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693 lines
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HTML
693 lines
29 KiB
HTML
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@licstart The following is the entire license notice for the
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Copyright (C) 2012-2019 Free Software Foundation, Inc.
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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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without even the implied warranty of MERCHANTABILITY or FITNESS
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may distribute non-source (e.g., minimized or compacted) forms of
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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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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Examples</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org798a684">1. Accessing sparse quantities</a>
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<ul>
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<li><a href="#org961885c">1.1. Fortran</a>
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<ul>
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<li><a href="#orgb24f836">1.1.1. Declare Temporary variables</a></li>
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<li><a href="#org6486017">1.1.2. Obtain the name of the TREXIO file from the command line, and open it for reading</a></li>
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<li><a href="#orgb9dde8e">1.1.3. Read the nuclear repulsion energy</a></li>
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<li><a href="#org72d2425">1.1.4. Read the number of molecular orbitals</a></li>
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<li><a href="#org1df619b">1.1.5. Allocate memory</a></li>
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<li><a href="#orgb80e7df">1.1.6. Read one-electron quantities</a></li>
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<li><a href="#org5f84e8c">1.1.7. Read two-electron quantities</a>
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<ul>
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<li><a href="#org16fc4d8">1.1.7.1. Electron repulsion integrals</a></li>
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<li><a href="#org9baa607">1.1.7.2. Reduced density matrix</a></li>
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</ul>
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</li>
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<li><a href="#orgd752ae6">1.1.8. Compute the energy</a></li>
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<li><a href="#orgd7175b7">1.1.9. Terminate</a></li>
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</ul>
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</li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org798a684" class="outline-2">
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<h2 id="org798a684"><span class="section-number-2">1</span> Accessing sparse quantities</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org961885c" class="outline-3">
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<h3 id="org961885c"><span class="section-number-3">1.1</span> Fortran</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #a020f0;">program</span> <span style="color: #0000ff;">print_energy</span>
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<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">trexio</span>
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<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
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<span style="color: #228b22;">character</span>*(128) ::<span style="color: #a0522d;"> filename </span>! <span style="color: #b22222;">Name of the input file</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> rc </span>! <span style="color: #b22222;">Return code for error checking</span>
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<span style="color: #228b22;">integer</span>(8) ::<span style="color: #a0522d;"> f </span>! <span style="color: #b22222;">TREXIO file handle</span>
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<span style="color: #228b22;">character</span>*(128) ::<span style="color: #a0522d;"> err_msg </span>! <span style="color: #b22222;">Error message</span>
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</pre>
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</div>
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<p>
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This program computes the energy as:
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</p>
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<p>
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\[
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E = E_{\text{NN}} + \sum_{ij} D_{ij}\, \langle i | h | j \rangle\,
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+\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle i j | k l
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\rangle\; \textrm{ with } \; 0 < i,j,k,l \le n
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\]
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</p>
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<p>
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One needs to read from the TREXIO file:
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</p>
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<dl class="org-dl">
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<dt>\(n\)</dt><dd>The number of molecular orbitals</dd>
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<dt>\(E_{\text{NN}}\)</dt><dd>The nuclear repulsion energy</dd>
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<dt>\(D_{ij}\)</dt><dd>The one-body reduced density matrix</dd>
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<dt>\(\langle i |h| j \rangle\)</dt><dd>The one-electron Hamiltonian integrals</dd>
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<dt>\(\Gamma_{ijkl}\)</dt><dd>The two-body reduced density matrix</dd>
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<dt>\(\langle i j | k l \rangle\)</dt><dd>The electron repulsion integrals</dd>
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</dl>
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> E, E_nn</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> D(:,:), h0(:,:)</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> G(:,:,:,:), W(:,:,:,:)</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb24f836" class="outline-4">
|
|
<h4 id="orgb24f836"><span class="section-number-4">1.1.1</span> Declare Temporary variables</h4>
|
|
<div class="outline-text-4" id="text-1-1-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> i, j, k, l, m</span>
|
|
<span style="color: #228b22;">integer</span>(8), <span style="color: #a020f0;">parameter</span> ::<span style="color: #a0522d;"> BUFSIZE = 100000_8</span>
|
|
<span style="color: #228b22;">integer</span>(8) ::<span style="color: #a0522d;"> offset, icount, size_max</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> buffer_index(4,BUFSIZE)</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> buffer_values(BUFSIZE)</span>
|
|
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">external</span> ::<span style="color: #a0522d;"> ddot </span>! <span style="color: #b22222;">BLAS dot product</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6486017" class="outline-4">
|
|
<h4 id="org6486017"><span class="section-number-4">1.1.2</span> Obtain the name of the TREXIO file from the command line, and open it for reading</h4>
|
|
<div class="outline-text-4" id="text-1-1-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(1, filename)
|
|
|
|
f = trexio_open (filename, <span style="color: #8b2252;">'r'</span>, TREXIO_HDF5, rc)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error opening TREXIO file: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb9dde8e" class="outline-4">
|
|
<h4 id="orgb9dde8e"><span class="section-number-4">1.1.3</span> Read the nuclear repulsion energy</h4>
|
|
<div class="outline-text-4" id="text-1-1-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = trexio_read_nucleus_repulsion(f, E_nn)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading nuclear repulsion: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org72d2425" class="outline-4">
|
|
<h4 id="org72d2425"><span class="section-number-4">1.1.4</span> Read the number of molecular orbitals</h4>
|
|
<div class="outline-text-4" id="text-1-1-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = trexio_read_mo_num(f, n)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading number of MOs: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1df619b" class="outline-4">
|
|
<h4 id="org1df619b"><span class="section-number-4">1.1.5</span> Allocate memory</h4>
|
|
<div class="outline-text-4" id="text-1-1-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">allocate</span>( D(n,n), h0(n,n) )
|
|
<span style="color: #a020f0;">allocate</span>( G(n,n,n,n), W(n,n,n,n) )
|
|
G(:,:,:,:) = 0.d0
|
|
W(:,:,:,:) = 0.d0
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb80e7df" class="outline-4">
|
|
<h4 id="orgb80e7df"><span class="section-number-4">1.1.6</span> Read one-electron quantities</h4>
|
|
<div class="outline-text-4" id="text-1-1-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = trexio_has_mo_1e_int_core_hamiltonian(f)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">stop</span> <span style="color: #8b2252;">'No core hamiltonian in file'</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
rc = trexio_read_mo_1e_int_core_hamiltonian(f, h0)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading core Hamiltonian: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
|
rc = trexio_has_rdm_1e(f)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">stop</span> <span style="color: #8b2252;">'No 1e RDM in file'</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
rc = trexio_read_rdm_1e(f, D)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading one-body RDM: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5f84e8c" class="outline-4">
|
|
<h4 id="org5f84e8c"><span class="section-number-4">1.1.7</span> Read two-electron quantities</h4>
|
|
<div class="outline-text-4" id="text-1-1-7">
|
|
<p>
|
|
Reading is done with OpenMP. Each thread reads its own buffer, and
|
|
the buffers are then processed in parallel.
|
|
</p>
|
|
|
|
<p>
|
|
Reading the file requires a lock, so it is done in a critical
|
|
section. The <code>offset</code> variable is shared, and it is incremented in
|
|
the critical section. For each read, the function returns in
|
|
<code>icount</code> the number of read integrals, so this variable needs also
|
|
to be protected in the critical section when modified.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org16fc4d8" class="outline-5">
|
|
<h5 id="org16fc4d8"><span class="section-number-5">1.1.7.1</span> Electron repulsion integrals</h5>
|
|
<div class="outline-text-5" id="text-1-1-7-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = trexio_has_mo_2e_int_eri(f)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">stop</span> <span style="color: #8b2252;">'No electron repulsion integrals in file'</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
rc = trexio_read_mo_2e_int_eri_size (f, size_max)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading number of ERIs: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
offset = 0_8
|
|
!<span style="color: #b22222;">$OMP PARALLEL DEFAULT(SHARED) PRIVATE(icount, i, j, k, l, &</span>
|
|
!<span style="color: #b22222;">$OMP buffer_index, buffer_values, m)</span>
|
|
icount = BUFSIZE
|
|
<span style="color: #a020f0;">do while</span> (icount == BUFSIZE)
|
|
!<span style="color: #b22222;">$OMP CRITICAL</span>
|
|
<span style="color: #a020f0;">if</span> (offset < size_max) <span style="color: #a020f0;">then</span>
|
|
rc = trexio_read_mo_2e_int_eri(f, offset, icount, buffer_index, buffer_values)
|
|
offset = offset + icount
|
|
<span style="color: #a020f0;">else</span>
|
|
icount = 0
|
|
<span style="color: #a020f0;">end if</span>
|
|
!<span style="color: #b22222;">$OMP END CRITICAL</span>
|
|
<span style="color: #a020f0;">do</span> m=1,icount
|
|
i = buffer_index(1,m)
|
|
j = buffer_index(2,m)
|
|
k = buffer_index(3,m)
|
|
l = buffer_index(4,m)
|
|
W(i,j,k,l) = buffer_values(m)
|
|
W(k,j,i,l) = buffer_values(m)
|
|
W(i,l,k,j) = buffer_values(m)
|
|
W(k,l,i,j) = buffer_values(m)
|
|
W(j,i,l,k) = buffer_values(m)
|
|
W(j,k,l,i) = buffer_values(m)
|
|
W(l,i,j,k) = buffer_values(m)
|
|
W(l,k,j,i) = buffer_values(m)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
!<span style="color: #b22222;">$OMP END PARALLEL</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9baa607" class="outline-5">
|
|
<h5 id="org9baa607"><span class="section-number-5">1.1.7.2</span> Reduced density matrix</h5>
|
|
<div class="outline-text-5" id="text-1-1-7-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = trexio_has_rdm_2e(f)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">stop</span> <span style="color: #8b2252;">'No two-body density matrix in file'</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
rc = trexio_read_rdm_2e_size (f, size_max)
|
|
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading number of 2-RDM elements: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
offset = 0_8
|
|
!<span style="color: #b22222;">$OMP PARALLEL DEFAULT(SHARED) PRIVATE(icount, i, j, k, l, &</span>
|
|
!<span style="color: #b22222;">$OMP buffer_index, buffer_values, m)</span>
|
|
icount = bufsize
|
|
<span style="color: #a020f0;">do while</span> (offset < size_max)
|
|
!<span style="color: #b22222;">$OMP CRITICAL</span>
|
|
<span style="color: #a020f0;">if</span> (offset < size_max) <span style="color: #a020f0;">then</span>
|
|
rc = trexio_read_rdm_2e(f, offset, icount, buffer_index, buffer_values)
|
|
offset = offset + icount
|
|
<span style="color: #a020f0;">else</span>
|
|
icount = 0
|
|
<span style="color: #a020f0;">end if</span>
|
|
!<span style="color: #b22222;">$OMP END CRITICAL</span>
|
|
<span style="color: #a020f0;">do</span> m=1,icount
|
|
i = buffer_index(1,m)
|
|
j = buffer_index(2,m)
|
|
k = buffer_index(3,m)
|
|
l = buffer_index(4,m)
|
|
G(i,j,k,l) = buffer_values(m)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
!<span style="color: #b22222;">$OMP END PARALLEL</span>
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd752ae6" class="outline-4">
|
|
<h4 id="orgd752ae6"><span class="section-number-4">1.1.8</span> Compute the energy</h4>
|
|
<div class="outline-text-4" id="text-1-1-8">
|
|
<p>
|
|
As \((n,m)\) 2D arrays are stored in memory as \((\n times m)\) 1D
|
|
arrays, we could pass the matrices to the <code>ddot</code> BLAS function to
|
|
perform the summations in a single call for the 1-electron quantities.
|
|
Instead, we prefer to interleave the 1-electron (negative) and
|
|
2-electron (positive) summations to have a better cancellation of
|
|
numerical errors.
|
|
</p>
|
|
|
|
<p>
|
|
Here \(n^4\) can be larger than the largest possible 32-bit integer,
|
|
so it is not safe to pass \(n^4\) to the <code>ddot</code> BLAS
|
|
function. Hence, we perform \(n^2\) loops, using vectors of size \(n^2\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">
|
|
E = 0.d0
|
|
<span style="color: #a020f0;">do</span> l=1,n
|
|
E = E + ddot( n, D(1,l), 1, h0(1,l), 1 )
|
|
<span style="color: #a020f0;">do</span> k=1,n
|
|
E = E + 0.5d0 * ddot( n*n, G(1,1,k,l), 1, W(1,1,k,l), 1 )
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
E = E + E_nn
|
|
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Energy: '</span>, E
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd7175b7" class="outline-4">
|
|
<h4 id="orgd7175b7"><span class="section-number-4">1.1.9</span> Terminate</h4>
|
|
<div class="outline-text-4" id="text-1-1-9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"> <span style="color: #a020f0;">deallocate</span>( D, h0, G, W )
|
|
|
|
<span style="color: #a020f0;">end program</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: TREX-CoE</p>
|
|
<p class="date">Created: 2021-12-23 Thu 17:22</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|