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<a accesskey="h" href=""> UP </a>
|
<a accesskey="H" href="index.html"> HOME </a>
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<h1 class="title">Examples</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
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<li><a href="#orgb52be26">1. Accessing sparse quantities</a>
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<ul>
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<li><a href="#org64925a5">1.1. Fortran</a>
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<ul>
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<li><a href="#orgafc7f4c">1.1.1. Declare Temporary variables</a></li>
<li><a href="#orge3620d4">1.1.2. Obtain the name of the TREXIO file from the command line, and open it for reading</a></li>
<li><a href="#orgf770b43">1.1.3. Read the nuclear repulsion energy</a></li>
<li><a href="#orga9abfd7">1.1.4. Read the number of molecular orbitals</a></li>
<li><a href="#orgf8f96eb">1.1.5. Allocate memory</a></li>
<li><a href="#org532fc04">1.1.6. Read one-electron quantities</a></li>
<li><a href="#org2620568">1.1.7. Read two-electron quantities</a>
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<ul>
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<li><a href="#orge3536c8">1.1.7.1. Electron repulsion integrals</a></li>
<li><a href="#orgdf25aec">1.1.7.2. Reduced density matrix</a></li>
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</ul>
</li>
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<li><a href="#org8977f5e">1.1.8. Compute the energy</a></li>
<li><a href="#org028f8ba">1.1.9. Terminate</a></li>
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</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
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<div id="outline-container-orgb52be26" class="outline-2">
<h2 id="orgb52be26"><span class="section-number-2">1</span> Accessing sparse quantities</h2>
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<div class="outline-text-2" id="text-1">
</div>
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<div id="outline-container-org64925a5" class="outline-3">
<h3 id="org64925a5"><span class="section-number-3">1.1</span> Fortran</h3>
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<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">program</span> <span style="color: #0000ff;">print_energy</span>
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">trexio</span>
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
<span style="color: #228b22;">character</span>*(128) ::<span style="color: #a0522d;"> filename </span>! <span style="color: #b22222;">Name of the input file</span>
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> rc </span>! <span style="color: #b22222;">Return code for error checking</span>
<span style="color: #228b22;">integer</span>(8) ::<span style="color: #a0522d;"> f </span>! <span style="color: #b22222;">TREXIO file handle</span>
<span style="color: #228b22;">character</span>*(128) ::<span style="color: #a0522d;"> err_msg </span>! <span style="color: #b22222;">Error message</span>
</pre>
</div>
<p>
This program computes the energy as:
</p>
<p>
\[
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E = E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle j | h | i \rangle\,
+\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle k l | i j
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\rangle\; \textrm{ with } \; 0 < i,j,k,l \le n
\]
One needs to read from the TREXIO file:
</p>
<dl class="org-dl">
<dt>\(n\)</dt><dd>The number of molecular orbitals</dd>
<dt>\(E_{\text{NN}}\)</dt><dd>The nuclear repulsion energy</dd>
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<dt>\(\gamma_{ij}\)</dt><dd>The one-body reduced density matrix</dd>
<dt>\(\langle j |h| i \rangle\)</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>\(\langle k l | i j \rangle\)</dt><dd>The electron repulsion integrals</dd>
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</dl>
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<div class="org-src-container">
<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>
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<div id="outline-container-orgafc7f4c" class="outline-4">
<h4 id="orgafc7f4c"><span class="section-number-4">1.1.1</span> Declare Temporary variables</h4>
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<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>
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<div id="outline-container-orge3620d4" class="outline-4">
<h4 id="orge3620d4"><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>
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<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>
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<div id="outline-container-orgf770b43" class="outline-4">
<h4 id="orgf770b43"><span class="section-number-4">1.1.3</span> Read the nuclear repulsion energy</h4>
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<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>
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<div id="outline-container-orga9abfd7" class="outline-4">
<h4 id="orga9abfd7"><span class="section-number-4">1.1.4</span> Read the number of molecular orbitals</h4>
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<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>
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<h4 id="orgf8f96eb"><span class="section-number-4">1.1.5</span> Allocate memory</h4>
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<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>
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<div id="outline-container-org532fc04" class="outline-4">
<h4 id="org532fc04"><span class="section-number-4">1.1.6</span> Read one-electron quantities</h4>
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<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>
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<div id="outline-container-org2620568" class="outline-4">
<h4 id="org2620568"><span class="section-number-4">1.1.7</span> Read two-electron quantities</h4>
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<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>
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<div id="outline-container-orge3536c8" class="outline-5">
<h5 id="orge3536c8"><span class="section-number-5">1.1.7.1</span> Electron repulsion integrals</h5>
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<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;">$OMP PARALLEL DEFAULT(SHARED) PRIVATE(icount, i, j, k, l, &amp;</span>
!<span style="color: #b22222;">$OMP buffer_index, buffer_values, m)</span>
icount = BUFSIZE
<span style="color: #a020f0;">do while</span> (icount == BUFSIZE)
!<span style="color: #b22222;">$OMP CRITICAL</span>
<span style="color: #a020f0;">if</span> (offset &lt; size_max) <span style="color: #a020f0;">then</span>
rc = trexio_read_mo_2e_int_eri(f, offset, icount, buffer_index, buffer_values)
offset = offset + icount
<span style="color: #a020f0;">else</span>
icount = 0
<span style="color: #a020f0;">end if</span>
!<span style="color: #b22222;">$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;">$OMP END PARALLEL</span>
</pre>
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<div id="outline-container-orgdf25aec" class="outline-5">
<h5 id="orgdf25aec"><span class="section-number-5">1.1.7.2</span> Reduced density matrix</h5>
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<div class="outline-text-5" id="text-1-1-7-2">
<div class="org-src-container">
<pre class="src src-f90">rc = trexio_has_rdm_2e(f)
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">stop</span> <span style="color: #8b2252;">'No two-body density matrix in file'</span>
<span style="color: #a020f0;">end if</span>
rc = trexio_read_rdm_2e_size (f, size_max)
<span style="color: #a020f0;">if</span> (rc /= TREXIO_SUCCESS) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">trexio_string_of_error</span>(rc, err_msg)
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error reading number of 2-RDM elements: '</span>//<span style="color: #a020f0;">trim</span>(err_msg)
<span style="color: #a020f0;">stop</span>
<span style="color: #a020f0;">end if</span>
offset = 0_8
!<span style="color: #b22222;">$OMP PARALLEL DEFAULT(SHARED) PRIVATE(icount, i, j, k, l, &amp;</span>
!<span style="color: #b22222;">$OMP buffer_index, buffer_values, m)</span>
icount = bufsize
<span style="color: #a020f0;">do while</span> (offset &lt; size_max)
!<span style="color: #b22222;">$OMP CRITICAL</span>
<span style="color: #a020f0;">if</span> (offset &lt; 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>
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<div id="outline-container-org8977f5e" class="outline-4">
<h4 id="org8977f5e"><span class="section-number-4">1.1.8</span> Compute the energy</h4>
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<div class="outline-text-4" id="text-1-1-8">
<p>
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When the orbitals are real, we can use
</p>
\begin{eqnarray*}
E &=& E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle j | h | i \rangle\,
+\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle k l | i j
\rangle \\
&=& E_{\text{NN}} + \sum_{ij} \gamma_{ij}\, \langle i | h | j \rangle\,
+\, \frac{1}{2} \sum_{ijkl} \Gamma_{ijkl}\, \langle i j | k l
\rangle \\
\end{eqnarray*}
<p>
As \((n,m)\) 2D arrays are stored in memory as \((n \times m)\) 1D
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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>
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<div id="outline-container-org028f8ba" class="outline-4">
<h4 id="org028f8ba"><span class="section-number-4">1.1.9</span> Terminate</h4>
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<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>
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<div id="postamble" class="status">
<p class="author">Author: TREX-CoE</p>
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<p class="date">Created: 2022-04-13 Wed 14:40</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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