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<a accesskey="h" href=""> UP </a>
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</div><div id="content">
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<h1 class="title">BLAS functions</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="#orga6ec933">1. Matrix operations</a>
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<ul>
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<li><a href="#orgc574087">1.1. <code>qmckl_dgemm</code></a></li>
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<li><a href="#org6196b4b">1.2. <code>qmckl_adjugate</code></a></li>
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</ul>
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</li>
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</div>
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<div id="outline-container-orga6ec933" class="outline-2">
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<h2 id="orga6ec933"><span class="section-number-2">1</span> Matrix operations</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-orgc574087" class="outline-3">
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<h3 id="orgc574087"><span class="section-number-3">1.1</span> <code>qmckl_dgemm</code></h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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Matrix multiplication:
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</p>
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<p>
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\[
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C_{ij} = \beta C_{ij} + \alpha \sum_{k} A_{ik} \cdot B_{kj}
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\]
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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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</tr>
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</thead>
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<tbody>
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<td class="org-left"><code>context</code></td>
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<td class="org-left"><code>qmckl_context</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Global state</td>
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</tr>
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<tr>
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<td class="org-left"><code>TransA</code></td>
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<td class="org-left"><code>char</code></td>
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<td class="org-left">in</td>
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<td class="org-left">'T' is transposed</td>
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<tr>
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<td class="org-left"><code>TransB</code></td>
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<td class="org-left"><code>char</code></td>
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<td class="org-left">in</td>
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<td class="org-left">'T' is transposed</td>
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</tr>
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<tr>
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<td class="org-left"><code>m</code></td>
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<td class="org-left"><code>int64_t</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Number of rows of the input matrix</td>
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</tr>
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<tr>
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<td class="org-left"><code>n</code></td>
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<td class="org-left"><code>int64_t</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Number of columns of the input matrix</td>
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</tr>
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<tr>
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<td class="org-left"><code>k</code></td>
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<td class="org-left"><code>int64_t</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Number of columns of the input matrix</td>
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</tr>
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<tr>
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<td class="org-left"><code>alpha</code></td>
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<td class="org-left"><code>double</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Number of columns of the input matrix</td>
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</tr>
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<tr>
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<td class="org-left"><code>A</code></td>
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|
<td class="org-left"><code>double[][lda]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the 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 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>beta</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the matrix \(B\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>C</code></td>
|
|
<td class="org-left"><code>double[][ldc]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Array containing the matrix \(B\)</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>B</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>k > 0</code></li>
|
|
<li><code>lda >= m</code></li>
|
|
<li><code>ldb >= n</code></li>
|
|
<li><code>ldc >= n</code></li>
|
|
<li><code>A</code> is allocated with at least \(m \times k \times 8\) bytes</li>
|
|
<li><code>B</code> is allocated with at least \(k \times n \times 8\) 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_dgemm</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;">int64_t</span> <span style="color: #a0522d;">k</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">alpha</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: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">beta</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: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_dgemm_f(context, TransA, TransB, </span><span style="color: #a020f0;">&</span>
|
|
m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC) <span style="color: #a020f0;">&</span>
|
|
<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>(qmckl_context), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">character</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> TransA, TransB</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> m, n, k</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> alpha, beta</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lda</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldb</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldc</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,*)</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> (k <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_6
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (LDA <= 0) <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> (LDB <= 0) <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;">if</span> (LDC <= 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_14
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">dgemm</span>(transA, transB, <span style="color: #a020f0;">int</span>(m,4), <span style="color: #a020f0;">int</span>(n,4), <span style="color: #a020f0;">int</span>(k,4), <span style="color: #a020f0;">&</span>
|
|
alpha, A, <span style="color: #a020f0;">int</span>(LDA,4), B, <span style="color: #a020f0;">int</span>(LDB,4), beta, C, <span style="color: #a020f0;">int</span>(LDC,4))
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_dgemm_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6196b4b" class="outline-3">
|
|
<h3 id="org6196b4b"><span class="section-number-3">1.2</span> <code>qmckl_adjugate</code></h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
Given a matrix \(\mathbf{A}\), the adjugate matrix
|
|
\(\text{adj}(\mathbf{A})\) is the transpose of the cofactors matrix
|
|
of \(\mathbf{A}\).
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
\mathbf{B} = \text{adj}(\mathbf{A}) = \text{det}(\mathbf{A}) \, \mathbf{A}^{-1}
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
See also: <a href="https://en.wikipedia.org/wiki/Adjugate_matrix">https://en.wikipedia.org/wiki/Adjugate_matrix</a>
|
|
</p>
|
|
|
|
<table id="orgd82ba41" 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>n</code></td>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of rows and columns of the input matrix</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 \(n \times n\) 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">out</td>
|
|
<td class="org-left">Adjugate of \(A\)</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>det_l</code></td>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">determinant of \(A\)</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>n > 0</code></li>
|
|
<li><code>lda >= m</code></li>
|
|
<li><code>A</code> is allocated with at least \(m \times m \times 8\) bytes</li>
|
|
<li><code>ldb >= m</code></li>
|
|
<li><code>B</code> is allocated with at least \(m \times m \times 8\) 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_adjugate</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;">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: #228b22;">double</span>* <span style="color: #a020f0;">const</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: #a0522d;">det_l</span> );
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
For small matrices (≤ 5× 5), we use specialized routines
|
|
for performance motivations. For larger sizes, we rely on the
|
|
LAPACK library.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_adjugate_f</span><span style="color: #000000; background-color: #ffffff;">(context, na, A, LDA, B, ldb, det_l)</span><span style="color: #a0522d;"> </span><span style="color: #a020f0;">&</span>
|
|
<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>(qmckl_context) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A (LDA,*)</span>
|
|
<span style="color: #228b22;">integer</span>*8, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> LDA</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> B (LDB,*)</span>
|
|
<span style="color: #228b22;">integer</span>*8, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> LDB</span>
|
|
<span style="color: #228b22;">integer</span>*8, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> na</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> det_l</span>
|
|
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> i,j</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> (na <= 0_8) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_2
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (LDA <= 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> (LDA < na) <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;">select case</span> (na)
|
|
<span style="color: #a020f0;">case</span> (5)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">adjugate5</span>(A,LDA,B,LDB,na,det_l)
|
|
<span style="color: #a020f0;">case</span> (4)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">adjugate4</span>(A,LDA,B,LDB,na,det_l)
|
|
<span style="color: #a020f0;">case</span> (3)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">adjugate3</span>(A,LDA,B,LDB,na,det_l)
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<span style="color: #a020f0;">case</span> (2)
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<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">adjugate2</span>(A,LDA,B,LDB,na,det_l)
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<span style="color: #a020f0;">case</span> (1)
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det_l = a(1,1)
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b(1,1) = 1.d0
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<span style="color: #a020f0;">case</span> default
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<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">adjugate_general</span>(context, na, A, LDA, B, LDB, det_l)
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<span style="color: #a020f0;">end select</span>
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<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_adjugate_f</span>
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #a020f0;">subroutine</span> <span style="color: #0000ff;">adjugate_general</span>(context, na, A, LDA, B, LDB, det_l)
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<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
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<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
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<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A (LDA,na)</span>
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<span style="color: #228b22;">integer</span>*8, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> LDA</span>
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> B (LDB,na)</span>
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<span style="color: #228b22;">integer</span>*8, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> LDB</span>
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<span style="color: #228b22;">integer</span>*8, <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> na</span>
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">intent</span>(inout) ::<span style="color: #a0522d;"> det_l</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> work(LDA*max(na,64))</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> inf</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> ipiv(LDA)</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lwork</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> i, j</span>
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</pre>
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</div>
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<p>
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We first copy the array <code>A</code> into array <code>B</code>.
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</p>
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<div class="org-src-container">
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<pre class="src src-f90">B(1:na,1:na) = A(1:na,1:na)
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</pre>
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</div>
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<p>
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Then, we compute the LU factorization \(LU=A\)
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using the <code>dgetrf</code> routine.
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</p>
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #a020f0;">call</span> <span style="color: #0000ff;">dgetrf</span>(na, na, B, LDB, ipiv, inf )
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</pre>
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</div>
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<p>
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By convention, the determinant of \(L\) is equal to one, so the
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determinant of \(A\) is equal to the determinant of \(U\), which is
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simply computed as the product of its diagonal elements.
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</p>
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|
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<div class="org-src-container">
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<pre class="src src-f90">det_l = 1.d0
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j=0
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<span style="color: #a020f0;">do</span> i=1,na
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j = j+<span style="color: #a020f0;">min</span>(<span style="color: #a020f0;">abs</span>(ipiv(i)-i),1)
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det_l = det_l*B(i,i)
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<span style="color: #a020f0;">enddo</span>
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</pre>
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</div>
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<p>
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As <code>dgetrf</code> returns \(PLU=A\) where \(P\) is a permutation matrix, the
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sign of the determinant is computed as \(-1^m\) where \(m\) is the
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number of permutations.
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</p>
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|
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(j,1) /= 0) <span style="color: #a020f0;">then</span>
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|
det_l = -det_l
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|
<span style="color: #a020f0;">endif</span>
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</pre>
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</div>
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|
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|
<p>
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|
Then, the inverse of \(A\) is computed using <code>dgetri</code>:
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</p>
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|
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|
<div class="org-src-container">
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<pre class="src src-f90">lwork = <span style="color: #a020f0;">SIZE</span>(work)
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<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">dgetri</span>(na, B, LDB, ipiv, work, lwork, inf )
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|
</pre>
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</div>
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|
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|
<p>
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|
and the adjugate matrix is computed as the product of the
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|
determinant with the inverse:
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</p>
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|
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|
<div class="org-src-container">
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<pre class="src src-f90"> B(:,:) = B(:,:)*det_l
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|
<span style="color: #a020f0;">end subroutine</span> <span style="color: #0000ff;">adjugate_general</span>
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|
</pre>
|
|
</div>
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</div>
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</div>
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</div>
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</div>
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|
<div id="postamble" class="status">
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<p class="author">Author: TREX CoE</p>
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<p class="date">Created: 2022-01-06 Thu 18:05</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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