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</head>
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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">Inter-particle distances</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="#orgf24c27b">1. Squared distance</a>
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<ul>
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<li><a href="#org461e1e0">1.1. <code>qmckl_distance_sq</code></a>
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<ul>
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<li><a href="#orgedc24a4">1.1.1. 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="#orgc681e01">2. Distance</a>
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<ul>
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<li><a href="#org085deae">2.1. <code>qmckl_distance</code></a>
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<ul>
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<li><a href="#org3b8e990">2.1.1. Requirements</a></li>
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<li><a href="#orgaf8bb31">2.1.2. C header</a></li>
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<li><a href="#org07619a8">2.1.3. Source</a></li>
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<li><a href="#org5c5d94c">2.1.4. 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="#orga17f9cf">3. Rescaled Distance</a>
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<ul>
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<li><a href="#org535ebf2">3.1. <code>qmckl_distance_rescaled</code></a>
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<ul>
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<li><a href="#org33b32bd">3.1.1. Requirements</a></li>
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<li><a href="#orge0285fb">3.1.2. C header</a></li>
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<li><a href="#org61f6138">3.1.3. Source</a></li>
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<li><a href="#org9ad623d">3.1.4. 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="#org672c272">4. Rescaled Distance Derivatives</a>
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<ul>
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<li><a href="#orgfecb018">4.1. <code>qmckl_distance_rescaled_gl</code></a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgf24c27b" class="outline-2">
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<h2 id="orgf24c27b"><span class="section-number-2">1</span> Squared distance</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org461e1e0" class="outline-3">
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<h3 id="org461e1e0"><span class="section-number-3">1.1</span> <code>qmckl_distance_sq</code></h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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<code>qmckl_distance_sq</code> computes the matrix of the squared distances
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between all pairs of points in two sets, one point within each set:
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</p>
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<p>
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\[
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C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2
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\]
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</p>
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<th scope="col" class="org-left">Variable</th>
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<th scope="col" class="org-left">Type</th>
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<th scope="col" class="org-left">In/Out</th>
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<th scope="col" class="org-left">Description</th>
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|
<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>transa</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>A</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>transb</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>B</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>m</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the first set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>n</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the second set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>A</code></td>
|
|
<td class="org-left"><code>double[][lda]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(m \times 3\) matrix \(A\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>lda</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>A</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>B</code></td>
|
|
<td class="org-left"><code>double[][ldb]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(n \times 3\) matrix \(B\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldb</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>B</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>C</code></td>
|
|
<td class="org-left"><code>double[n][ldc]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Array containing the \(m \times n\) matrix \(C\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldc</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>C</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Requirements:
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>m > 0</code></li>
|
|
<li><code>n > 0</code></li>
|
|
<li><code>lda >= 3</code> if <code>transa == 'N'</code></li>
|
|
<li><code>lda >= m</code> if <code>transa == 'T'</code></li>
|
|
<li><code>ldb >= 3</code> if <code>transb == 'N'</code></li>
|
|
<li><code>ldb >= n</code> if <code>transb == 'T'</code></li>
|
|
<li><code>ldc >= m</code></li>
|
|
<li><code>A</code> is allocated with at least \(3 \times m \times 8\) bytes</li>
|
|
<li><code>B</code> is allocated with at least \(3 \times n \times 8\) bytes</li>
|
|
<li><code>C</code> is allocated with at least \(m \times n \times 8\) bytes</li>
|
|
</ul>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance_sq</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;">char</span> <span style="color: #a0522d;">transa</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">transb</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">A</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">lda</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">B</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldb</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">C</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldc</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance_sq</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&</span>
|
|
A, LDA, B, LDB, C, LDC) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
|
<span style="color: #228b22;">integer</span> (qmckl_context) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,n)</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> info</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> x, y, z</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<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: #a020f0;">if</span> (m <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_5
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transa == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 0
|
|
<span style="color: #a020f0;">else if</span> (transa == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 1
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transb == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">continue</span>
|
|
<span style="color: #a020f0;">else if</span> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = transab + 2
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transab < 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_1
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDA < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 1 <span style="color: #a020f0;">.and.</span> LDA < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 0 <span style="color: #a020f0;">.and.</span> LDB < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 2 <span style="color: #a020f0;">.and.</span> LDB < n) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
<span style="color: #a020f0;">select case</span> (transab)
|
|
|
|
<span style="color: #a020f0;">case</span>(0)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(1,j)
|
|
y = A(2,i) - B(2,j)
|
|
z = A(3,i) - B(3,j)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(1)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(1,j)
|
|
y = A(i,2) - B(2,j)
|
|
z = A(i,3) - B(3,j)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(2)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(j,1)
|
|
y = A(2,i) - B(j,2)
|
|
z = A(3,i) - B(j,3)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(3)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(j,1)
|
|
y = A(i,2) - B(j,2)
|
|
z = A(i,3) - B(j,3)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end select</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_distance_sq</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgedc24a4" class="outline-4">
|
|
<h4 id="orgedc24a4"><span class="section-number-4">1.1.1</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-1-1-1">
|
|
<p>
|
|
This function is more efficient when <code>A</code> and <code>B</code> are
|
|
transposed.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgc681e01" class="outline-2">
|
|
<h2 id="orgc681e01"><span class="section-number-2">2</span> Distance</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
<div id="outline-container-org085deae" class="outline-3">
|
|
<h3 id="org085deae"><span class="section-number-3">2.1</span> <code>qmckl_distance</code></h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
<code>qmckl_distance</code> computes the matrix of the distances between all
|
|
pairs of points in two sets, one point within each set:
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
C_{ij} = \sqrt{\sum_{k=1}^3 (A_{k,i}-B_{k,j})^2}
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
If the input array is normal (<code>'N'</code>), the xyz coordinates are in
|
|
the leading dimension: <code>[n][3]</code> in C and <code>(3,n)</code> in Fortran.
|
|
</p>
|
|
|
|
<table id="org6dbdfc4" 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>transa</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>A</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>transb</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>B</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>m</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the first set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>n</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the second set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>A</code></td>
|
|
<td class="org-left"><code>double[][lda]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(m \times 3\) matrix \(A\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>lda</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>A</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>B</code></td>
|
|
<td class="org-left"><code>double[][ldb]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(n \times 3\) matrix \(B\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldb</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>B</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>C</code></td>
|
|
<td class="org-left"><code>double[n][ldc]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Array containing the \(m \times n\) matrix \(C\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldc</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>C</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
|
|
<div id="outline-container-org3b8e990" class="outline-4">
|
|
<h4 id="org3b8e990"><span class="section-number-4">2.1.1</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-2-1-1">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>m > 0</code></li>
|
|
<li><code>n > 0</code></li>
|
|
<li><code>lda >= 3</code> if <code>transa == 'N'</code></li>
|
|
<li><code>lda >= m</code> if <code>transa == 'T'</code></li>
|
|
<li><code>ldb >= 3</code> if <code>transb == 'N'</code></li>
|
|
<li><code>ldb >= n</code> if <code>transb == 'T'</code></li>
|
|
<li><code>ldc >= m</code></li>
|
|
<li><code>A</code> is allocated with at least \(3 \times m \times 8\) bytes</li>
|
|
<li><code>B</code> is allocated with at least \(3 \times n \times 8\) bytes</li>
|
|
<li><code>C</code> is allocated with at least \(m \times n \times 8\) bytes</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgaf8bb31" class="outline-4">
|
|
<h4 id="orgaf8bb31"><span class="section-number-4">2.1.2</span> C header</h4>
|
|
<div class="outline-text-4" id="text-2-1-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance</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;">char</span> <span style="color: #a0522d;">transa</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">transb</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">A</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">lda</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">B</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldb</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">C</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldc</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org07619a8" class="outline-4">
|
|
<h4 id="org07619a8"><span class="section-number-4">2.1.3</span> Source</h4>
|
|
<div class="outline-text-4" id="text-2-1-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&</span>
|
|
A, LDA, B, LDB, C, LDC) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,n)</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_exit_code) ::<span style="color: #a0522d;"> info</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> x, y, z</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<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: #a020f0;">if</span> (m <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_5
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transa == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 0
|
|
<span style="color: #a020f0;">else if</span> (transa == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 1
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transb == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">continue</span>
|
|
<span style="color: #a020f0;">else if</span> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = transab + 2
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transab < 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_1
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDA</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDA < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 1 <span style="color: #a020f0;">.and.</span> LDA < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDB</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDB < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 1 <span style="color: #a020f0;">.and.</span> LDB < n) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDC</span>
|
|
<span style="color: #a020f0;">if</span> (LDC < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_11
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
<span style="color: #a020f0;">select case</span> (transab)
|
|
|
|
<span style="color: #a020f0;">case</span>(0)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(1,j)
|
|
y = A(2,i) - B(2,j)
|
|
z = A(3,i) - B(3,j)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
C(:,j) = dsqrt(C(:,j))
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(1)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(1,j)
|
|
y = A(i,2) - B(2,j)
|
|
z = A(i,3) - B(3,j)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
C(:,j) = dsqrt(C(:,j))
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(2)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(j,1)
|
|
y = A(2,i) - B(j,2)
|
|
z = A(3,i) - B(j,3)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
C(:,j) = dsqrt(C(:,j))
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(3)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(j,1)
|
|
y = A(i,2) - B(j,2)
|
|
z = A(i,3) - B(j,3)
|
|
C(i,j) = x*x + y*y + z*z
|
|
<span style="color: #a020f0;">end do</span>
|
|
C(:,j) = dsqrt(C(:,j))
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end select</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_distance</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5c5d94c" class="outline-4">
|
|
<h4 id="org5c5d94c"><span class="section-number-4">2.1.4</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-2-1-4">
|
|
<p>
|
|
This function is more efficient when <code>A</code> and <code>B</code> are transposed.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga17f9cf" class="outline-2">
|
|
<h2 id="orga17f9cf"><span class="section-number-2">3</span> Rescaled Distance</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
</div>
|
|
<div id="outline-container-org535ebf2" class="outline-3">
|
|
<h3 id="org535ebf2"><span class="section-number-3">3.1</span> <code>qmckl_distance_rescaled</code></h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
<code>qmckl_distance_rescaled</code> computes the matrix of the rescaled distances between all
|
|
pairs of points in two sets, one point within each set:
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
C_{ij} = \frac{ 1 - e^{-\kappa r_{ij}}}{\kappa}
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
If the input array is normal (<code>'N'</code>), the xyz coordinates are in
|
|
the leading dimension: <code>[n][3]</code> in C and <code>(3,n)</code> in Fortran.
|
|
</p>
|
|
|
|
<table id="org1061984" 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>transa</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>A</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>transb</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>B</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>m</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the first set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>n</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the second set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>A</code></td>
|
|
<td class="org-left"><code>double[][lda]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(m \times 3\) matrix \(A\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>lda</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>A</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>B</code></td>
|
|
<td class="org-left"><code>double[][ldb]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(n \times 3\) matrix \(B\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldb</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>B</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>C</code></td>
|
|
<td class="org-left"><code>double[n][ldc]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Array containing the \(m \times n\) matrix \(C\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldc</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>C</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>rescale_factor_kappa</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Factor for calculating rescaled distances</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
|
|
<div id="outline-container-org33b32bd" class="outline-4">
|
|
<h4 id="org33b32bd"><span class="section-number-4">3.1.1</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-3-1-1">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>m > 0</code></li>
|
|
<li><code>n > 0</code></li>
|
|
<li><code>lda >= 3</code> if <code>transa == 'N'</code></li>
|
|
<li><code>lda >= m</code> if <code>transa == 'T'</code></li>
|
|
<li><code>ldb >= 3</code> if <code>transb == 'N'</code></li>
|
|
<li><code>ldb >= n</code> if <code>transb == 'T'</code></li>
|
|
<li><code>ldc >= m</code></li>
|
|
<li><code>A</code> is allocated with at least \(3 \times m \times 8\) bytes</li>
|
|
<li><code>B</code> is allocated with at least \(3 \times n \times 8\) bytes</li>
|
|
<li><code>C</code> is allocated with at least \(m \times n \times 8\) bytes</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge0285fb" class="outline-4">
|
|
<h4 id="orge0285fb"><span class="section-number-4">3.1.2</span> C header</h4>
|
|
<div class="outline-text-4" id="text-3-1-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance_rescaled</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;">char</span> <span style="color: #a0522d;">transa</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">transb</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">A</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">lda</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">B</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldb</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">C</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldc</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">rescale_factor_kappa</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org61f6138" class="outline-4">
|
|
<h4 id="org61f6138"><span class="section-number-4">3.1.3</span> Source</h4>
|
|
<div class="outline-text-4" id="text-3-1-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance_rescaled</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&</span>
|
|
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> rescale_factor_kappa</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,n)</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> info</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> x, y, z, dist, rescale_factor_kappa_inv</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
|
|
|
|
rescale_factor_kappa_inv = 1.0d0/rescale_factor_kappa;
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<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: #a020f0;">if</span> (m <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_5
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transa == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 0
|
|
<span style="color: #a020f0;">else if</span> (transa == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 1
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transb == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">continue</span>
|
|
<span style="color: #a020f0;">else if</span> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = transab + 2
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDA</span>
|
|
<span style="color: #a020f0;">if</span> (transab < 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_1
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDA < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 1 <span style="color: #a020f0;">.and.</span> LDA < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDB</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 0 <span style="color: #a020f0;">.and.</span> LDB < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 2 <span style="color: #a020f0;">.and.</span> LDB < n) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDC</span>
|
|
<span style="color: #a020f0;">if</span> (LDC < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_11
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
<span style="color: #a020f0;">select case</span> (transab)
|
|
|
|
<span style="color: #a020f0;">case</span>(0)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(1,j)
|
|
y = A(2,i) - B(2,j)
|
|
z = A(3,i) - B(3,j)
|
|
dist = dsqrt(x*x + y*y + z*z)
|
|
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(1)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(1,j)
|
|
y = A(i,2) - B(2,j)
|
|
z = A(i,3) - B(3,j)
|
|
dist = dsqrt(x*x + y*y + z*z)
|
|
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(2)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(j,1)
|
|
y = A(2,i) - B(j,2)
|
|
z = A(3,i) - B(j,3)
|
|
dist = dsqrt(x*x + y*y + z*z)
|
|
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(3)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(j,1)
|
|
y = A(i,2) - B(j,2)
|
|
z = A(i,3) - B(j,3)
|
|
dist = dsqrt(x*x + y*y + z*z)
|
|
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end select</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_distance_rescaled</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9ad623d" class="outline-4">
|
|
<h4 id="org9ad623d"><span class="section-number-4">3.1.4</span> Performance</h4>
|
|
<div class="outline-text-4" id="text-3-1-4">
|
|
<p>
|
|
This function is more efficient when <code>A</code> and <code>B</code> are transposed.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org672c272" class="outline-2">
|
|
<h2 id="org672c272"><span class="section-number-2">4</span> Rescaled Distance Derivatives</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
</div>
|
|
<div id="outline-container-orgfecb018" class="outline-3">
|
|
<h3 id="orgfecb018"><span class="section-number-3">4.1</span> <code>qmckl_distance_rescaled_gl</code></h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
<code>qmckl_distance_rescaled_gl</code> computes the matrix of the gradient and Laplacian of the
|
|
rescaled distance with respect to the electron coordinates. The derivative is a rank 3 tensor.
|
|
The first dimension has a dimension of 4 of which the first three coordinates
|
|
contains the gradient vector and the last index is the Laplacian.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
\[
|
|
C(r_{ij}) = \left( 1 - \exp(-\kappa\, r_{ij})\right)/\kappa
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
Here the gradient is defined as follows:
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
\nabla_i C(r_{ij}) = \left(\frac{\partial C(r_{ij})}{\partial x_i},\frac{\partial C(r_{ij})}{\partial y_i},\frac{\partial C(r_{ij})}{\partial z_i} \right)
|
|
\]
|
|
and the Laplacian is defined as follows:
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
\Delta_i C(r_{ij}) = \frac{\partial^2}{\partial x_i^2} + \frac{\partial^2}{\partial y_i^2} + \frac{\partial^2}{\partial z_i^2}
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
Using the above three formulas, the expression for the gradient and Laplacian is:
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
\frac{\partial C(r_{ij})}{\partial x_i} = \frac{|(x_i -
|
|
x_j)|}{r_{ij}} \exp (- \kappa \, r_{ij})
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
\Delta C_{ij}(r_{ij}) = \left[ \frac{2}{r_{ij}} - \kappa \right] \exp (- \kappa \, r_{ij})
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
If the input array is normal (<code>'N'</code>), the xyz coordinates are in
|
|
the leading dimension: <code>[n][3]</code> in C and <code>(3,n)</code> in Fortran.
|
|
</p>
|
|
|
|
<table id="orgab8ff46" 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>transa</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>A</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>transb</code></td>
|
|
<td class="org-left"><code>char</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array <code>B</code> is <code>'N'</code>: Normal, <code>'T'</code>: Transposed</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>m</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the first set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>n</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of points in the second set</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>A</code></td>
|
|
<td class="org-left"><code>double[][lda]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(m \times 3\) matrix \(A\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>lda</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>A</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>B</code></td>
|
|
<td class="org-left"><code>double[][ldb]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the \(n \times 3\) matrix \(B\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldb</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>B</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>C</code></td>
|
|
<td class="org-left"><code>double[n][ldc][4]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Array containing the \(4 \times m \times n\) matrix \(C\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldc</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>C</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>rescale_factor_kappa</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Factor for calculating rescaled distances derivatives</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Requirements:
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>m > 0</code></li>
|
|
<li><code>n > 0</code></li>
|
|
<li><code>lda >= 3</code> if <code>transa == 'N'</code></li>
|
|
<li><code>lda >= m</code> if <code>transa == 'T'</code></li>
|
|
<li><code>ldb >= 3</code> if <code>transb == 'N'</code></li>
|
|
<li><code>ldb >= n</code> if <code>transb == 'T'</code></li>
|
|
<li><code>ldc >= m</code></li>
|
|
<li><code>A</code> is allocated with at least \(3 \times m \times 8\) bytes</li>
|
|
<li><code>B</code> is allocated with at least \(3 \times n \times 8\) bytes</li>
|
|
<li><code>C</code> is allocated with at least \(4 \times m \times n \times 8\) bytes</li>
|
|
</ul>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance_rescaled_gl</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;">char</span> <span style="color: #a0522d;">transa</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">transb</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">A</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">lda</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">B</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldb</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">C</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldc</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">rescale_factor_kappa</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance_rescaled_gl</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&</span>
|
|
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> info</span>
|
|
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
|
|
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
|
|
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> rescale_factor_kappa</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
|
|
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(4,ldc,n)</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> x, y, z, dist, dist_inv</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> rij</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<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: #a020f0;">if</span> (m <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_5
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transa == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 0
|
|
<span style="color: #a020f0;">else if</span> (transa == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = 1
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (transb == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">continue</span>
|
|
<span style="color: #a020f0;">else if</span> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
|
transab = transab + 2
|
|
<span style="color: #a020f0;">else</span>
|
|
transab = -100
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDA</span>
|
|
<span style="color: #a020f0;">if</span> (transab < 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_1
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDA < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 1 <span style="color: #a020f0;">.and.</span> LDA < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDB</span>
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 0 <span style="color: #a020f0;">.and.</span> LDB < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 2 <span style="color: #a020f0;">.and.</span> LDB < n) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">check for LDC</span>
|
|
<span style="color: #a020f0;">if</span> (LDC < m) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_11
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
<span style="color: #a020f0;">select case</span> (transab)
|
|
|
|
<span style="color: #a020f0;">case</span>(0)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(1,j)
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y = A(2,i) - B(2,j)
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z = A(3,i) - B(3,j)
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dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
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dist_inv = 1.0d0/dist
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rij = dexp(-rescale_factor_kappa * dist)
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C(1,i,j) = x * dist_inv * rij
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C(2,i,j) = y * dist_inv * rij
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C(3,i,j) = z * dist_inv * rij
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C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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<span style="color: #a020f0;">end do</span>
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<span style="color: #a020f0;">end do</span>
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|
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<span style="color: #a020f0;">case</span>(1)
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<span style="color: #a020f0;">do</span> j=1,n
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<span style="color: #a020f0;">do</span> i=1,m
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x = A(i,1) - B(1,j)
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y = A(i,2) - B(2,j)
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z = A(i,3) - B(3,j)
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dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
|
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dist_inv = 1.0d0/dist
|
|
rij = dexp(-rescale_factor_kappa * dist)
|
|
C(1,i,j) = x * dist_inv * rij
|
|
C(2,i,j) = y * dist_inv * rij
|
|
C(3,i,j) = z * dist_inv * rij
|
|
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
|
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<span style="color: #a020f0;">end do</span>
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<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(2)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(1,i) - B(j,1)
|
|
y = A(2,i) - B(j,2)
|
|
z = A(3,i) - B(j,3)
|
|
dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
|
|
dist_inv = 1.0d0/dist
|
|
rij = dexp(-rescale_factor_kappa * dist)
|
|
C(1,i,j) = x * dist_inv * rij
|
|
C(2,i,j) = y * dist_inv * rij
|
|
C(3,i,j) = z * dist_inv * rij
|
|
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">case</span>(3)
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,m
|
|
x = A(i,1) - B(j,1)
|
|
y = A(i,2) - B(j,2)
|
|
z = A(i,3) - B(j,3)
|
|
dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
|
|
dist_inv = 1.0d0/dist
|
|
rij = dexp(-rescale_factor_kappa * dist)
|
|
C(1,i,j) = x * dist_inv * rij
|
|
C(2,i,j) = y * dist_inv * rij
|
|
C(3,i,j) = z * dist_inv * rij
|
|
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
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<span style="color: #a020f0;">end select</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_distance_rescaled_gl</span>
|
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</pre>
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</div>
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|
|
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<p>
|
|
This function is more efficient when <code>A</code> and <code>B</code> are transposed.
|
|
</p>
|
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</div>
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</div>
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</div>
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|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: TREX CoE</p>
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|
<p class="date">Created: 2024-02-23 Fri 23:19</p>
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|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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