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2023-09-13 16:23:56 +02:00
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2022-09-28 18:04:21 +02:00
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2022-11-18 14:16:53 +01:00
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2022-11-18 14:16:53 +01:00
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2022-09-28 18:04:21 +02:00
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2022-11-18 14:16:53 +01:00
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Copyright (C) 2012-2020 Free Software Foundation, Inc.
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2022-09-28 18:04:21 +02:00
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The JavaScript code in this tag is free software: you can
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redistribute it and/or modify it under the terms of the GNU
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General Public License (GNU GPL) as published by the Free Software
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Foundation, either version 3 of the License, or (at your option)
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any later version. The code is distributed WITHOUT ANY WARRANTY;
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without even the implied warranty of MERCHANTABILITY or FITNESS
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FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
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As additional permission under GNU GPL version 3 section 7, you
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may distribute non-source (e.g., minimized or compacted) forms of
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that code without the copy of the GNU GPL normally required by
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section 4, provided you include this license notice and a URL
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through which recipients can access the Corresponding Source.
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@licend The above is the entire license notice
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for the JavaScript code in this tag.
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*/
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org_html_manager.set("TOC_DEPTH", "4");
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<script type="text/javascript">
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/*
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@licstart The following is the entire license notice for the
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2022-11-18 14:16:53 +01:00
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Copyright (C) 2012-2020 Free Software Foundation, Inc.
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2022-09-28 18:04:21 +02:00
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The JavaScript code in this tag is free software: you can
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redistribute it and/or modify it under the terms of the GNU
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General Public License (GNU GPL) as published by the Free Software
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Foundation, either version 3 of the License, or (at your option)
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any later version. The code is distributed WITHOUT ANY WARRANTY;
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without even the implied warranty of MERCHANTABILITY or FITNESS
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<body>
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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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<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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2023-09-13 16:23:56 +02:00
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<li><a href="#org3ee5d90">-</a></li>
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<li><a href="#org987d788">1. Data types</a>
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2022-09-28 18:04:21 +02:00
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<ul>
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2023-09-13 16:23:56 +02:00
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<li><a href="#orgb988f6b">1.1. Vector</a></li>
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<li><a href="#orge20a4d4">1.2. Matrix</a></li>
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<li><a href="#org43e52c0">1.3. Tensor</a></li>
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<li><a href="#org9a88c52">1.4. Reshaping</a>
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2022-09-28 18:04:21 +02:00
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<ul>
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2023-09-13 16:23:56 +02:00
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<li><a href="#org4a39035">1.4.1. Vector -> Matrix</a></li>
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<li><a href="#org0a26599">1.4.2. Vector -> Tensor</a></li>
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<li><a href="#orgec07f9d">1.4.3. Matrix -> Vector</a></li>
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<li><a href="#orgfaff3d8">1.4.4. Matrix -> Tensor</a></li>
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<li><a href="#orge37a199">1.4.5. Tensor -> Vector</a></li>
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<li><a href="#orged87f01">1.4.6. Tensor -> Matrix</a></li>
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2022-09-28 18:04:21 +02:00
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</ul>
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</li>
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2023-09-13 16:23:56 +02:00
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<li><a href="#orge60cec9">1.5. Access macros</a></li>
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<li><a href="#orgad8fd14">1.6. Set all elements</a>
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2022-09-28 18:04:21 +02:00
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<ul>
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2023-09-13 16:23:56 +02:00
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<li><a href="#org8ce6bc5">1.6.1. Vector</a></li>
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<li><a href="#orgf96f54e">1.6.2. Matrix</a></li>
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<li><a href="#orgc4c5a03">1.6.3. Tensor</a></li>
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2022-09-28 18:04:21 +02:00
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</ul>
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</li>
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2023-09-13 16:23:56 +02:00
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<li><a href="#orgb3a225b">1.7. Copy to/from to <code>double*</code></a></li>
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<li><a href="#orgb150823">1.8. Allocate and copy to <code>double*</code></a></li>
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2022-09-28 18:04:21 +02:00
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</ul>
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</li>
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2023-09-13 16:23:56 +02:00
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<li><a href="#orga9c6878">2. Matrix operations</a>
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2022-09-28 18:04:21 +02:00
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<ul>
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2023-09-13 16:23:56 +02:00
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<li><a href="#org37d622b">2.1. <code>qmckl_dgemm</code></a></li>
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<li><a href="#org73f76d2">2.2. <code>qmckl_dgemm_safe</code></a></li>
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<li><a href="#org0a14dd2">2.3. <code>qmckl_matmul</code></a></li>
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<li><a href="#org921a737">2.4. <code>qmckl_adjugate</code></a></li>
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<li><a href="#org8eb8314">2.5. <code>qmckl_adjugate_safe</code></a>
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2022-09-28 18:04:21 +02:00
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<ul>
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2023-09-13 16:23:56 +02:00
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<li><a href="#org206794f">2.5.1. C interface</a></li>
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2022-09-28 18:04:21 +02:00
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</ul>
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</li>
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2023-09-13 16:23:56 +02:00
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<li><a href="#orgdadeee4">2.6. <code>qmckl_transpose</code></a></li>
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2022-09-28 18:04:21 +02:00
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</ul>
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</li>
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2023-09-13 16:23:56 +02:00
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<li><a href="#org36156f3">3. Utilities</a></li>
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2022-09-28 18:04:21 +02:00
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</ul>
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</div>
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</div>
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2023-09-13 16:23:56 +02:00
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<div id="outline-container-org3ee5d90" class="outline-2">
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<h2 id="org3ee5d90">-</h2>
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<div class="outline-text-2" id="text-org3ee5d90">
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2022-09-28 18:04:21 +02:00
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<p>
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Basic linear algebra data types and operations are described in this file.
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The data types are private, so that HPC implementations can use
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whatever data structures they prefer.
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</p>
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<p>
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These data types are expected to be used internally in QMCkl. They
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are not intended to be passed to external codes.
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</p>
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</div>
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</div>
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2023-09-13 16:23:56 +02:00
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<div id="outline-container-org987d788" class="outline-2">
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<h2 id="org987d788"><span class="section-number-2">1</span> Data types</h2>
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2022-09-28 18:04:21 +02:00
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<div class="outline-text-2" id="text-1">
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2023-09-13 16:23:56 +02:00
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<div id="outline-container-orgb988f6b" class="outline-3">
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<h3 id="orgb988f6b"><span class="section-number-3">1.1</span> Vector</h3>
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2022-09-28 18:04:21 +02:00
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<div class="outline-text-3" id="text-1-1">
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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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">Description</th>
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<tbody>
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<td class="org-left"><code>size</code></td>
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<td class="org-left"><code>int64_t</code></td>
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<td class="org-left">Dimension of the vector</td>
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</tr>
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<tr>
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<td class="org-left"><code>data</code></td>
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<td class="org-left"><code>double*</code></td>
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<td class="org-left">Elements</td>
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</tbody>
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</table>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_vector</span>
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<span style="color: #0000ff;">qmckl_vector_alloc</span>( <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size</span>);
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</pre>
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</div>
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<p>
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Allocates a new vector. If the allocation failed the size is zero.
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</p>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
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<span style="color: #0000ff;">qmckl_vector_free</span>( <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
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<span style="color: #228b22;">qmckl_vector</span>* <span style="color: #a0522d;">vector</span>);
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</pre>
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</div>
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</div>
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</div>
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2023-09-13 16:23:56 +02:00
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<div id="outline-container-orge20a4d4" class="outline-3">
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<h3 id="orge20a4d4"><span class="section-number-3">1.2</span> Matrix</h3>
|
2022-09-28 18:04:21 +02:00
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<div class="outline-text-3" id="text-1-2">
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<thead>
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<tr>
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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">Description</th>
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<tbody>
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<tr>
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<td class="org-left"><code>size</code></td>
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<td class="org-left"><code>int64_t[2]</code></td>
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<td class="org-left">Dimension of each component</td>
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</tr>
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<tr>
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<td class="org-left"><code>data</code></td>
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<td class="org-left"><code>double*</code></td>
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<td class="org-left">Elements</td>
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</tr>
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</tbody>
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</table>
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<p>
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|
The dimensions use Fortran ordering: two elements differing by one
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in the first dimension are consecutive in memory.
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</p>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_matrix</span>
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|
<span style="color: #0000ff;">qmckl_matrix_alloc</span>( <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
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|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size1</span>,
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|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size2</span>);
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</pre>
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</div>
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<p>
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Allocates a new matrix. If the allocation failed the sizes are zero.
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|
</p>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
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|
<span style="color: #0000ff;">qmckl_matrix_free</span>( <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
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|
<span style="color: #228b22;">qmckl_matrix</span>* <span style="color: #a0522d;">matrix</span>);
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</pre>
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</div>
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</div>
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</div>
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2023-09-13 16:23:56 +02:00
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<div id="outline-container-org43e52c0" class="outline-3">
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<h3 id="org43e52c0"><span class="section-number-3">1.3</span> Tensor</h3>
|
2022-09-28 18:04:21 +02:00
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<div class="outline-text-3" id="text-1-3">
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<thead>
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<tr>
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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">Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left"><code>order</code></td>
|
2023-03-17 14:57:01 +01:00
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<td class="org-left"><code>int32_t</code></td>
|
2022-09-28 18:04:21 +02:00
|
|
|
<td class="org-left">Order of the tensor</td>
|
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|
|
|
</tr>
|
|
|
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|
|
|
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|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>size</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t[QMCKL_TENSOR_ORDER_MAX]</code></td>
|
|
|
|
|
<td class="org-left">Dimension of each component</td>
|
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|
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|
</tr>
|
|
|
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|
|
<tr>
|
|
|
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|
<td class="org-left"><code>data</code></td>
|
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<td class="org-left"><code>double*</code></td>
|
|
|
|
|
<td class="org-left">Elements</td>
|
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|
|
|
</tr>
|
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</tbody>
|
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|
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|
</table>
|
|
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|
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<p>
|
|
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|
The dimensions use Fortran ordering: two elements differing by one
|
|
|
|
|
in the first dimension are consecutive in memory.
|
|
|
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|
</p>
|
|
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|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_tensor</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_tensor_alloc</span>( <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
2023-03-17 14:57:01 +01:00
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">order</span>,
|
2022-09-28 18:04:21 +02:00
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">size</span>);
|
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|
|
</pre>
|
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|
</div>
|
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<p>
|
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|
Allocates memory for a tensor. If the allocation failed, the size
|
|
|
|
|
is zero.
|
|
|
|
|
</p>
|
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|
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|
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|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_tensor_free</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #228b22;">qmckl_tensor</span>* <span style="color: #a0522d;">tensor</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
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|
</div>
|
|
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|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org9a88c52" class="outline-3">
|
|
|
|
|
<h3 id="org9a88c52"><span class="section-number-3">1.4</span> Reshaping</h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-1-4">
|
|
|
|
|
<p>
|
|
|
|
|
Reshaping occurs in-place and the pointer to the data is copied.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
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|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org4a39035" class="outline-4">
|
|
|
|
|
<h4 id="org4a39035"><span class="section-number-4">1.4.1</span> Vector -> Matrix</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-4-1">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_matrix</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_matrix_of_vector</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_vector</span> <span style="color: #a0522d;">vector</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size1</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size2</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Reshapes a vector into a matrix.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org0a26599" class="outline-4">
|
|
|
|
|
<h4 id="org0a26599"><span class="section-number-4">1.4.2</span> Vector -> Tensor</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-4-2">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_tensor</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_tensor_of_vector</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_vector</span> <span style="color: #a0522d;">vector</span>,
|
2023-03-17 14:57:01 +01:00
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">order</span>,
|
2022-09-28 18:04:21 +02:00
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">size</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Reshapes a vector into a tensor.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgec07f9d" class="outline-4">
|
|
|
|
|
<h4 id="orgec07f9d"><span class="section-number-4">1.4.3</span> Matrix -> Vector</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-4-3">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_vector</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_vector_of_matrix</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">matrix</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Reshapes a matrix into a vector.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgfaff3d8" class="outline-4">
|
|
|
|
|
<h4 id="orgfaff3d8"><span class="section-number-4">1.4.4</span> Matrix -> Tensor</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-4-4">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_tensor</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_tensor_of_matrix</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">matrix</span>,
|
2023-03-17 14:57:01 +01:00
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">order</span>,
|
2022-09-28 18:04:21 +02:00
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">size</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Reshapes a matrix into a tensor.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orge37a199" class="outline-4">
|
|
|
|
|
<h4 id="orge37a199"><span class="section-number-4">1.4.5</span> Tensor -> Vector</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-4-5">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_vector</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_vector_of_tensor</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">tensor</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Reshapes a tensor into a vector.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orged87f01" class="outline-4">
|
|
|
|
|
<h4 id="orged87f01"><span class="section-number-4">1.4.6</span> Tensor -> Matrix</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-4-6">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_matrix</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_matrix_of_tensor</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">tensor</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size1</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size2</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Reshapes a tensor into a vector.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orge60cec9" class="outline-3">
|
|
|
|
|
<h3 id="orge60cec9"><span class="section-number-3">1.5</span> Access macros</h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-1-5">
|
|
|
|
|
<p>
|
|
|
|
|
Macros are provided to ease the access to vectors, matrices and
|
|
|
|
|
tensors. Matrices use column-major ordering, as in Fortran.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_vec</span> (<span style="color: #228b22;">qmckl_vector</span> <span style="color: #a0522d;">v</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">i</span>); // <span style="color: #b22222;">v[i]</span>
|
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_mat</span> (<span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">m</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">i</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">j</span>) // <span style="color: #b22222;">m[j][i]</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_ten3</span>(<span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">t</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">i</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">j</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">k</span>); // <span style="color: #b22222;">t[k][j][i]</span>
|
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_ten4</span>(<span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">t</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">i</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">j</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">k</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">l</span>);
|
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_ten5</span>(<span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">t</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">i</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">j</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">k</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">l</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>);
|
2023-04-11 19:18:24 +02:00
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #0000ff;">qmckl_ten6</span>(<span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">t</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">i</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">j</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">k</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">l</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>, <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>);
|
2022-09-28 18:04:21 +02:00
|
|
|
...
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
For example:
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgad8fd14" class="outline-3">
|
|
|
|
|
<h3 id="orgad8fd14"><span class="section-number-3">1.6</span> Set all elements</h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-1-6">
|
|
|
|
|
</div>
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org8ce6bc5" class="outline-4">
|
|
|
|
|
<h4 id="org8ce6bc5"><span class="section-number-4">1.6.1</span> Vector</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-6-1">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_vector</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_vector_set</span>(<span style="color: #228b22;">qmckl_vector</span> <span style="color: #a0522d;">vector</span>, <span style="color: #228b22;">double</span> <span style="color: #a0522d;">value</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgf96f54e" class="outline-4">
|
|
|
|
|
<h4 id="orgf96f54e"><span class="section-number-4">1.6.2</span> Matrix</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-4" id="text-1-6-2">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_matrix</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_matrix_set</span>(<span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">matrix</span>, <span style="color: #228b22;">double</span> <span style="color: #a0522d;">value</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgc4c5a03" class="outline-4">
|
|
|
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|
<h4 id="orgc4c5a03"><span class="section-number-4">1.6.3</span> Tensor</h4>
|
2022-09-28 18:04:21 +02:00
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<div class="outline-text-4" id="text-1-6-3">
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_tensor</span>
|
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|
|
|
<span style="color: #0000ff;">qmckl_tensor_set</span>(<span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">tensor</span>, <span style="color: #228b22;">double</span> <span style="color: #a0522d;">value</span>);
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</pre>
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</div>
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</div>
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</div>
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</div>
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|
2023-09-13 16:23:56 +02:00
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<div id="outline-container-orgb3a225b" class="outline-3">
|
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|
<h3 id="orgb3a225b"><span class="section-number-3">1.7</span> Copy to/from to <code>double*</code></h3>
|
2022-09-28 18:04:21 +02:00
|
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|
<div class="outline-text-3" id="text-1-7">
|
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|
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
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|
<span style="color: #0000ff;">qmckl_double_of_vector</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
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|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_vector</span> <span style="color: #a0522d;">vector</span>,
|
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|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">target</span>,
|
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|
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|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size_max</span>);
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</pre>
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</div>
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<p>
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Converts a vector to a <code>double*</code>.
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</p>
|
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|
<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
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|
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|
<span style="color: #0000ff;">qmckl_double_of_matrix</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">matrix</span>,
|
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|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">target</span>,
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|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size_max</span>);
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</pre>
|
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|
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</div>
|
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<p>
|
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Converts a matrix to a <code>double*</code>.
|
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</p>
|
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|
<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
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|
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|
<span style="color: #0000ff;">qmckl_double_of_tensor</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
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|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_tensor</span> <span style="color: #a0522d;">tensor</span>,
|
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|
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|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">target</span>,
|
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|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size_max</span>);
|
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|
|
</pre>
|
|
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|
|
</div>
|
|
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|
|
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|
<p>
|
|
|
|
|
Converts a tensor to a <code>double*</code>.
|
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|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
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|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
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|
|
|
<span style="color: #0000ff;">qmckl_vector_of_double</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">target</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size_max</span>,
|
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|
|
|
<span style="color: #228b22;">qmckl_vector</span>* <span style="color: #a0522d;">vector</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
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|
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|
|
|
|
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|
<p>
|
|
|
|
|
Converts a <code>double*</code> to a vector.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_matrix_of_double</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">target</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size_max</span>,
|
|
|
|
|
<span style="color: #228b22;">qmckl_matrix</span>* <span style="color: #a0522d;">matrix</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Converts a <code>double*</code> to a matrix.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_tensor_of_double</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">target</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">size_max</span>,
|
|
|
|
|
<span style="color: #228b22;">qmckl_tensor</span>* <span style="color: #a0522d;">tensor</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Converts a <code>double*</code> to a tensor.
|
|
|
|
|
</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2023-03-17 14:57:01 +01:00
|
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|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgb150823" class="outline-3">
|
|
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|
|
<h3 id="orgb150823"><span class="section-number-3">1.8</span> Allocate and copy to <code>double*</code></h3>
|
2023-03-17 14:57:01 +01:00
|
|
|
<div class="outline-text-3" id="text-1-8">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span>* <span style="color: #0000ff;">qmckl_alloc_double_of_vector</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;">qmckl_vector</span> <span style="color: #a0522d;">vector</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span>* <span style="color: #0000ff;">qmckl_alloc_double_of_matrix</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;">qmckl_matrix</span> <span style="color: #a0522d;">matrix</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
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|
|
|
|
|
|
|
|
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|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span>* <span style="color: #0000ff;">qmckl_alloc_double_of_tensor</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;">qmckl_tensor</span> <span style="color: #a0522d;">tensor</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2022-09-28 18:04:21 +02:00
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orga9c6878" class="outline-2">
|
|
|
|
|
<h2 id="orga9c6878"><span class="section-number-2">2</span> Matrix operations</h2>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-2" id="text-2">
|
|
|
|
|
</div>
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org37d622b" class="outline-3">
|
|
|
|
|
<h3 id="org37d622b"><span class="section-number-3">2.1</span> <code>qmckl_dgemm</code></h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-2-1">
|
|
|
|
|
<p>
|
|
|
|
|
Matrix multiplication with a BLAS interface:
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
\[
|
|
|
|
|
C_{ij} = \beta C_{ij} + \alpha \sum_{k} A_{ik} \cdot B_{kj}
|
|
|
|
|
\]
|
|
|
|
|
</p>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<table id="org6e03ef8" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2022-09-28 18:04:21 +02:00
|
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<colgroup>
|
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|
<col class="org-left" />
|
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|
|
|
|
|
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|
<col class="org-left" />
|
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|
<col class="org-left" />
|
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|
<col class="org-left" />
|
|
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|
|
</colgroup>
|
|
|
|
|
<thead>
|
|
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|
|
<tr>
|
|
|
|
|
<th scope="col" class="org-left">Variable</th>
|
|
|
|
|
<th scope="col" class="org-left">Type</th>
|
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|
<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>
|
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|
</tr>
|
|
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|
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|
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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>
|
|
|
|
|
<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>TransB</code></td>
|
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|
|
|
<td class="org-left"><code>char</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<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>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<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>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Number of columns of the input matrix</td>
|
|
|
|
|
</tr>
|
|
|
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|
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|
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|
<tr>
|
|
|
|
|
<td class="org-left"><code>k</code></td>
|
|
|
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|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<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">α</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>
|
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|
|
|
</tr>
|
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<tr>
|
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|
<td class="org-left"><code>lda</code></td>
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|
<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>
|
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|
|
</tr>
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<tr>
|
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|
<td class="org-left"><code>B</code></td>
|
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|
|
<td class="org-left"><code>double[][ldb]</code></td>
|
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|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Array containing the matrix \(B\)</td>
|
|
|
|
|
</tr>
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<tr>
|
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|
<td class="org-left"><code>ldb</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>
|
|
|
|
|
<td class="org-left">Leading dimension of array <code>B</code></td>
|
|
|
|
|
</tr>
|
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|
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|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>beta</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">β</td>
|
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</tr>
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<tr>
|
|
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|
<td class="org-left"><code>C</code></td>
|
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|
|
|
<td class="org-left"><code>double[][ldc]</code></td>
|
|
|
|
|
<td class="org-left">out</td>
|
|
|
|
|
<td class="org-left">Array containing the matrix \(C\)</td>
|
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|
|
|
</tr>
|
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|
<tr>
|
|
|
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|
<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>
|
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|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
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|
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|
|
|
|
<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>
|
|
|
|
|
</div>
|
|
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|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org73f76d2" class="outline-3">
|
|
|
|
|
<h3 id="org73f76d2"><span class="section-number-3">2.2</span> <code>qmckl_dgemm_safe</code></h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-2-2">
|
|
|
|
|
<p>
|
|
|
|
|
"Size-safe" proxy function with the same functionality as <code>qmckl_dgemm</code>
|
|
|
|
|
but with 3 additional arguments. These arguments <code>size_max_M</code> (where <code>M</code> is a matix)
|
|
|
|
|
are required primarily for the Python API, where compatibility with
|
|
|
|
|
NumPy arrays implies that sizes of the input and output arrays are provided.
|
|
|
|
|
</p>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<table id="org2741fc4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2022-09-28 18:04:21 +02:00
|
|
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|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
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|
|
|
|
|
<col class="org-left" />
|
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|
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|
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|
<col class="org-left" />
|
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|
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|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<thead>
|
|
|
|
|
<tr>
|
|
|
|
|
<th scope="col" class="org-left">Variable</th>
|
|
|
|
|
<th scope="col" class="org-left">Type</th>
|
|
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|
|
<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">'T' is 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">'T' is 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 rows of the input matrix</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 columns of the input matrix</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>k</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Number of columns of the input matrix</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>alpha</code></td>
|
|
|
|
|
<td class="org-left"><code>double</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">α</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 matrix \(A\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>size_max_A</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Size of 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>size_max_B</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Size of 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">β</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 \(C\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>size_max_C</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Size of the 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>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>
|
|
|
|
|
<li><code>size_max_A >= m * k</code></li>
|
|
|
|
|
<li><code>size_max_B >= k * n</code></li>
|
|
|
|
|
<li><code>size_max_C >= m * n</code></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_safe</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;">size_max_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;">size_max_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;">size_max_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>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org0a14dd2" class="outline-3">
|
|
|
|
|
<h3 id="org0a14dd2"><span class="section-number-3">2.3</span> <code>qmckl_matmul</code></h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-2-3">
|
|
|
|
|
<p>
|
|
|
|
|
Matrix multiplication using the <code>qmckl_matrix</code> data type:
|
|
|
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</p>
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<p>
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\[
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|
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|
C_{ij} = \beta C_{ij} + \alpha \sum_{k} A_{ik} \cdot B_{kj}
|
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|
|
\]
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</p>
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2023-09-13 16:23:56 +02:00
|
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<table id="orgff22b92" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2022-09-28 18:04:21 +02:00
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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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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<tr>
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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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<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>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">α</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>qmckl_matrix</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Matrix \(A\)</td>
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</tr>
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<tr>
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<td class="org-left"><code>B</code></td>
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<td class="org-left"><code>qmckl_matrix</code></td>
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<td class="org-left">in</td>
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<td class="org-left">Matrix \(B\)</td>
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</tr>
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<tr>
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<td class="org-left"><code>beta</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">β</td>
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</tr>
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<tr>
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<td class="org-left"><code>C</code></td>
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<td class="org-left"><code>qmckl_matrix</code></td>
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<td class="org-left">out</td>
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<td class="org-left">Matrix \(C\)</td>
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</tr>
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</tbody>
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</table>
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_matmul</span> (
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">TransA</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">TransB</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">alpha</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">A</span>,
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|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">B</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">beta</span>,
|
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|
|
|
<span style="color: #228b22;">qmckl_matrix</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">C</span> );
|
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|
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|
</pre>
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</div>
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</div>
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</div>
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|
2023-09-13 16:23:56 +02:00
|
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|
<div id="outline-container-org921a737" class="outline-3">
|
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|
<h3 id="org921a737"><span class="section-number-3">2.4</span> <code>qmckl_adjugate</code></h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-2-4">
|
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|
<p>
|
|
|
|
|
Given a matrix \(\mathbf{A}\), the adjugate matrix
|
|
|
|
|
\(\text{adj}(\mathbf{A})\) is the transpose of the cofactors matrix
|
|
|
|
|
of \(\mathbf{A}\).
|
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|
|
</p>
|
|
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|
|
|
|
|
|
<p>
|
|
|
|
|
\[
|
|
|
|
|
\mathbf{B} = \text{adj}(\mathbf{A}) = \text{det}(\mathbf{A}) \, \mathbf{A}^{-1}
|
|
|
|
|
\]
|
|
|
|
|
</p>
|
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|
<p>
|
|
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|
See also: <a href="https://en.wikipedia.org/wiki/Adjugate_matrix">https://en.wikipedia.org/wiki/Adjugate_matrix</a>
|
|
|
|
|
</p>
|
|
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|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<table id="orgc5121a9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2022-09-28 18:04:21 +02:00
|
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<colgroup>
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|
<col class="org-left" />
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|
|
|
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|
<col class="org-left" />
|
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|
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|
|
|
|
|
<col class="org-left" />
|
|
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|
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|
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|
<col class="org-left" />
|
|
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|
|
</colgroup>
|
|
|
|
|
<thead>
|
|
|
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|
<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>
|
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|
<tr>
|
|
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|
|
<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>
|
|
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|
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|
|
|
|
<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>
|
|
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|
|
|
|
|
<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: #a020f0;">subroutine</span> <span style="color: #0000ff;">adjugate_general</span>(context, na, A, LDA, B, LDB, det_l)
|
|
|
|
|
<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,na)</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,na)</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;">double precision</span> ::<span style="color: #a0522d;"> work(LDA*max(na,64))</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> inf</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> ipiv(LDA)</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lwork</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span>(8) ::<span style="color: #a0522d;"> i, j</span>
|
|
|
|
|
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
We first copy the array <code>A</code> into array <code>B</code>.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-f90">B(1:na,1:na) = A(1:na,1:na)
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Then, we compute the LU factorization \(LU=A\)
|
|
|
|
|
using the <code>dgetrf</code> routine.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-f90"><span style="color: #a020f0;">call</span> <span style="color: #0000ff;">dgetrf</span>(na, na, B, LDB, ipiv, inf )
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
By convention, the determinant of \(L\) is equal to one, so the
|
|
|
|
|
determinant of \(A\) is equal to the determinant of \(U\), which is
|
|
|
|
|
simply computed as the product of its diagonal elements.
|
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|
|
|
</p>
|
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|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-f90">det_l = 1.d0
|
|
|
|
|
j=0_8
|
|
|
|
|
<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)
|
|
|
|
|
det_l = det_l*B(i,i)
|
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|
|
<span style="color: #a020f0;">enddo</span>
|
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|
|
|
</pre>
|
|
|
|
|
</div>
|
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|
|
|
<p>
|
|
|
|
|
As <code>dgetrf</code> returns \(PLU=A\) where \(P\) is a permutation matrix, the
|
|
|
|
|
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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<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_8) /= 0_8) <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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|
<p>
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|
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|
Then, the inverse of \(A\) is computed using <code>dgetri</code>:
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|
|
|
</p>
|
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|
<div class="org-src-container">
|
|
|
|
|
<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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|
<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">
|
|
|
|
|
<pre class="src src-f90"> B(:,:) = B(:,:)*det_l
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|
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|
|
|
|
<span style="color: #a020f0;">end subroutine</span> <span style="color: #0000ff;">adjugate_general</span>
|
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|
|
|
</pre>
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|
</div>
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|
</div>
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|
</div>
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|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org8eb8314" class="outline-3">
|
|
|
|
|
<h3 id="org8eb8314"><span class="section-number-3">2.5</span> <code>qmckl_adjugate_safe</code></h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-2-5">
|
|
|
|
|
<p>
|
|
|
|
|
"Size-safe" proxy function with the same functionality as <code>qmckl_adjugate</code>
|
|
|
|
|
but with 2 additional arguments. These arguments <code>size_max_M</code> (where <code>M</code> is a matix)
|
|
|
|
|
are required primarily for the Python API, where compatibility with
|
|
|
|
|
NumPy arrays implies that sizes of the input and output arrays are provided.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<table id="orgfbfee17" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2022-09-28 18:04:21 +02:00
|
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|
|
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|
|
<colgroup>
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|
|
|
<col class="org-left" />
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|
|
|
|
<col class="org-left" />
|
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|
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|
|
|
|
|
<col class="org-left" />
|
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|
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|
|
|
|
|
|
<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>
|
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|
|
|
<th scope="col" class="org-left">Description</th>
|
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|
|
|
</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>size_max_A</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Size of 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">out</td>
|
|
|
|
|
<td class="org-left">Adjugate of \(A\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>size_max_B</code></td>
|
|
|
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Size of 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>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>
|
|
|
|
|
<li><code>size_max_A >= m * m</code></li>
|
|
|
|
|
<li><code>size_max_B >= m * m</code></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_safe</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;">size_max_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;">size_max_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>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org206794f" class="outline-4">
|
|
|
|
|
<h4 id="org206794f"><span class="section-number-4">2.5.1</span> C interface</h4>
|
2022-09-28 18:04:21 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-orgdadeee4" class="outline-3">
|
|
|
|
|
<h3 id="orgdadeee4"><span class="section-number-3">2.6</span> <code>qmckl_transpose</code></h3>
|
2022-09-28 18:04:21 +02:00
|
|
|
<div class="outline-text-3" id="text-2-6">
|
|
|
|
|
<p>
|
|
|
|
|
Transposes a matrix: \(A^\dagger_{ji} = A_{ij}\).
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<table 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>A</code></td>
|
|
|
|
|
<td class="org-left"><code>qmckl_matrix</code></td>
|
|
|
|
|
<td class="org-left">in</td>
|
|
|
|
|
<td class="org-left">Input matrix</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>At</code></td>
|
|
|
|
|
<td class="org-left"><code>qmckl_matrix</code></td>
|
|
|
|
|
<td class="org-left">out</td>
|
|
|
|
|
<td class="org-left">Transposed matrix</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_transpose</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">A</span>,
|
|
|
|
|
<span style="color: #228b22;">qmckl_matrix</span> <span style="color: #a0522d;">At</span> );
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2023-06-14 09:14:10 +02:00
|
|
|
|
2023-09-13 16:23:56 +02:00
|
|
|
<div id="outline-container-org36156f3" class="outline-2">
|
|
|
|
|
<h2 id="org36156f3"><span class="section-number-2">3</span> Utilities</h2>
|
2023-06-14 09:14:10 +02:00
|
|
|
<div class="outline-text-2" id="text-3">
|
|
|
|
|
<p>
|
|
|
|
|
Trick to make MKL efficient on AMD
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
2023-06-14 11:47:13 +02:00
|
|
|
<pre class="src src-c"><span style="color: #228b22;">int</span> <span style="color: #0000ff;">mkl_serv_intel_cpu_true</span>() {
|
|
|
|
|
<span style="color: #a020f0;">return</span> 1;
|
|
|
|
|
}
|
|
|
|
|
|
2023-06-14 09:14:10 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2022-09-28 18:04:21 +02:00
|
|
|
</div>
|
|
|
|
|
<div id="postamble" class="status">
|
|
|
|
|
<p class="author">Author: TREX CoE</p>
|
2023-09-13 16:23:56 +02:00
|
|
|
<p class="date">Created: 2023-09-13 Wed 14:23</p>
|
2022-09-28 18:04:21 +02:00
|
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
|
|
|
</div>
|
|
|
|
|
</body>
|
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|
</html>
|
