrict determinant) {</span>
|
|
|
|
<span style="color: #8b2252;"> if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {</span>
|
|
<span style="color: #8b2252;"> return qmckl_failwith(</span>
|
|
<span style="color: #8b2252;"> context,</span>
|
|
<span style="color: #8b2252;"> QMCKL_NULL_CONTEXT,</span>
|
|
<span style="color: #8b2252;"> "qmckl_sm_splitting_core_{Dim}",</span>
|
|
<span style="color: #8b2252;"> NULL);</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> double __attribute__((aligned(8))) C[D{Dim}_P];</span>
|
|
<span style="color: #8b2252;"> double __attribute__((aligned(8))) D[D{Dim}_P];</span>
|
|
|
|
<span style="color: #8b2252;"> uint64_t l = 0;</span>
|
|
<span style="color: #8b2252;"> // For each update</span>
|
|
<span style="color: #8b2252;"> while (l < N_updates) {</span>
|
|
<span style="color: #8b2252;"> // C = S^{-1} x U_l</span>
|
|
<span style="color: #8b2252;"> for (uint64_t i = 0; i < {Dim}; i++) {</span>
|
|
<span style="color: #8b2252;"> C[i] = 0.0f;</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t j = 0; j < D{Dim}_P; j++) {</span>
|
|
<span style="color: #8b2252;"> C[i] += Slater_inv[i * D{Dim}_P + j] * Updates[l * D{Dim}_P + j];</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> // Denominator</span>
|
|
<span style="color: #8b2252;"> const int cui = Updates_index[l] - 1;</span>
|
|
<span style="color: #8b2252;"> double den = 1.0f + C[cui];</span>
|
|
<span style="color: #8b2252;"> if (fabs(den) < breakdown) {</span>
|
|
<span style="color: #8b2252;"> // U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
<span style="color: #8b2252;"> // second halve in later_updates</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t i = 0; i < D{Dim}_P; i++) {</span>
|
|
<span style="color: #8b2252;"> later_updates[*later * D{Dim}_P + i] = Updates[l * D{Dim}_P + i] * 0.5f;</span>
|
|
<span style="color: #8b2252;"> C[i] *= 0.5f;</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> later_index[*later] = Updates_index[l];</span>
|
|
<span style="color: #8b2252;"> (*later)++;</span>
|
|
|
|
<span style="color: #8b2252;"> den = 1.0f + C[cui];</span>
|
|
<span style="color: #8b2252;"> } // From here onwards we continue with applying the first halve of the</span>
|
|
<span style="color: #8b2252;"> // update to Slater_inv</span>
|
|
<span style="color: #8b2252;"> double iden = 1.0f / den;</span>
|
|
|
|
<span style="color: #8b2252;"> if (determinant)</span>
|
|
<span style="color: #8b2252;"> *determinant *= den;</span>
|
|
|
|
<span style="color: #8b2252;"> // D = v^T x S^{-1} : 1 x D{Dim}_P</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t j = 0; j < D{Dim}_P; j++) {</span>
|
|
<span style="color: #8b2252;"> D[j] = Slater_inv[cui * D{Dim}_P + j];</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> // S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #8b2252;"> for (uint64_t i = 0; i < {Dim}; i++) {</span>
|
|
<span style="color: #8b2252;"> IVDEP</span>
|
|
<span style="color: #8b2252;"> ALIGNED</span>
|
|
<span style="color: #8b2252;"> for (uint64_t j = 0; j < D{Dim}_P; j++) {</span>
|
|
<span style="color: #8b2252;"> const double update = C[i] * D[j] * iden;</span>
|
|
<span style="color: #8b2252;"> Slater_inv[i * D{Dim}_P + j] -= update;</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
<span style="color: #8b2252;"> l += 1;</span>
|
|
<span style="color: #8b2252;"> }</span>
|
|
|
|
<span style="color: #8b2252;"> return QMCKL_SUCCESS;</span>
|
|
<span style="color: #8b2252;">}</span>
|
|
<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #a0522d;">result</span> = []
|
|
<span style="color: #a020f0;">for</span> Dim <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(2, 22):
|
|
<span style="color: #a0522d;">Dim</span>=<span style="color: #483d8b;">str</span>(Dim)
|
|
result.append(text.replace(<span style="color: #8b2252;">"{Dim}"</span>,Dim) )
|
|
|
|
<span style="color: #a020f0;">return</span> <span style="color: #8b2252;">''</span>.join(result)
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python" id="org1e0392f"><span style="color: #a0522d;">text</span>=<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #8b2252;">case {Dim}: {</span>
|
|
<span style="color: #8b2252;"> return qmckl_sm_splitting_core_{Dim}(</span>
|
|
<span style="color: #8b2252;"> context,</span>
|
|
<span style="color: #8b2252;"> N_updates,</span>
|
|
<span style="color: #8b2252;"> Updates,</span>
|
|
<span style="color: #8b2252;"> Updates_index,</span>
|
|
<span style="color: #8b2252;"> breakdown,</span>
|
|
<span style="color: #8b2252;"> Slater_inv,</span>
|
|
<span style="color: #8b2252;"> later_updates,</span>
|
|
<span style="color: #8b2252;"> later_index,</span>
|
|
<span style="color: #8b2252;"> later,</span>
|
|
<span style="color: #8b2252;"> determinant);</span>
|
|
<span style="color: #8b2252;">}"""</span>
|
|
<span style="color: #a0522d;">result</span> = []
|
|
<span style="color: #a020f0;">for</span> Dim <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(2, 22):
|
|
<span style="color: #a0522d;">Dim</span>=<span style="color: #483d8b;">str</span>(Dim)
|
|
result.append(text.replace(<span style="color: #8b2252;">"{Dim}"</span>,Dim) )
|
|
|
|
<span style="color: #a020f0;">return</span> <span style="color: #8b2252;">''</span>.join(result)
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_2</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_2"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D2_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D2_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
C[i] += Slater_inv[i * D2_P + j] * Updates[l * D2_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D2_P; i++) {
|
|
later_updates[*later * D2_P + i] = Updates[l * D2_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D2_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
D[j] = Slater_inv[cui * D2_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D2_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_3</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_3"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D3_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D3_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
C[i] += Slater_inv[i * D3_P + j] * Updates[l * D3_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D3_P; i++) {
|
|
later_updates[*later * D3_P + i] = Updates[l * D3_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D3_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
D[j] = Slater_inv[cui * D3_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D3_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_4</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_4"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D4_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D4_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
C[i] += Slater_inv[i * D4_P + j] * Updates[l * D4_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D4_P; i++) {
|
|
later_updates[*later * D4_P + i] = Updates[l * D4_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D4_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
D[j] = Slater_inv[cui * D4_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D4_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_5</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_5"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D5_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D5_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
C[i] += Slater_inv[i * D5_P + j] * Updates[l * D5_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D5_P; i++) {
|
|
later_updates[*later * D5_P + i] = Updates[l * D5_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D5_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
D[j] = Slater_inv[cui * D5_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D5_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_6</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_6"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D6_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D6_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
C[i] += Slater_inv[i * D6_P + j] * Updates[l * D6_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D6_P; i++) {
|
|
later_updates[*later * D6_P + i] = Updates[l * D6_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D6_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
D[j] = Slater_inv[cui * D6_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D6_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_7</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_7"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D7_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D7_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
C[i] += Slater_inv[i * D7_P + j] * Updates[l * D7_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D7_P; i++) {
|
|
later_updates[*later * D7_P + i] = Updates[l * D7_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D7_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
D[j] = Slater_inv[cui * D7_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D7_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_8</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_8"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D8_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D8_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
C[i] += Slater_inv[i * D8_P + j] * Updates[l * D8_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D8_P; i++) {
|
|
later_updates[*later * D8_P + i] = Updates[l * D8_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D8_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
D[j] = Slater_inv[cui * D8_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D8_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_9</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_9"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D9_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D9_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
C[i] += Slater_inv[i * D9_P + j] * Updates[l * D9_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D9_P; i++) {
|
|
later_updates[*later * D9_P + i] = Updates[l * D9_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D9_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
D[j] = Slater_inv[cui * D9_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D9_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_10</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_10"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D10_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D10_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
C[i] += Slater_inv[i * D10_P + j] * Updates[l * D10_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D10_P; i++) {
|
|
later_updates[*later * D10_P + i] = Updates[l * D10_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D10_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
D[j] = Slater_inv[cui * D10_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D10_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_11</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_11"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D11_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D11_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
C[i] += Slater_inv[i * D11_P + j] * Updates[l * D11_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D11_P; i++) {
|
|
later_updates[*later * D11_P + i] = Updates[l * D11_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D11_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
D[j] = Slater_inv[cui * D11_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D11_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_12</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_12"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D12_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D12_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
C[i] += Slater_inv[i * D12_P + j] * Updates[l * D12_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D12_P; i++) {
|
|
later_updates[*later * D12_P + i] = Updates[l * D12_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D12_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
D[j] = Slater_inv[cui * D12_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D12_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_13</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_13"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D13_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D13_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
C[i] += Slater_inv[i * D13_P + j] * Updates[l * D13_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D13_P; i++) {
|
|
later_updates[*later * D13_P + i] = Updates[l * D13_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D13_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
D[j] = Slater_inv[cui * D13_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D13_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_14</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_14"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D14_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D14_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
C[i] += Slater_inv[i * D14_P + j] * Updates[l * D14_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D14_P; i++) {
|
|
later_updates[*later * D14_P + i] = Updates[l * D14_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D14_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
D[j] = Slater_inv[cui * D14_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D14_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_15</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_15"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D15_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D15_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
C[i] += Slater_inv[i * D15_P + j] * Updates[l * D15_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D15_P; i++) {
|
|
later_updates[*later * D15_P + i] = Updates[l * D15_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D15_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
D[j] = Slater_inv[cui * D15_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D15_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_16</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_16"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D16_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D16_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
C[i] += Slater_inv[i * D16_P + j] * Updates[l * D16_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D16_P; i++) {
|
|
later_updates[*later * D16_P + i] = Updates[l * D16_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D16_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
D[j] = Slater_inv[cui * D16_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D16_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_17</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_17"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D17_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D17_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
C[i] += Slater_inv[i * D17_P + j] * Updates[l * D17_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D17_P; i++) {
|
|
later_updates[*later * D17_P + i] = Updates[l * D17_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D17_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
D[j] = Slater_inv[cui * D17_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D17_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_18</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_18"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D18_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D18_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
C[i] += Slater_inv[i * D18_P + j] * Updates[l * D18_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D18_P; i++) {
|
|
later_updates[*later * D18_P + i] = Updates[l * D18_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D18_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
D[j] = Slater_inv[cui * D18_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D18_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_19</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_19"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D19_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D19_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
C[i] += Slater_inv[i * D19_P + j] * Updates[l * D19_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D19_P; i++) {
|
|
later_updates[*later * D19_P + i] = Updates[l * D19_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D19_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
D[j] = Slater_inv[cui * D19_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D19_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_20</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_20"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D20_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D20_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
C[i] += Slater_inv[i * D20_P + j] * Updates[l * D20_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D20_P; i++) {
|
|
later_updates[*later * D20_P + i] = Updates[l * D20_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D20_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
D[j] = Slater_inv[cui * D20_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D20_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core_21</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_core_21"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[D21_P];
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">D</span>[D21_P];
|
|
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">l</span> = 0;
|
|
// <span style="color: #b22222;">For each update</span>
|
|
<span style="color: #a020f0;">while</span> (l < N_updates) {
|
|
// <span style="color: #b22222;">C = S^{-1} x U_l</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
C[i] = 0.0f;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
C[i] += Slater_inv[i * D21_P + j] * Updates[l * D21_P + j];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Denominator</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">cui</span> = Updates_index[l] - 1;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">den</span> = 1.0f + C[cui];
|
|
<span style="color: #a020f0;">if</span> (fabs(den) < breakdown) {
|
|
// <span style="color: #b22222;">U_l = U_l / 2: split the update in 2 equal halves and save the</span>
|
|
// <span style="color: #b22222;">second halve in later_updates</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < D21_P; i++) {
|
|
later_updates[*later * D21_P + i] = Updates[l * D21_P + i] * 0.5f;
|
|
C[i] *= 0.5f;
|
|
}
|
|
later_index[*later] = Updates_index[l];
|
|
(*later)++;
|
|
|
|
den = 1.0f + C[cui];
|
|
} // <span style="color: #b22222;">From here onwards we continue with applying the first halve of the</span>
|
|
// <span style="color: #b22222;">update to Slater_inv</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">iden</span> = 1.0f / den;
|
|
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= den;
|
|
|
|
// <span style="color: #b22222;">D = v^T x S^{-1} : 1 x D21_P</span>
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
D[j] = Slater_inv[cui * D21_P + j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">S^{-1} = S^{-1} - C x D / den</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">update</span> = C[i] * D[j] * iden;
|
|
Slater_inv[i * D21_P + j] -= update;
|
|
}
|
|
}
|
|
l += 1;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_core</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">later_updates</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later_index</span>,
|
|
<span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">later</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #483d8b;"> #ifdef</span> HAVE_HPC__BROKEN_WITH_CRAY
|
|
<span style="color: #a020f0;">if</span> (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // <span style="color: #b22222;">Most cases</span>
|
|
<span style="color: #a020f0;">switch</span> (Dim) {
|
|
<span style="color: #a020f0;">case</span> 2: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_2(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 3: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_3(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 4: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_4(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 5: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_5(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 6: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_6(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 7: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_7(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 8: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_8(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 9: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_9(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 10: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_10(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 11: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_11(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 12: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_12(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 13: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_13(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 14: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_14(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 15: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_15(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 16: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_16(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 17: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_17(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 18: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_18(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 19: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_19(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 20: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_20(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">case</span> 21: {
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_21(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #a020f0;">default</span>: {
|
|
assert(0 == 1 && <span style="color: #8b2252;">"TEMPLATE NOT IMPLEMENTED!"</span>);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
}
|
|
}
|
|
<span style="color: #a020f0;">else</span> { // <span style="color: #b22222;">Updating smaller sub-matrix</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_hpc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
}
|
|
<span style="color: #483d8b;"> #else</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_core_doc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index,
|
|
later,
|
|
determinant);
|
|
<span style="color: #483d8b;"> #endif</span>
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcb39007" class="outline-4">
|
|
<h4 id="orgcb39007"><span class="section-number-4">3.1.7</span> Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</h4>
|
|
<div class="outline-text-4" id="text-3-1-7">
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga519336" class="outline-4">
|
|
<h4 id="orga519336"><span class="section-number-4">3.1.8</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-3-1-8">
|
|
<p>
|
|
This function cannot be used by itself and is used in Sherman-Morrison with update splitting and Woodbury 3x3 and 2x2
|
|
with Sherman-Morrison and update splitting. Please look at the performance reccomendations for those two kernels.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org5966f29" class="outline-2">
|
|
<h2 id="org5966f29"><span class="section-number-2">4</span> Woodbury 2x2</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
</div>
|
|
<div id="outline-container-orgd214ab8" class="outline-3">
|
|
<h3 id="orgd214ab8"><span class="section-number-3">4.1</span> <code>qmckl_woodbury_2x2</code></h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
</div>
|
|
|
|
<div id="outline-container-org47cf931" class="outline-4">
|
|
<h4 id="org47cf931"><span class="section-number-4">4.1.1</span> Introduction</h4>
|
|
<div class="outline-text-4" id="text-4-1-1">
|
|
<p>
|
|
The Woodbury 2x2 kernel. It is used to apply two rank-1 updates at once. The formula used in
|
|
this algorithm is called the Woodbury Matrix Id
|
|
\[
|
|
(S + U V)^{-1} = S^{-1} - C B^{-1} D
|
|
\]
|
|
where
|
|
\(S\) is the Slater-matrix
|
|
\(U\) and \(V\) are the matrices containing the updates and the canonical basis matrix
|
|
\(S^{-1}\) is the inverse of the Slater-matrix
|
|
\(C:= S^{-1}U\), a Dim \(\times 2\) matrix
|
|
\(B := 1 + VC\), the \(2 \times 2\) matrix that is going to be inverted
|
|
\(D := VS^{-1}\), a \(2 \times Dim\) matrix
|
|
</p>
|
|
|
|
<p>
|
|
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
|
|
from applying the updates to the original matrix.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9f51aa5" class="outline-4">
|
|
<h4 id="org9f51aa5"><span class="section-number-4">4.1.2</span> API</h4>
|
|
<div class="outline-text-4" id="text-4-1-2">
|
|
<table id="org220e811" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Variable</th>
|
|
<th scope="col" class="org-left">Type</th>
|
|
<th scope="col" class="org-left">In/Out</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left"><code>qmckl_context</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>LDS</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Dim</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates</code></td>
|
|
<td class="org-left"><code>double[2*Dim]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates_index</code></td>
|
|
<td class="org-left"><code>uint64_t[2]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the rank-1 updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>breakdown</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Break-down parameter on which to fail or not</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Slater_inv</code></td>
|
|
<td class="org-left"><code>double[LDS*Dim]</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the inverse of a Slater-matrix</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>determinant</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Determinant of Slater-matrix</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org62cfa70" class="outline-4">
|
|
<h4 id="org62cfa70"><span class="section-number-4">4.1.3</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-4-1-3">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>qmckl_null_context</code></li>
|
|
<li><code>LDS >= 2</code></li>
|
|
<li><code>Dim >= 2</code></li>
|
|
<li><code>Updates</code> is allocated with \(2 \times Dim\) elements</li>
|
|
<li><code>Updates_index</code> is allocated with \(2\) elements</li>
|
|
<li><code>breakdown</code> is a small number such that \(0 < breakdown << 1\)</li>
|
|
<li><code>Slater_inv</code> is allocated with \(Dim \times Dim\) elements</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5e27e71" class="outline-4">
|
|
<h4 id="org5e27e71"><span class="section-number-4">4.1.4</span> Pedagogical kernel source (in Fortran)</h4>
|
|
<div class="outline-text-4" id="text-4-1-4">
|
|
<p>
|
|
The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
|
|
able to do numerically correct computations, it does not do it in the most efficient way possible. It should therefore
|
|
not be used in real workloads.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_woodbury_2x2_doc_f(</span><span style="color: #a020f0;">&</span>
|
|
context, <span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
upds, <span style="color: #a020f0;">&</span>
|
|
updates_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
determinant) <span style="color: #a020f0;">result</span>(info)
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lds, dim</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> updates_index(2)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> upds(2 * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> breakdown</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> s_inv(dim * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> determinant</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">dimension</span>(2, dim) ::<span style="color: #a0522d;"> V</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">dimension</span>(2, 2) ::<span style="color: #a0522d;"> Id</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, dim) ::<span style="color: #a0522d;"> Inverse</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, 2) ::<span style="color: #a0522d;"> Updates, C</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(2, 2) ::<span style="color: #a0522d;"> D, invD</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(2, dim) ::<span style="color: #a0522d;"> E, F</span>
|
|
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> detD, idenominator, update</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i, j, k, l</span>
|
|
|
|
info = QMCKL_FAILURE
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">Construct V(2, dim) matrix</span>
|
|
V = 0
|
|
V(1, updates_index(1)) = 1
|
|
V(2, updates_index(2)) = 1
|
|
|
|
! <span style="color: #b22222;">Construct Id(2, 2) matrix</span>
|
|
Id = 0
|
|
Id(1, 1) = 1
|
|
Id(2, 2) = 1
|
|
|
|
! <span style="color: #b22222;">Convert 'upds' and 's_inv' into the more easily readable Fortran</span>
|
|
! <span style="color: #b22222;">matrices 'Updates' and 'Inverse'.</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">convert</span>(upds, s_inv, Updates, Inverse, <span style="color: #a020f0;">int</span>(2,8), lds, dim)
|
|
|
|
! <span style="color: #b22222;">Compute C(dim, 2) = Inverse(dim, dim) x Updates(dim, 2)</span>
|
|
C = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
<span style="color: #a020f0;">do</span> j = 1, 2
|
|
<span style="color: #a020f0;">do</span> k = 1, dim
|
|
C(i, j) = C(i, j) + Inverse(i, k) * Updates(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Construct matrix D(2, 2) := I(2, 2) + V(2, dim) x C(dim, 2)</span>
|
|
D = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, 2
|
|
<span style="color: #a020f0;">do</span> j = 1, 2
|
|
<span style="color: #a020f0;">do</span> k = 2, dim
|
|
D(i, j) = D(i, j) + V(i, k) * C(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
D = Id + D
|
|
|
|
! <span style="color: #b22222;">Compute determinant := det(D) explicitly</span>
|
|
detD = D(1,1) * D(2,2) - D(1,2) * D(2,1)
|
|
|
|
! <span style="color: #b22222;">Return early if det(D) is too small</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">abs</span>(detD) < breakdown) <span style="color: #a020f0;">return</span>
|
|
|
|
! <span style="color: #b22222;">Update det(S)</span>
|
|
determinant = determinant * detD
|
|
|
|
! <span style="color: #b22222;">Compute inv(D) explicitly</span>
|
|
invD(1,1) = D(2,2)
|
|
invD(1,2) = - D(1,2)
|
|
invD(2,1) = - D(2,1)
|
|
invD(2,2) = D(1,1)
|
|
invD = invD / detD
|
|
|
|
! <span style="color: #b22222;">Compute E(2, dim) := V(2, dim) x Inverse(dim, dim)</span>
|
|
E = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, 2
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
<span style="color: #a020f0;">do</span> k = 1, dim
|
|
E(i, j) = E(i, j) + V(i, k) * Inverse(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Compute F(2, dim) := invD(2, 2) x E(2, dim)</span>
|
|
F = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, 2
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
<span style="color: #a020f0;">do</span> k = 1, 2
|
|
F(i, j) = F(i, j) + invD(i, k) * E(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Compute Inverse(dim, dim) := Inverse(dim, dim) - C(dim, 2) x F(2, dim)</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
<span style="color: #a020f0;">do</span> k = 1, 2
|
|
Inverse(i, j) = Inverse(i, j) - C(i, k) * F(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Copy updated inverse and later updates</span>
|
|
! <span style="color: #b22222;">back to s_inv and later_upds</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">copy_back_inv</span>(Inverse, s_inv, lds, dim)
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_doc_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2493bf0" class="outline-5">
|
|
<h5 id="org2493bf0"><span class="section-number-5">4.1.4.1</span> C interface (not directly exposed)</h5>
|
|
<div class="outline-text-5" id="text-4-1-4-1">
|
|
<p>
|
|
The function <code>qmckl_sm_splitting_core_doc</code> makes sure that
|
|
<code>qmckl_sm_splitting_core_doc_f</code> can be called from C using the
|
|
<code>ISO_C_BINDING</code>. Function <code>qmckl_sm_splitting_core_doc</code> will be
|
|
exposed in <code>qmckl.h</code> and <code>qmckl_f.F90</code>, but
|
|
<code>qmckl_sm_splitting_core_doc_f</code> will not.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgeedd6dc" class="outline-4">
|
|
<h4 id="orgeedd6dc"><span class="section-number-4">4.1.5</span> C headers (exposed in qmckl.h)</h4>
|
|
<div class="outline-text-4" id="text-4-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_hpc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_doc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1366ddc" class="outline-4">
|
|
<h4 id="org1366ddc"><span class="section-number-4">4.1.6</span> C sources</h4>
|
|
<div class="outline-text-4" id="text-4-1-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_hpc</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_hpc"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : Dim x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * Dim];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < LDS; k++) {
|
|
C[i * 2] += Slater_inv[i * LDS + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x LDS</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * LDS];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * LDS]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * LDS]);
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[LDS + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : Dim x LDS</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
Slater_inv[i * LDS + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * LDS + j] -= C[i * 2 + 1] * tmp[LDS + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c" id="org5a56b91"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">qmckl_woodbury_2x2_</span>{Dim}(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_{Dim}"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : {Dim} x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * {Dim}];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D{Dim}_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D{Dim}_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D{Dim}_P + k] * Updates[D{Dim}_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D{Dim}_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D{Dim}_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D{Dim}_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D{Dim}_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D{Dim}_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : {Dim} x D{Dim}_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
Slater_inv[i * D{Dim}_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D{Dim}_P + j] -= C[i * 2 + 1] * tmp[D{Dim}_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_2</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_2"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 2 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 2];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D2_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D2_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D2_P + k] * Updates[D2_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D2_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D2_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D2_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D2_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D2_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 2 x D2_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
Slater_inv[i * D2_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D2_P + j] -= C[i * 2 + 1] * tmp[D2_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_3</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_3"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 3 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 3];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D3_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D3_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D3_P + k] * Updates[D3_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D3_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D3_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D3_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D3_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D3_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 3 x D3_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
Slater_inv[i * D3_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D3_P + j] -= C[i * 2 + 1] * tmp[D3_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_4</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_4"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 4 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 4];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D4_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D4_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D4_P + k] * Updates[D4_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D4_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D4_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D4_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D4_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D4_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 4 x D4_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
Slater_inv[i * D4_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D4_P + j] -= C[i * 2 + 1] * tmp[D4_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_5</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_5"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 5 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 5];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D5_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D5_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D5_P + k] * Updates[D5_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D5_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D5_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D5_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D5_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D5_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 5 x D5_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
Slater_inv[i * D5_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D5_P + j] -= C[i * 2 + 1] * tmp[D5_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_6</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_6"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 6 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 6];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D6_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D6_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D6_P + k] * Updates[D6_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D6_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D6_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D6_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D6_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D6_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 6 x D6_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
Slater_inv[i * D6_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D6_P + j] -= C[i * 2 + 1] * tmp[D6_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_7</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_7"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 7 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 7];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D7_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D7_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D7_P + k] * Updates[D7_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D7_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D7_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D7_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D7_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D7_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 7 x D7_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
Slater_inv[i * D7_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D7_P + j] -= C[i * 2 + 1] * tmp[D7_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_8</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_8"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 8 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 8];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D8_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D8_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D8_P + k] * Updates[D8_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D8_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D8_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D8_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D8_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D8_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 8 x D8_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
Slater_inv[i * D8_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D8_P + j] -= C[i * 2 + 1] * tmp[D8_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_9</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_9"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 9 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 9];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D9_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D9_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D9_P + k] * Updates[D9_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D9_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D9_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D9_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D9_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D9_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 9 x D9_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
Slater_inv[i * D9_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D9_P + j] -= C[i * 2 + 1] * tmp[D9_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_10</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_10"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 10 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 10];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D10_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D10_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D10_P + k] * Updates[D10_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D10_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D10_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D10_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D10_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D10_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 10 x D10_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
Slater_inv[i * D10_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D10_P + j] -= C[i * 2 + 1] * tmp[D10_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_11</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_11"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 11 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 11];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D11_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D11_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D11_P + k] * Updates[D11_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D11_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D11_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D11_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D11_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D11_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 11 x D11_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
Slater_inv[i * D11_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D11_P + j] -= C[i * 2 + 1] * tmp[D11_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_12</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_12"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 12 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 12];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D12_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D12_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D12_P + k] * Updates[D12_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D12_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D12_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D12_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D12_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D12_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 12 x D12_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
Slater_inv[i * D12_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D12_P + j] -= C[i * 2 + 1] * tmp[D12_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_13</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_13"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 13 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 13];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D13_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D13_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D13_P + k] * Updates[D13_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D13_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D13_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D13_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D13_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D13_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 13 x D13_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
Slater_inv[i * D13_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D13_P + j] -= C[i * 2 + 1] * tmp[D13_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_14</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_14"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 14 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 14];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D14_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D14_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D14_P + k] * Updates[D14_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D14_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D14_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D14_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D14_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D14_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 14 x D14_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
Slater_inv[i * D14_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D14_P + j] -= C[i * 2 + 1] * tmp[D14_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_15</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_15"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 15 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 15];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D15_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D15_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D15_P + k] * Updates[D15_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D15_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D15_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D15_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D15_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D15_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 15 x D15_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
Slater_inv[i * D15_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D15_P + j] -= C[i * 2 + 1] * tmp[D15_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_16</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_16"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 16 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 16];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D16_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D16_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D16_P + k] * Updates[D16_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D16_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D16_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D16_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D16_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D16_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 16 x D16_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
Slater_inv[i * D16_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D16_P + j] -= C[i * 2 + 1] * tmp[D16_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_17</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_17"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 17 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 17];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D17_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D17_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D17_P + k] * Updates[D17_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D17_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D17_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D17_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D17_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D17_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 17 x D17_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
Slater_inv[i * D17_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D17_P + j] -= C[i * 2 + 1] * tmp[D17_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_18</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_18"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 18 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 18];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D18_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D18_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D18_P + k] * Updates[D18_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D18_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D18_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D18_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D18_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D18_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 18 x D18_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
Slater_inv[i * D18_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D18_P + j] -= C[i * 2 + 1] * tmp[D18_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_19</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_19"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 19 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 19];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D19_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D19_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D19_P + k] * Updates[D19_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D19_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D19_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D19_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D19_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D19_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 19 x D19_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
Slater_inv[i * D19_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D19_P + j] -= C[i * 2 + 1] * tmp[D19_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_20</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_20"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 20 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 20];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D20_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D20_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D20_P + k] * Updates[D20_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D20_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D20_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D20_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D20_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D20_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 20 x D20_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
Slater_inv[i * D20_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D20_P + j] -= C[i * 2 + 1] * tmp[D20_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2_21</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 2</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 2 x 2</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 2 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2_21"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 21 x 2</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[2 * 21];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
C[i * 2] = 0;
|
|
C[i * 2 + 1] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D21_P; k++) {
|
|
C[i * 2] += Slater_inv[i * D21_P + k] * Updates[k];
|
|
C[i * 2 + 1] += Slater_inv[i * D21_P + k] * Updates[D21_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 2 x 2</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 2] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 2 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row2 * 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 2 + 1] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span> = B0 * B3 - B1 * B2;
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[4], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = idet * B3;
|
|
Binv[1] = -1.0 * idet * B1;
|
|
Binv[2] = -1.0 * idet * B2;
|
|
Binv[3] = idet * B0;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x D21_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[2 * D21_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D21_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D21_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
|
tmp[D21_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 21 x D21_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
Slater_inv[i * D21_P + j] -= C[i * 2] * tmp[j];
|
|
Slater_inv[i * D21_P + j] -= C[i * 2 + 1] * tmp[D21_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_2x2</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_2x2"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #ifdef</span> HAVE_HPC__BROKEN_WITH_CRAY
|
|
<span style="color: #a020f0;">if</span> (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // <span style="color: #b22222;">Most cases</span>
|
|
<span style="color: #a020f0;">switch</span> (Dim) {
|
|
<span style="color: #a020f0;">case</span> 2:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_2(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 3:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_3(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 4:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_4(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 5:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_5(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 6:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_6(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 7:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_7(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 8:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_8(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 9:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_9(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 10:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_10(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 11:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_11(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 12:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_12(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 13:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_13(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 14:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_14(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 15:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_15(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 16:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_16(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 17:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_17(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 18:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_18(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 19:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_19(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 20:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_20(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 21:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_21(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
}
|
|
}
|
|
<span style="color: #a020f0;">else</span> { // <span style="color: #b22222;">Updating smaller sub-matrix</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_hpc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
}
|
|
<span style="color: #483d8b;"> #else</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_2x2_doc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
// <span style="color: #b22222;">return qmckl_woodbury_2x2_hpc(</span>
|
|
// <span style="color: #b22222;">context,</span>
|
|
// <span style="color: #b22222;">LDS,</span>
|
|
// <span style="color: #b22222;">Dim,</span>
|
|
// <span style="color: #b22222;">Updates,</span>
|
|
// <span style="color: #b22222;">Updates_index,</span>
|
|
// <span style="color: #b22222;">breakdown,</span>
|
|
// <span style="color: #b22222;">Slater_inv,</span>
|
|
// <span style="color: #b22222;">determinant);</span>
|
|
<span style="color: #483d8b;"> #endif</span>
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9360748" class="outline-4">
|
|
<h4 id="org9360748"><span class="section-number-4">4.1.7</span> Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</h4>
|
|
<div class="outline-text-4" id="text-4-1-7">
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4fea646" class="outline-4">
|
|
<h4 id="org4fea646"><span class="section-number-4">4.1.8</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-4-1-8">
|
|
<p>
|
|
This function is most efficient when used in cases where there are only 2 rank-1 updates and
|
|
it is sure they will not result in a singular matrix.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5defcbf" class="outline-4">
|
|
<h4 id="org5defcbf"><span class="section-number-4">4.1.9</span> Tests</h4>
|
|
<div class="outline-text-4" id="text-4-1-9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #0000ff;">assert</span>(Updates2 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Updates_index2 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Slater_inv2 != <span style="color: #008b8b;">NULL</span>);
|
|
det = -1.4432116661319376e-11;
|
|
rc = qmckl_woodbury_2x2(context, LDS, Dim, Updates2, Updates_index2, breakdown, Slater_inv2, &det);
|
|
<span style="color: #0000ff;">assert</span>(fabs(det-2.367058141251457e-10) < 1e-15);
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
res[i * Dim + j] = 0;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">k</span> = 0; k < Dim; k++) {
|
|
res[i * Dim + j] += Slater2[i * Dim + k] * Slater_inv2[k * LDS + j];
|
|
}
|
|
}
|
|
}
|
|
rc = QMCKL_SUCCESS;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
<span style="color: #a020f0;">if</span> (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #a020f0;">if</span> (i != j && fabs(res[i * Dim + j]) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
}
|
|
}
|
|
<span style="color: #0000ff;">assert</span>(rc == QMCKL_SUCCESS);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgcbc617b" class="outline-2">
|
|
<h2 id="orgcbc617b"><span class="section-number-2">5</span> Woodbury 3x3</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
</div>
|
|
<div id="outline-container-org1c111ec" class="outline-3">
|
|
<h3 id="org1c111ec"><span class="section-number-3">5.1</span> <code>qmckl_woodbury_3x3</code></h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
</div>
|
|
|
|
<div id="outline-container-org8896d6f" class="outline-4">
|
|
<h4 id="org8896d6f"><span class="section-number-4">5.1.1</span> Introduction</h4>
|
|
<div class="outline-text-4" id="text-5-1-1">
|
|
<p>
|
|
The Woodbury 3x3 kernel. It is used to apply two rank-1 updates at once. The formula used in
|
|
this algorithm is called the Woodbury Matrix Id
|
|
\[
|
|
(S + U V)^{-1} = S^{-1} - C B^{-1} D
|
|
\]
|
|
where
|
|
\(S\) is the Slater-matrix
|
|
\(U\) and \(V\) are the matrices containing the updates and the canonical basis matrix
|
|
\(S^{-1}\) is the inverse of the Slater-matrix
|
|
\(C:= S^{-1}U\), a Dim \(\times 3\) matrix
|
|
\(B := 1 + VC\), the \(3 \times 3\) matrix that is going to be inverted
|
|
\(D := VS^{-1}\), a \(3 \times Dim\) matrix
|
|
</p>
|
|
|
|
<p>
|
|
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
|
|
from applying the updates to the original matrix.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd817e2a" class="outline-4">
|
|
<h4 id="orgd817e2a"><span class="section-number-4">5.1.2</span> API</h4>
|
|
<div class="outline-text-4" id="text-5-1-2">
|
|
<table id="org18cde76" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Variable</th>
|
|
<th scope="col" class="org-left">Type</th>
|
|
<th scope="col" class="org-left">In/Out</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left"><code>qmckl_context</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>LDS</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Dim</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates</code></td>
|
|
<td class="org-left"><code>double[3*Dim]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Updates_index</code></td>
|
|
<td class="org-left"><code>uint64_t[3]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the rank-1 updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>breakdown</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Break-down parameter on which to fail or not</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>Slater_inv</code></td>
|
|
<td class="org-left"><code>double[LDS*Dim]</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the inverse of a Slater-matrix</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>determinant</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Determinant of Slater-matrix</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org79e256f" class="outline-4">
|
|
<h4 id="org79e256f"><span class="section-number-4">5.1.3</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-5-1-3">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>qmckl_null_context</code></li>
|
|
<li><code>LDS >= 3</code></li>
|
|
<li><code>Dim >= 3</code></li>
|
|
<li><code>Updates</code> is allocated with \(3 \times Dim\) elements</li>
|
|
<li><code>Updates_index</code> is allocated with \(3\) elements</li>
|
|
<li><code>breakdown</code> is a small number such that \(0 < breakdown << 1\)</li>
|
|
<li><code>Slater_inv</code> is allocated with \(Dim \times Dim\) elements</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4cf6603" class="outline-4">
|
|
<h4 id="org4cf6603"><span class="section-number-4">5.1.4</span> Pedagogical kernel source (in Fortran)</h4>
|
|
<div class="outline-text-4" id="text-5-1-4">
|
|
<p>
|
|
The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
|
|
able to do numerically correct computations, it does not do it in the most efficient way possible. It should therefore
|
|
not be used in real workloads.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_woodbury_3x3_doc_f(</span><span style="color: #a020f0;">&</span>
|
|
context, <span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
upds, <span style="color: #a020f0;">&</span>
|
|
updates_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
determinant) <span style="color: #a020f0;">result</span>(info)
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lds, dim</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> updates_index(3)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> upds(3 * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> breakdown</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> s_inv(dim * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> determinant</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">dimension</span>(3, dim) ::<span style="color: #a0522d;"> V</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">dimension</span>(3, 3) ::<span style="color: #a0522d;"> Id</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, dim) ::<span style="color: #a0522d;"> Inverse</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(dim, 3) ::<span style="color: #a0522d;"> Updates, C</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(3, 3) ::<span style="color: #a0522d;"> D, invD</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(3, dim) ::<span style="color: #a0522d;"> E, F</span>
|
|
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> detD, idetD, idenominator, update</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i, j, k, l</span>
|
|
|
|
info = QMCKL_FAILURE
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">Construct V(3, dim) matrix</span>
|
|
V = 0
|
|
V(1, updates_index(1)) = 1
|
|
V(2, updates_index(2)) = 1
|
|
V(3, updates_index(3)) = 1
|
|
|
|
! <span style="color: #b22222;">Construct Id(3, 3) matrix</span>
|
|
Id = 0
|
|
Id(1, 1) = 1
|
|
Id(2, 2) = 1
|
|
Id(3, 3) = 1
|
|
|
|
! <span style="color: #b22222;">Convert 'upds' and 's_inv' into the more easily readable Fortran</span>
|
|
! <span style="color: #b22222;">matrices 'Updates' and 'Inverse'.</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">convert</span>(upds, s_inv, Updates, Inverse, <span style="color: #a020f0;">int</span>(3,8), lds, dim)
|
|
|
|
! <span style="color: #b22222;">Compute C(dim, 3) = Inverse(dim, dim) x Updates(dim, 3)</span>
|
|
C = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
<span style="color: #a020f0;">do</span> j = 1, 3
|
|
<span style="color: #a020f0;">do</span> k = 1, dim
|
|
C(i, j) = C(i, j) + Inverse(i, k) * Updates(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Construct matrix D(3, 3) := I(3, 3) + V(3, dim) x C(dim, 3)</span>
|
|
D = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, 3
|
|
<span style="color: #a020f0;">do</span> j = 1, 3
|
|
<span style="color: #a020f0;">do</span> k = 3, dim
|
|
D(i, j) = D(i, j) + V(i, k) * C(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
D = Id + D
|
|
|
|
! <span style="color: #b22222;">Compute determinant := det(D) explicitly</span>
|
|
detD = D(1,1) * (D(2,2) * D(3,3) - D(2,3) * D(3,2)) - <span style="color: #a020f0;">&</span>
|
|
D(1,2) * (D(2,1) * D(3,3) - D(2,3) * D(3,1)) + <span style="color: #a020f0;">&</span>
|
|
D(1,3) * (D(2,1) * D(3,2) - D(2,2) * D(3,1))
|
|
|
|
! <span style="color: #b22222;">Return early if det(D) is too small</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">abs</span>(detD) < breakdown) <span style="color: #a020f0;">return</span>
|
|
|
|
! <span style="color: #b22222;">Update det(S)</span>
|
|
determinant = determinant * detD
|
|
|
|
idetD = 1.0d0 / detD
|
|
! <span style="color: #b22222;">Compute inv(D) explicitly</span>
|
|
invD(1,1) = (D(2,2) * D(3,3) - D(3,2) * D(2,3)) * idetD
|
|
invD(1,2) = -(D(1,2) * D(3,3) - D(3,2) * D(1,3)) * idetD
|
|
invD(1,3) = (D(1,2) * D(2,3) - D(2,2) * D(1,3)) * idetD
|
|
invD(2,1) = -(D(2,1) * D(3,3) - D(3,1) * D(2,3)) * idetD
|
|
invD(2,2) = (D(1,1) * D(3,3) - D(3,1) * D(1,3)) * idetD
|
|
invD(2,3) = -(D(1,1) * D(2,3) - D(2,1) * D(1,3)) * idetD
|
|
invD(3,1) = (D(2,1) * D(3,2) - D(3,1) * D(2,2)) * idetD
|
|
invD(3,2) = -(D(1,1) * D(3,2) - D(3,1) * D(1,2)) * idetD
|
|
invD(3,3) = (D(1,1) * D(2,2) - D(2,1) * D(1,2)) * idetD
|
|
|
|
! <span style="color: #b22222;">Compute E(3, dim) := V(3, dim) x Inverse(dim, dim)</span>
|
|
E = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, 3
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
<span style="color: #a020f0;">do</span> k = 1, dim
|
|
E(i, j) = E(i, j) + V(i, k) * Inverse(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Compute F(3, dim) := invD(3, 3) x E(3, dim)</span>
|
|
F = 0
|
|
<span style="color: #a020f0;">do</span> i = 1, 3
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
<span style="color: #a020f0;">do</span> k = 1, 3
|
|
F(i, j) = F(i, j) + invD(i, k) * E(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Compute Inverse(dim, dim) := Inverse(dim, dim) - C(dim, 3) x F(3, dim)</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, dim
|
|
<span style="color: #a020f0;">do</span> j = 1, dim
|
|
<span style="color: #a020f0;">do</span> k = 1, 3
|
|
Inverse(i, j) = Inverse(i, j) - C(i, k) * F(k, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Copy updated inverse and later updates</span>
|
|
! <span style="color: #b22222;">back to s_inv and later_upds</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">copy_back_inv</span>(Inverse, s_inv, lds, dim)
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_doc_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org743b142" class="outline-5">
|
|
<h5 id="org743b142"><span class="section-number-5">5.1.4.1</span> C interface (not directly exposed)</h5>
|
|
<div class="outline-text-5" id="text-5-1-4-1">
|
|
<p>
|
|
The function <code>qmckl_sm_splitting_core_doc</code> makes sure that
|
|
<code>qmckl_sm_splitting_core_doc_f</code> can be called from C using the
|
|
<code>ISO_C_BINDING</code>. Function <code>qmckl_sm_splitting_core_doc</code> will be
|
|
exposed in <code>qmckl.h</code> and <code>qmckl_f.F90</code>, but
|
|
<code>qmckl_sm_splitting_core_doc_f</code> will not.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd16448f" class="outline-4">
|
|
<h4 id="orgd16448f"><span class="section-number-4">5.1.5</span> C headers (exposed in qmckl.h)</h4>
|
|
<div class="outline-text-4" id="text-5-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_hpc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_doc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org75c9b2f" class="outline-4">
|
|
<h4 id="org75c9b2f"><span class="section-number-4">5.1.6</span> C sources</h4>
|
|
<div class="outline-text-4" id="text-5-1-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_hpc</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_hpc"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : Dim x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * Dim];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < LDS; k++) {
|
|
C[i * 3] += Slater_inv[i * LDS + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
|
|
C[i * 3 + 2] += Slater_inv[i * LDS + k] * Updates[2 * LDS + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of inverted matrix is not zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(S) when passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 2 x 2 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 2 x LDS</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * LDS];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * LDS]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * LDS]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * LDS]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[LDS + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * LDS + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : Dim x LDS</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < LDS; j++) {
|
|
Slater_inv[i * LDS + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * LDS + j] -= C[i * 3 + 1] * tmp[LDS + j];
|
|
Slater_inv[i * LDS + j] -= C[i * 3 + 2] * tmp[2 * LDS + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c" id="org323624c"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">qmckl_woodbury_3x3_</span>{Dim}(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_{Dim}"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : {Dim} x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * {Dim}];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D{Dim}_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D{Dim}_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D{Dim}_P + k] * Updates[D{Dim}_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D{Dim}_P + k] * Updates[2 * D{Dim}_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D{Dim}_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D{Dim}_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D{Dim}_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D{Dim}_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D{Dim}_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D{Dim}_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D{Dim}_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : {Dim} x D{Dim}_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < {Dim}; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D{Dim}_P; j++) {
|
|
Slater_inv[i * D{Dim}_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D{Dim}_P + j] -= C[i * 3 + 1] * tmp[D{Dim}_P + j];
|
|
Slater_inv[i * D{Dim}_P + j] -= C[i * 3 + 2] * tmp[2 * D{Dim}_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_2</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_2"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 2 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 2];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D2_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D2_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D2_P + k] * Updates[D2_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D2_P + k] * Updates[2 * D2_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D2_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D2_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D2_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D2_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D2_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D2_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D2_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 2 x D2_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 2; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D2_P; j++) {
|
|
Slater_inv[i * D2_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D2_P + j] -= C[i * 3 + 1] * tmp[D2_P + j];
|
|
Slater_inv[i * D2_P + j] -= C[i * 3 + 2] * tmp[2 * D2_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_3</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_3"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 3 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 3];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D3_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D3_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D3_P + k] * Updates[D3_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D3_P + k] * Updates[2 * D3_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D3_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D3_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D3_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D3_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D3_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D3_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D3_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 3 x D3_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 3; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D3_P; j++) {
|
|
Slater_inv[i * D3_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D3_P + j] -= C[i * 3 + 1] * tmp[D3_P + j];
|
|
Slater_inv[i * D3_P + j] -= C[i * 3 + 2] * tmp[2 * D3_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_4</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_4"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 4 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 4];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D4_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D4_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D4_P + k] * Updates[D4_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D4_P + k] * Updates[2 * D4_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D4_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D4_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D4_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D4_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D4_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D4_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D4_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 4 x D4_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 4; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D4_P; j++) {
|
|
Slater_inv[i * D4_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D4_P + j] -= C[i * 3 + 1] * tmp[D4_P + j];
|
|
Slater_inv[i * D4_P + j] -= C[i * 3 + 2] * tmp[2 * D4_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_5</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_5"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 5 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 5];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D5_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D5_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D5_P + k] * Updates[D5_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D5_P + k] * Updates[2 * D5_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D5_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D5_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D5_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D5_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D5_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D5_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D5_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 5 x D5_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 5; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D5_P; j++) {
|
|
Slater_inv[i * D5_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D5_P + j] -= C[i * 3 + 1] * tmp[D5_P + j];
|
|
Slater_inv[i * D5_P + j] -= C[i * 3 + 2] * tmp[2 * D5_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_6</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_6"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 6 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 6];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D6_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D6_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D6_P + k] * Updates[D6_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D6_P + k] * Updates[2 * D6_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D6_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D6_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D6_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D6_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D6_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D6_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D6_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 6 x D6_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 6; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D6_P; j++) {
|
|
Slater_inv[i * D6_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D6_P + j] -= C[i * 3 + 1] * tmp[D6_P + j];
|
|
Slater_inv[i * D6_P + j] -= C[i * 3 + 2] * tmp[2 * D6_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_7</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_7"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 7 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 7];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D7_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D7_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D7_P + k] * Updates[D7_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D7_P + k] * Updates[2 * D7_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D7_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D7_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D7_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D7_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D7_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D7_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D7_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 7 x D7_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 7; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D7_P; j++) {
|
|
Slater_inv[i * D7_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D7_P + j] -= C[i * 3 + 1] * tmp[D7_P + j];
|
|
Slater_inv[i * D7_P + j] -= C[i * 3 + 2] * tmp[2 * D7_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_8</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_8"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 8 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 8];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D8_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D8_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D8_P + k] * Updates[D8_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D8_P + k] * Updates[2 * D8_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D8_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D8_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D8_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D8_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D8_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D8_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D8_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 8 x D8_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 8; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D8_P; j++) {
|
|
Slater_inv[i * D8_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D8_P + j] -= C[i * 3 + 1] * tmp[D8_P + j];
|
|
Slater_inv[i * D8_P + j] -= C[i * 3 + 2] * tmp[2 * D8_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_9</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_9"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 9 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 9];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D9_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D9_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D9_P + k] * Updates[D9_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D9_P + k] * Updates[2 * D9_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D9_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D9_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D9_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D9_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D9_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D9_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D9_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 9 x D9_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 9; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D9_P; j++) {
|
|
Slater_inv[i * D9_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D9_P + j] -= C[i * 3 + 1] * tmp[D9_P + j];
|
|
Slater_inv[i * D9_P + j] -= C[i * 3 + 2] * tmp[2 * D9_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_10</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_10"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 10 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 10];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D10_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D10_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D10_P + k] * Updates[D10_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D10_P + k] * Updates[2 * D10_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D10_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D10_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D10_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D10_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D10_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D10_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D10_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 10 x D10_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 10; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D10_P; j++) {
|
|
Slater_inv[i * D10_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D10_P + j] -= C[i * 3 + 1] * tmp[D10_P + j];
|
|
Slater_inv[i * D10_P + j] -= C[i * 3 + 2] * tmp[2 * D10_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_11</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_11"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 11 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 11];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D11_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D11_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D11_P + k] * Updates[D11_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D11_P + k] * Updates[2 * D11_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D11_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D11_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D11_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D11_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D11_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D11_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D11_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 11 x D11_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 11; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D11_P; j++) {
|
|
Slater_inv[i * D11_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D11_P + j] -= C[i * 3 + 1] * tmp[D11_P + j];
|
|
Slater_inv[i * D11_P + j] -= C[i * 3 + 2] * tmp[2 * D11_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_12</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_12"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 12 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 12];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D12_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D12_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D12_P + k] * Updates[D12_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D12_P + k] * Updates[2 * D12_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D12_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D12_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D12_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D12_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D12_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D12_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D12_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 12 x D12_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 12; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D12_P; j++) {
|
|
Slater_inv[i * D12_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D12_P + j] -= C[i * 3 + 1] * tmp[D12_P + j];
|
|
Slater_inv[i * D12_P + j] -= C[i * 3 + 2] * tmp[2 * D12_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_13</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_13"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 13 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 13];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D13_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D13_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D13_P + k] * Updates[D13_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D13_P + k] * Updates[2 * D13_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D13_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D13_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D13_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D13_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D13_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D13_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D13_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 13 x D13_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 13; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D13_P; j++) {
|
|
Slater_inv[i * D13_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D13_P + j] -= C[i * 3 + 1] * tmp[D13_P + j];
|
|
Slater_inv[i * D13_P + j] -= C[i * 3 + 2] * tmp[2 * D13_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_14</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_14"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 14 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 14];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D14_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D14_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D14_P + k] * Updates[D14_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D14_P + k] * Updates[2 * D14_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D14_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D14_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D14_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D14_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D14_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D14_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D14_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 14 x D14_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 14; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D14_P; j++) {
|
|
Slater_inv[i * D14_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D14_P + j] -= C[i * 3 + 1] * tmp[D14_P + j];
|
|
Slater_inv[i * D14_P + j] -= C[i * 3 + 2] * tmp[2 * D14_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_15</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_15"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 15 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 15];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D15_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D15_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D15_P + k] * Updates[D15_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D15_P + k] * Updates[2 * D15_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D15_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D15_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D15_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D15_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D15_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D15_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D15_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 15 x D15_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 15; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D15_P; j++) {
|
|
Slater_inv[i * D15_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D15_P + j] -= C[i * 3 + 1] * tmp[D15_P + j];
|
|
Slater_inv[i * D15_P + j] -= C[i * 3 + 2] * tmp[2 * D15_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_16</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_16"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 16 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 16];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D16_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D16_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D16_P + k] * Updates[D16_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D16_P + k] * Updates[2 * D16_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D16_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D16_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D16_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D16_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D16_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D16_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D16_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 16 x D16_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 16; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D16_P; j++) {
|
|
Slater_inv[i * D16_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D16_P + j] -= C[i * 3 + 1] * tmp[D16_P + j];
|
|
Slater_inv[i * D16_P + j] -= C[i * 3 + 2] * tmp[2 * D16_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_17</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_17"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 17 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 17];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D17_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D17_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D17_P + k] * Updates[D17_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D17_P + k] * Updates[2 * D17_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D17_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D17_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D17_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D17_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D17_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D17_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D17_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 17 x D17_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 17; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D17_P; j++) {
|
|
Slater_inv[i * D17_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D17_P + j] -= C[i * 3 + 1] * tmp[D17_P + j];
|
|
Slater_inv[i * D17_P + j] -= C[i * 3 + 2] * tmp[2 * D17_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_18</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_18"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 18 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 18];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D18_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D18_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D18_P + k] * Updates[D18_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D18_P + k] * Updates[2 * D18_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D18_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D18_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D18_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D18_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D18_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D18_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D18_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 18 x D18_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 18; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D18_P; j++) {
|
|
Slater_inv[i * D18_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D18_P + j] -= C[i * 3 + 1] * tmp[D18_P + j];
|
|
Slater_inv[i * D18_P + j] -= C[i * 3 + 2] * tmp[2 * D18_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_19</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_19"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 19 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 19];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D19_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D19_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D19_P + k] * Updates[D19_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D19_P + k] * Updates[2 * D19_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D19_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D19_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D19_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D19_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D19_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D19_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D19_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 19 x D19_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 19; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D19_P; j++) {
|
|
Slater_inv[i * D19_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D19_P + j] -= C[i * 3 + 1] * tmp[D19_P + j];
|
|
Slater_inv[i * D19_P + j] -= C[i * 3 + 2] * tmp[2 * D19_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_20</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_20"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 20 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 20];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D20_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D20_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D20_P + k] * Updates[D20_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D20_P + k] * Updates[2 * D20_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D20_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D20_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D20_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D20_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D20_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D20_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D20_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 20 x D20_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 20; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D20_P; j++) {
|
|
Slater_inv[i * D20_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D20_P + j] -= C[i * 3 + 1] * tmp[D20_P + j];
|
|
Slater_inv[i * D20_P + j] -= C[i * 3 + 2] * tmp[2 * D20_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
|
|
<span style="color: #a020f0;">static</span> <span style="color: #a020f0;">inline</span> <span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3_21</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">restrict</span> <span style="color: #a0522d;">determinant</span>) {
|
|
/*
|
|
<span style="color: #b22222;"> C := S^{-1} * U, dim x 3</span>
|
|
<span style="color: #b22222;"> B := 1 + V * C, 3 x 3</span>
|
|
<span style="color: #b22222;"> D := V * S^{-1}, 3 x dim</span>
|
|
*/
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3_21"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row1</span> = (Updates_index[0] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row2</span> = (Updates_index[1] - 1);
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">row3</span> = (Updates_index[2] - 1);
|
|
|
|
// <span style="color: #b22222;">Compute C = (S^T)^{-1}U : 21 x 3</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">C</span>[3 * 21];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
C[i * 3] = 0;
|
|
C[i * 3 + 1] = 0;
|
|
C[i * 3 + 2] = 0;
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">k</span> = 0; k < D21_P; k++) {
|
|
C[i * 3] += Slater_inv[i * D21_P + k] * Updates[k];
|
|
C[i * 3 + 1] += Slater_inv[i * D21_P + k] * Updates[D21_P + k];
|
|
C[i * 3 + 2] += Slater_inv[i * D21_P + k] * Updates[2 * D21_P + k];
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute B = 1 + VC : 3 x 3</span>
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B0</span> = C[row1 * 3] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B1</span> = C[row1 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B2</span> = C[row1 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B3</span> = C[row2 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B4</span> = C[row2 * 3 + 1] + 1;
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B5</span> = C[row2 * 3 + 2];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B6</span> = C[row3 * 3];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B7</span> = C[row3 * 3 + 1];
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">B8</span> = C[row3 * 3 + 2] + 1;
|
|
|
|
// <span style="color: #b22222;">Check if determinant of B is not too close to zero</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">det</span>;
|
|
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
|
B2 * (B3 * B7 - B4 * B6);
|
|
<span style="color: #a020f0;">if</span> (fabs(det) < breakdown) {
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
// <span style="color: #b22222;">Update det(Slater) if passed</span>
|
|
<span style="color: #a020f0;">if</span> (determinant)
|
|
*determinant *= det;
|
|
|
|
// <span style="color: #b22222;">Compute B^{-1} with explicit formula for 3 x 3 inversion</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">Binv</span>[9], <span style="color: #a0522d;">idet</span> = 1.0 / det;
|
|
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
|
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
|
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
|
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
|
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
|
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
|
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
|
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
|
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
|
|
|
// <span style="color: #b22222;">tmp = B^{-1}D : 3 x D21_P</span>
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">tmp</span>[3 * D21_P];
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r1dim</span> = &(Slater_inv[row1 * D21_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r2dim</span> = &(Slater_inv[row2 * D21_P]);
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">r3dim</span> = &(Slater_inv[row3 * D21_P]);
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j] + Binv[2] * r3dim[j];
|
|
tmp[D21_P + j] =
|
|
Binv[3] * r1dim[j] + Binv[4] * r2dim[j] + Binv[5] * r3dim[j];
|
|
tmp[2 * D21_P + j] =
|
|
Binv[6] * r1dim[j] + Binv[7] * r2dim[j] + Binv[8] * r3dim[j];
|
|
}
|
|
|
|
// <span style="color: #b22222;">Compute (S^T)^{-1} - C * tmp : 21 x D21_P</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">i</span> = 0; i < 21; i++) {
|
|
<span style="color: #228b22;">IVDEP</span>
|
|
<span style="color: #0000ff;">ALIGNED</span>
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">j</span> = 0; j < D21_P; j++) {
|
|
Slater_inv[i * D21_P + j] -= C[i * 3] * tmp[j];
|
|
Slater_inv[i * D21_P + j] -= C[i * 3 + 1] * tmp[D21_P + j];
|
|
Slater_inv[i * D21_P + j] -= C[i * 3 + 2] * tmp[2 * D21_P + j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_woodbury_3x3</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_woodbury_3x3"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #483d8b;"> #ifdef</span> HAVE_HPC__BROKEN_WITH_CRAY
|
|
<span style="color: #a020f0;">if</span> (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // <span style="color: #b22222;">Most cases</span>
|
|
<span style="color: #a020f0;">switch</span> (Dim) {
|
|
<span style="color: #a020f0;">case</span> 2:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_2(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 3:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_3(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 4:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_4(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 5:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_5(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 6:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_6(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 7:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_7(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 8:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_8(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 9:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_9(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 10:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_10(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 11:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_11(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 12:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_12(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 13:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_13(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 14:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_14(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 15:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_15(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 16:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_16(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 17:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_17(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 18:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_18(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 19:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_19(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 20:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_20(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #a020f0;">case</span> 21:
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_21(context,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
}
|
|
}
|
|
<span style="color: #a020f0;">else</span> { // <span style="color: #b22222;">Updating smaller sub-matrix</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_hpc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
}
|
|
<span style="color: #483d8b;"> #else</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_woodbury_3x3_doc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
// <span style="color: #b22222;">return qmckl_woodbury_3x3_hpc(</span>
|
|
// <span style="color: #b22222;">context,</span>
|
|
// <span style="color: #b22222;">LDS,</span>
|
|
// <span style="color: #b22222;">Dim,</span>
|
|
// <span style="color: #b22222;">Updates,</span>
|
|
// <span style="color: #b22222;">Updates_index,</span>
|
|
// <span style="color: #b22222;">breakdown,</span>
|
|
// <span style="color: #b22222;">Slater_inv,</span>
|
|
// <span style="color: #b22222;">determinant);</span>
|
|
<span style="color: #483d8b;"> #endif</span>
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8208ea2" class="outline-4">
|
|
<h4 id="org8208ea2"><span class="section-number-4">5.1.7</span> Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</h4>
|
|
<div class="outline-text-4" id="text-5-1-7">
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9ecbdf0" class="outline-4">
|
|
<h4 id="org9ecbdf0"><span class="section-number-4">5.1.8</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-5-1-8">
|
|
<p>
|
|
This function is most efficient when used in cases where there are only 3 rank-1 updates and
|
|
it is sure they will not result in a singular matrix.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5272284" class="outline-4">
|
|
<h4 id="org5272284"><span class="section-number-4">5.1.9</span> Tests</h4>
|
|
<div class="outline-text-4" id="text-5-1-9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #0000ff;">assert</span>(Updates3 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Updates_index3 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Slater_inv3_1 != <span style="color: #008b8b;">NULL</span>);
|
|
det = -1.23743195512859e-09;
|
|
rc = qmckl_woodbury_3x3(context, LDS, Dim, Updates3, Updates_index3, breakdown, Slater_inv3_1, &det);
|
|
<span style="color: #0000ff;">assert</span>(fabs(det - 1.602708950725074e-10) < 1e-15);
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
res[i * Dim + j] = 0;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">k</span> = 0; k < Dim; k++) {
|
|
res[i * Dim + j] += Slater3[i * Dim + k] * Slater_inv3_1[k * LDS + j];
|
|
}
|
|
}
|
|
}
|
|
rc = QMCKL_SUCCESS;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
<span style="color: #a020f0;">if</span> (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #a020f0;">if</span> (i != j && fabs(res[i * Dim + j]) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
}
|
|
}
|
|
<span style="color: #0000ff;">assert</span>(rc == QMCKL_SUCCESS);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgedd101f" class="outline-2">
|
|
<h2 id="orgedd101f"><span class="section-number-2">6</span> Sherman-Morrison with Slagel Splitting</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
</div>
|
|
<div id="outline-container-orgb5b525b" class="outline-3">
|
|
<h3 id="orgb5b525b"><span class="section-number-3">6.1</span> <code>qmckl_sm_splitting</code></h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
</div>
|
|
|
|
<div id="outline-container-org2ae2358" class="outline-4">
|
|
<h4 id="org2ae2358"><span class="section-number-4">6.1.1</span> Introduction</h4>
|
|
<div class="outline-text-4" id="text-6-1-1">
|
|
<p>
|
|
This is a variation on the 'Naive' Sherman-Morrison kernel. Whenever the denominator \(1+v_j^T S^{-1} u_j\) in
|
|
the Sherman-Morrison formula is deemed to be too close to zero, the update \(u_j\) is split in half:
|
|
\(u_j \rightarrow \frac{1}{2} u_j\). One half is applied immediately –necessarily increasing the value of the
|
|
denominator because of the split– while the other halve is put in a queue that will be applied when all the
|
|
remaining updates have been treated.
|
|
</p>
|
|
|
|
<p>
|
|
The kernel is executed recursively until the queue is eiter empty and all
|
|
updates are applied successfully, or the size of the queue equals the number of initial updates. In the last
|
|
case the Slater-matrix that would have resulted from applying the updates is singular and therefore the
|
|
kernel exits with an exit code.
|
|
</p>
|
|
|
|
<p>
|
|
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
|
|
from applying the updates to the original matrix.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org876c69a" class="outline-4">
|
|
<h4 id="org876c69a"><span class="section-number-4">6.1.2</span> API</h4>
|
|
<div class="outline-text-4" id="text-6-1-2">
|
|
<table id="org355d6b8" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Variable</th>
|
|
<th scope="col" class="org-left">Type</th>
|
|
<th scope="col" class="org-left">In/Out</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">context</td>
|
|
<td class="org-left">qmckl<sub>context</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">LDS</td>
|
|
<td class="org-left">uint64<sub>t</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Dim</td>
|
|
<td class="org-left">uint64<sub>t</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Dimension of Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">N<sub>updates</sub></td>
|
|
<td class="org-left">uint64<sub>t</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of rank-1 updates to be applied to Slater<sub>inv</sub></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Updates</td>
|
|
<td class="org-left">double[N<sub>updates</sub>*LDS]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Updates<sub>index</sub></td>
|
|
<td class="org-left">uint64<sub>t</sub>[N<sub>updates</sub>]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the rank-1 updates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">breakdown</td>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Break-down parameter on which to fail or not</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Slater<sub>inv</sub></td>
|
|
<td class="org-left">double[Dim*LDS]</td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Array containing the inverse of a Slater-matrix</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">determinant</td>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Determinant of the Slater-matrix</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org514f002" class="outline-4">
|
|
<h4 id="org514f002"><span class="section-number-4">6.1.3</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-6-1-3">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>LDS >= 2</code></li>
|
|
<li><code>Dim >= 2</code></li>
|
|
<li><code>N_updates >= 1</code></li>
|
|
<li><code>Updates</code> is allocated with \(N_updates \times Dim\) elements</li>
|
|
<li><code>Updates_index</code> is allocated with \(N_updates\) elements</li>
|
|
<li><code>breakdown</code> is a small number such that \(0 < breakdown << 1\)</li>
|
|
<li><code>Slater_inv</code> is allocated with \(Dim \times Dim\) elements</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf81577e" class="outline-4">
|
|
<h4 id="orgf81577e"><span class="section-number-4">6.1.4</span> Pedagogical kernel source (in Fortran)</h4>
|
|
<div class="outline-text-4" id="text-6-1-4">
|
|
<p>
|
|
The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
|
|
able to do numerically correct computations, it does not do it in the most efficient way possible. It should therefore
|
|
not be used in real workloads.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> recursive function qmckl_sm_splitting_doc_f( </span><span style="color: #a020f0;">&</span>
|
|
context, <span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
nupdates, <span style="color: #a020f0;">&</span>
|
|
upds, <span style="color: #a020f0;">&</span>
|
|
updates_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
determinant) <span style="color: #a020f0;">result</span>(info)
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lds, dim</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nupdates</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> updates_index(nupdates)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> upds(lds * nupdates)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> breakdown</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> s_inv(dim * lds)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> determinant</span>
|
|
|
|
<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">external</span> ::<span style="color: #a0522d;"> qmckl_sm_splitting_core_doc_f</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> Later</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">dimension</span>(nupdates) ::<span style="color: #a0522d;"> Later_index</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">dimension</span>(lds * nupdates) ::<span style="color: #a0522d;"> Later_updates</span>
|
|
|
|
info = QMCKL_FAILURE
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
Later = 0
|
|
Later_index = 0
|
|
Later_updates = 0
|
|
|
|
info = qmckl_sm_splitting_core_doc_f( <span style="color: #a020f0;">&</span>
|
|
context, <span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
nupdates, <span style="color: #a020f0;">&</span>
|
|
upds, <span style="color: #a020f0;">&</span>
|
|
updates_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
Later_updates, <span style="color: #a020f0;">&</span>
|
|
Later_index, <span style="color: #a020f0;">&</span>
|
|
Later, <span style="color: #a020f0;">&</span>
|
|
determinant)
|
|
|
|
<span style="color: #a020f0;">if</span> (Later > 0) <span style="color: #a020f0;">then</span>
|
|
info = qmckl_sm_splitting_doc_f( <span style="color: #a020f0;">&</span>
|
|
context, <span style="color: #a020f0;">&</span>
|
|
lds, dim, <span style="color: #a020f0;">&</span>
|
|
Later, <span style="color: #a020f0;">&</span>
|
|
Later_updates, <span style="color: #a020f0;">&</span>
|
|
Later_index, <span style="color: #a020f0;">&</span>
|
|
breakdown, <span style="color: #a020f0;">&</span>
|
|
s_inv, <span style="color: #a020f0;">&</span>
|
|
determinant)
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_sm_splitting_doc_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2442936" class="outline-5">
|
|
<h5 id="org2442936"><span class="section-number-5">6.1.4.1</span> C interface to the pedagogical kernel (not directly exposed)</h5>
|
|
<div class="outline-text-5" id="text-6-1-4-1">
|
|
<p>
|
|
The following Fortran function <code>qmckl_sm_splitting_core_doc</code> makes sure
|
|
that the pedagogical kernel <code>qmckl_sm_splitting_core_doc_f</code>, written in
|
|
Fortran, can be called from C using the <code>ISO_C_BINDING</code>. The Fortran function
|
|
<code>qmckl_sm_splitting_core_doc</code> will be exposed in the header file 'qmckl.h'
|
|
for C users and in the module file 'qmckl<sub>f.F90</sub>' for Fortran users.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org85f3506" class="outline-4">
|
|
<h4 id="org85f3506"><span class="section-number-4">6.1.5</span> C headers (exposed in qmckl.h)</h4>
|
|
<div class="outline-text-4" id="text-6-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_hpc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_doc</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org42d9709" class="outline-4">
|
|
<h4 id="org42d9709"><span class="section-number-4">6.1.6</span> C source</h4>
|
|
<div class="outline-text-4" id="text-6-1-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-python" id="org194ad48"><span style="color: #a0522d;">text</span>=<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #8b2252;">case {Dim}: {</span>
|
|
<span style="color: #8b2252;"> rc = qmckl_sm_splitting_core_{Dim}(</span>
|
|
<span style="color: #8b2252;"> context,</span>
|
|
<span style="color: #8b2252;"> N_updates,</span>
|
|
<span style="color: #8b2252;"> Updates,</span>
|
|
<span style="color: #8b2252;"> Updates_index,</span>
|
|
<span style="color: #8b2252;"> breakdown,</span>
|
|
<span style="color: #8b2252;"> Slater_inv,</span>
|
|
<span style="color: #8b2252;"> later_updates,</span>
|
|
<span style="color: #8b2252;"> later_index, &later, determinant);</span>
|
|
<span style="color: #8b2252;"> break;</span>
|
|
<span style="color: #8b2252;">}</span>
|
|
<span style="color: #8b2252;">"""</span>
|
|
<span style="color: #a0522d;">result</span> = []
|
|
<span style="color: #a020f0;">for</span> Dim <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(2, 22):
|
|
<span style="color: #a0522d;">Dim</span>=<span style="color: #483d8b;">str</span>(Dim)
|
|
result.append(text.replace(<span style="color: #8b2252;">"{Dim}"</span>,Dim) )
|
|
|
|
<span style="color: #a020f0;">return</span> <span style="color: #8b2252;">'\n'</span>.join(result)
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting_hpc</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting_hpc"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a020f0;">__attribute__</span>((aligned(8))) <span style="color: #a0522d;">later_updates</span>[LDS * N_updates];
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">later_index</span>[N_updates];
|
|
<span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">later</span> = 0;
|
|
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">rc</span>;
|
|
<span style="color: #a020f0;">if</span> (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) {
|
|
<span style="color: #a020f0;">switch</span> (Dim) {
|
|
<span style="color: #a020f0;">case</span> 2: {
|
|
rc = qmckl_sm_splitting_core_2(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 3: {
|
|
rc = qmckl_sm_splitting_core_3(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 4: {
|
|
rc = qmckl_sm_splitting_core_4(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 5: {
|
|
rc = qmckl_sm_splitting_core_5(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 6: {
|
|
rc = qmckl_sm_splitting_core_6(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 7: {
|
|
rc = qmckl_sm_splitting_core_7(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 8: {
|
|
rc = qmckl_sm_splitting_core_8(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 9: {
|
|
rc = qmckl_sm_splitting_core_9(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 10: {
|
|
rc = qmckl_sm_splitting_core_10(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 11: {
|
|
rc = qmckl_sm_splitting_core_11(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 12: {
|
|
rc = qmckl_sm_splitting_core_12(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 13: {
|
|
rc = qmckl_sm_splitting_core_13(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 14: {
|
|
rc = qmckl_sm_splitting_core_14(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 15: {
|
|
rc = qmckl_sm_splitting_core_15(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 16: {
|
|
rc = qmckl_sm_splitting_core_16(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 17: {
|
|
rc = qmckl_sm_splitting_core_17(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 18: {
|
|
rc = qmckl_sm_splitting_core_18(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 19: {
|
|
rc = qmckl_sm_splitting_core_19(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 20: {
|
|
rc = qmckl_sm_splitting_core_20(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
|
|
<span style="color: #a020f0;">case</span> 21: {
|
|
rc = qmckl_sm_splitting_core_21(
|
|
context,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
later_updates,
|
|
later_index, &later, determinant);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
<span style="color: #a020f0;">default</span>: {
|
|
assert(0 == 1 && <span style="color: #8b2252;">"TEMPLATE NOT IMPLEMENTED!"</span>);
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
}
|
|
} <span style="color: #a020f0;">else</span> {
|
|
rc = qmckl_sm_splitting_core_hpc(
|
|
context, LDS, Dim, N_updates, Updates, Updates_index,
|
|
breakdown, Slater_inv, later_updates,
|
|
later_index, &later, determinant);
|
|
}
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) <span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
|
|
<span style="color: #a020f0;">if</span> (later > 0) {
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">rc</span> = qmckl_sm_splitting_hpc(
|
|
context, LDS, Dim, later,
|
|
later_updates, later_index,
|
|
breakdown, Slater_inv, determinant);
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) <span style="color: #a020f0;">return</span> QMCKL_FAILURE;
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_sm_splitting</span>(
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">LDS</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">Dim</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span> <span style="color: #a0522d;">N_updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Updates</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">uint64_t</span>* <span style="color: #a0522d;">Updates_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">breakdown</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">Slater_inv</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">determinant</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> qmckl_failwith(
|
|
context,
|
|
QMCKL_NULL_CONTEXT,
|
|
<span style="color: #8b2252;">"qmckl_sm_splitting"</span>,
|
|
<span style="color: #008b8b;">NULL</span>);
|
|
}
|
|
<span style="color: #483d8b;"> #ifdef</span> HAVE_HPC__BROKEN_WITH_CRAY
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_hpc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #483d8b;"> #else</span>
|
|
<span style="color: #a020f0;">return</span> qmckl_sm_splitting_doc(
|
|
context,
|
|
LDS,
|
|
Dim,
|
|
N_updates,
|
|
Updates,
|
|
Updates_index,
|
|
breakdown,
|
|
Slater_inv,
|
|
determinant);
|
|
<span style="color: #483d8b;"> #endif</span>
|
|
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org39ce850" class="outline-4">
|
|
<h4 id="org39ce850"><span class="section-number-4">6.1.7</span> Fortran interfaces (exposed in qmckl<sub>f.F90</sub>)</h4>
|
|
<div class="outline-text-4" id="text-6-1-7">
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf37d972" class="outline-4">
|
|
<h4 id="orgf37d972"><span class="section-number-4">6.1.8</span> Performance…</h4>
|
|
<div class="outline-text-4" id="text-6-1-8">
|
|
<p>
|
|
This kernel performs best when there are 2 or more rank-1 update cycles and fail-rate is high.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5a86004" class="outline-4">
|
|
<h4 id="org5a86004"><span class="section-number-4">6.1.9</span> Test</h4>
|
|
<div class="outline-text-4" id="text-6-1-9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #0000ff;">assert</span>(Updates3 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Updates_index3 != <span style="color: #008b8b;">NULL</span>);
|
|
<span style="color: #0000ff;">assert</span>(Slater_inv3_2 != <span style="color: #008b8b;">NULL</span>);
|
|
det = -1.23743195512859e-09;
|
|
rc = qmckl_sm_splitting(context, LDS, Dim, N_updates3, Updates3, Updates_index3, breakdown, Slater_inv3_2, &det);
|
|
<span style="color: #0000ff;">assert</span>(fabs(det - 1.602708950725074e-10) < 1e-15);
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
res[i * Dim + j] = 0;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">k</span> = 0; k < Dim; k++) {
|
|
res[i * Dim + j] += Slater3[i * Dim + k] * Slater_inv3_2[k * LDS + j];
|
|
}
|
|
}
|
|
}
|
|
rc = QMCKL_SUCCESS;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span> = 0; i < Dim; i++) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">unsigned</span> <span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span> = 0; j < Dim; j++) {
|
|
<span style="color: #a020f0;">if</span> (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
<span style="color: #a020f0;">if</span> (i != j && fabs(res[i * Dim + j]) > tolerance) {
|
|
rc = QMCKL_FAILURE;
|
|
}
|
|
}
|
|
}
|
|
<span style="color: #0000ff;">assert</span>(rc == QMCKL_SUCCESS);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="outline-container-org00488f9" class="outline-2">
|
|
<h2 id="org00488f9"><span class="section-number-2">7</span> End of files</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #0000ff;">assert</span> (<span style="color: #228b22;">qmckl_context_destroy</span>(<span style="color: #a0522d;">context</span>) == QMCKL_SUCCESS);
|
|
<span style="color: #a020f0;">return</span> 0;
|
|
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: TREX CoE</p>
|
|
<p class="date">Created: 2024-02-26 Mon 08:24</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|