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1359 lines
63 KiB
HTML
1359 lines
63 KiB
HTML
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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">Code 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="#orgac014fe">1. Overlap matrix in the MO basis</a>
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<ul>
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<li><a href="#org6a9fe84">1.1. Python</a></li>
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<li><a href="#org5874187">1.2. C</a></li>
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<li><a href="#org95d497b">1.3. Fortran</a></li>
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</ul>
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</li>
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<li><a href="#orgfab8044">2. Fortran</a>
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<ul>
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<li><a href="#org4a8436e">2.1. Checking errors</a></li>
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<li><a href="#org6e86986">2.2. Computing an atomic orbital on a grid</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgac014fe" class="outline-2">
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<h2 id="orgac014fe"><span class="section-number-2">1</span> Overlap matrix in the MO basis</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The focal point of this example is the numerical evaluation of the overlap
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matrix in the MO basis. Utilizing QMCkl, we approximate the MOs at
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discrete grid points to compute the overlap matrix \( S_{ij} \) as follows:
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\[
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S_{ij} = \int \phi_i(\mathbf{r})\, \phi_j(\mathbf{r}) \text{d}\mathbf{r} \approx
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\sum_k \phi_i(\mathbf{r}_k)\, \phi_j(\mathbf{r}_k) \delta\mathbf{r}
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\]
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</p>
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<p>
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The code starts by reading a wave function from a TREXIO file. This is
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accomplished using the <code>qmckl_trexio_read</code> function, which populates a
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<code>qmckl_context</code> with the necessary wave function parameters. The context
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serves as the primary interface for interacting with the QMCkl library,
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encapsulating the state and configurations of the system.
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Subsequently, the code retrieves various attributes such as the number of
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nuclei <code>nucl_num</code> and coordinates <code>nucl_coord</code>.
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These attributes are essential for setting up the integration grid.
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</p>
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<p>
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The core of the example lies in the numerical computation of the overlap
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matrix. To achieve this, the code employs a regular grid in three-dimensional
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space, and the grid points are then populated into the <code>qmckl_context</code> using
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the <code>qmckl_set_point</code> function.
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</p>
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<p>
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The MO values at these grid points are computed using the
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<code>qmckl_get_mo_basis_mo_value</code> function. These values are then used to
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calculate the overlap matrix through a matrix multiplication operation
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facilitated by the <code>qmckl_dgemm</code> function.
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</p>
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<p>
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The code is also instrumented to measure the execution time for the MO
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value computation, providing an empirical assessment of the computational
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efficiency. Error handling is robustly implemented at each stage to ensure the
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reliability of the simulation.
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</p>
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<p>
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In summary, this example serves as a holistic guide for leveraging the QMCkl
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library, demonstrating its ease of use. It provides a concrete starting point
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for researchers and developers interested in integrating QMCkl into their QMC
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code.
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</p>
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</div>
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<div id="outline-container-org6a9fe84" class="outline-3">
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<h3 id="org6a9fe84"><span class="section-number-3">1.1</span> Python</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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In this example, we will compute numerically the overlap
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between the molecular orbitals:
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</p>
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<p>
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\[
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S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
|
|
\text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
|
|
\phi_j(\mathbf{r}_k) \delta \mathbf{r}
|
|
\]
|
|
\[
|
|
S_{ij} = \langle \phi_i | \phi_j \rangle
|
|
\sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
|
|
\langle \mathbf{r}_k | \phi_j \rangle
|
|
\]
|
|
</p>
|
|
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a020f0;">import</span> numpy <span style="color: #a020f0;">as</span> np
|
|
<span style="color: #a020f0;">import</span> qmckl
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
First, we create a context for the QMCkl calculation, and load the
|
|
wave function stored in <code>h2o_5z.h5</code> inside it. It is a Hartree-Fock
|
|
determinant for the water molecule in the cc-pV5Z basis set.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a0522d;">trexio_filename</span> = <span style="color: #8b2252;">"..//share/qmckl/test_data/h2o_5z.h5"</span>
|
|
|
|
<span style="color: #a0522d;">context</span> = qmckl.context_create()
|
|
qmckl.trexio_read(context, trexio_filename)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We now define the grid points \(\mathbf{r}_k\) as a regular grid around the
|
|
molecule.
|
|
</p>
|
|
|
|
<p>
|
|
We fetch the nuclear coordinates from the context,
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a0522d;">nucl_num</span> = qmckl.get_nucleus_num(context)
|
|
|
|
<span style="color: #a0522d;">nucl_charge</span> = qmckl.get_nucleus_charge(context, nucl_num)
|
|
|
|
<span style="color: #a0522d;">nucl_coord</span> = qmckl.get_nucleus_coord(context, <span style="color: #8b2252;">'N'</span>, nucl_num*3)
|
|
<span style="color: #a0522d;">nucl_coord</span> = np.reshape(nucl_coord, (3, nucl_num))
|
|
|
|
<span style="color: #a020f0;">for</span> i <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(nucl_num):
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"%d %+f %+f %+f"</span>%(<span style="color: #483d8b;">int</span>(nucl_charge[i]),
|
|
nucl_coord[i,0],
|
|
nucl_coord[i,1],
|
|
nucl_coord[i,2]) )
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
8 +0.000000 +0.000000 +0.000000
|
|
1 -1.430429 +0.000000 -1.107157
|
|
1 +1.430429 +0.000000 -1.107157
|
|
</pre>
|
|
|
|
<p>
|
|
and compute the coordinates of the grid points:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a0522d;">nx</span> = ( 120, 120, 120 )
|
|
<span style="color: #a0522d;">shift</span> = np.array([5.,5.,5.])
|
|
<span style="color: #a0522d;">point_num</span> = nx[0] * nx[1] * nx[2]
|
|
|
|
<span style="color: #a0522d;">rmin</span> = np.array( <span style="color: #483d8b;">list</span>([ np.<span style="color: #483d8b;">min</span>(nucl_coord[:,a]) <span style="color: #a020f0;">for</span> a <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]) )
|
|
<span style="color: #a0522d;">rmax</span> = np.array( <span style="color: #483d8b;">list</span>([ np.<span style="color: #483d8b;">max</span>(nucl_coord[:,a]) <span style="color: #a020f0;">for</span> a <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]) )
|
|
|
|
|
|
<span style="color: #a0522d;">linspace</span> = [ <span style="color: #008b8b;">None</span> <span style="color: #a020f0;">for</span> i <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]
|
|
<span style="color: #a0522d;">step</span> = [ <span style="color: #008b8b;">None</span> <span style="color: #a020f0;">for</span> i <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]
|
|
<span style="color: #a020f0;">for</span> a <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3):
|
|
linspace[a], <span style="color: #a0522d;">step</span>[a] = np.linspace(rmin[a]-shift[a],
|
|
rmax[a]+shift[a],
|
|
num=nx[a],
|
|
retstep=<span style="color: #008b8b;">True</span>)
|
|
|
|
<span style="color: #a0522d;">dr</span> = step[0] * step[1] * step[2]
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Now the grid is ready, we can create the list of grid points
|
|
\(\mathbf{r}_k\) on which the MOs \(\phi_i\) will be evaluated, and
|
|
transfer them to the QMCkl context:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a0522d;">point</span> = []
|
|
<span style="color: #a020f0;">for</span> x <span style="color: #a020f0;">in</span> linspace[0]:
|
|
<span style="color: #a020f0;">for</span> y <span style="color: #a020f0;">in</span> linspace[1]:
|
|
<span style="color: #a020f0;">for</span> z <span style="color: #a020f0;">in</span> linspace[2]:
|
|
<span style="color: #a0522d;">point</span> += [ [x, y, z] ]
|
|
|
|
<span style="color: #a0522d;">point</span> = np.array(point)
|
|
<span style="color: #a0522d;">point_num</span> = <span style="color: #483d8b;">len</span>(point)
|
|
qmckl.set_point(context, <span style="color: #8b2252;">'N'</span>, point_num, np.reshape(point, (point_num*3)))
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then, we evaluate all the MOs at the grid points (and time the execution),
|
|
and thus obtain the matrix \(M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle =
|
|
\phi_i(\mathbf{r}_k)\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a020f0;">import</span> time
|
|
|
|
<span style="color: #a0522d;">mo_num</span> = qmckl.get_mo_basis_mo_num(context)
|
|
|
|
<span style="color: #a0522d;">before</span> = time.time()
|
|
<span style="color: #a0522d;">mo_value</span> = qmckl.get_mo_basis_mo_value(context, point_num*mo_num)
|
|
<span style="color: #a0522d;">after</span> = time.time()
|
|
|
|
<span style="color: #a0522d;">mo_value</span> = np.reshape( mo_value, (point_num, mo_num) ).T # <span style="color: #b22222;">Transpose to get mo_num x point_num</span>
|
|
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"Number of MOs: "</span>, mo_num)
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"Number of grid points: "</span>, point_num)
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"Execution time : "</span>, (after - before), <span style="color: #8b2252;">"seconds"</span>)
|
|
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
Number of MOs: 201
|
|
Number of grid points: 1728000
|
|
Execution time : 5.577778577804565 seconds
|
|
</pre>
|
|
|
|
<p>
|
|
and finally we compute the overlap between all the MOs as
|
|
\(M.M^\dagger\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-python"><span style="color: #a0522d;">overlap</span> = mo_value @ mo_value.T * dr
|
|
<span style="color: #a020f0;">print</span> (overlap)
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
[[ 9.88693941e-01 2.34719693e-03 -1.50518232e-08 ... 3.12084178e-09
|
|
-5.81064929e-10 3.70130091e-02]
|
|
[ 2.34719693e-03 9.99509628e-01 3.18930040e-09 ... -2.46888958e-10
|
|
-1.06064273e-09 -7.65567973e-03]
|
|
[-1.50518232e-08 3.18930040e-09 9.99995073e-01 ... -5.84882580e-06
|
|
-1.21598117e-06 4.59036468e-08]
|
|
...
|
|
[ 3.12084178e-09 -2.46888958e-10 -5.84882580e-06 ... 1.00019107e+00
|
|
-2.03342837e-04 -1.36954855e-08]
|
|
[-5.81064929e-10 -1.06064273e-09 -1.21598117e-06 ... -2.03342837e-04
|
|
9.99262427e-01 1.18264754e-09]
|
|
[ 3.70130091e-02 -7.65567973e-03 4.59036468e-08 ... -1.36954855e-08
|
|
1.18264754e-09 8.97215950e-01]]
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5874187" class="outline-3">
|
|
<h3 id="org5874187"><span class="section-number-3">1.2</span> C</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
In this example, electron-nucleus cusp fitting is added.
|
|
</p>
|
|
|
|
<p>
|
|
In this example, we will compute numerically the overlap
|
|
between the molecular orbitals:
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
|
|
\text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
|
|
\phi_j(\mathbf{r}_k) \delta \mathbf{r}
|
|
\]
|
|
\[
|
|
S_{ij} = \langle \phi_i | \phi_j \rangle
|
|
\sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
|
|
\langle \mathbf{r}_k | \phi_j \rangle
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
We apply the cusp fitting procedure, so the MOs might deviate
|
|
slightly from orthonormality.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><qmckl.h></span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><stdio.h></span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><string.h></span>
|
|
<span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><sys/time.h></span>
|
|
|
|
<span style="color: #228b22;">int</span> <span style="color: #0000ff;">main</span>(<span style="color: #228b22;">int</span> <span style="color: #a0522d;">argc</span>, <span style="color: #228b22;">char</span>** <span style="color: #a0522d;">argv</span>)
|
|
{
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span>* <span style="color: #a0522d;">trexio_filename</span> = <span style="color: #8b2252;">"..//share/qmckl/test_data/h2o_5z.h5"</span>;
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #a0522d;">rc</span> = QMCKL_SUCCESS;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
First, we create a context for the QMCkl calculation, and load the
|
|
wave function stored in <code>h2o_5z.h5</code> inside it. It is a Hartree-Fock
|
|
determinant for the water molecule in the cc-pV5Z basis set.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span> = qmckl_context_create();
|
|
|
|
rc = qmckl_trexio_read(context, trexio_filename, strlen(trexio_filename));
|
|
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error reading TREXIO file:\n%s\n"</span>, qmckl_string_of_error(rc));
|
|
exit(1);
|
|
}
|
|
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We impose the electron-nucleus cusp fitting to occur when the
|
|
electrons are close to the nuclei. The critical distance
|
|
is 0.5 atomic units for hydrogens and 0.1 for the oxygen.
|
|
To identify which atom is an oxygen and which are hydrogens, we
|
|
fetch the nuclear charges from the context.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">nucl_num</span>;
|
|
|
|
rc = qmckl_get_nucleus_num(context, &nucl_num);
|
|
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error getting nucl_num:\n%s\n"</span>, qmckl_string_of_error(rc));
|
|
exit(1);
|
|
}
|
|
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">nucl_charge</span>[nucl_num];
|
|
|
|
rc = qmckl_get_nucleus_charge(context, &(nucl_charge[0]), nucl_num);
|
|
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error getting nucl_charge:\n%s\n"</span>, qmckl_string_of_error(rc));
|
|
exit(1);
|
|
}
|
|
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">r_cusp</span>[nucl_num];
|
|
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">i</span>=0 ; i<nucl_num ; ++i) {
|
|
|
|
<span style="color: #a020f0;">switch</span> ((<span style="color: #228b22;">int</span>) nucl_charge[i]) {
|
|
|
|
<span style="color: #a020f0;">case</span> 1:
|
|
r_cusp[i] = 0.5;
|
|
<span style="color: #a020f0;">break</span>;
|
|
|
|
<span style="color: #a020f0;">case</span> 8:
|
|
r_cusp[i] = 0.1;
|
|
<span style="color: #a020f0;">break</span>;
|
|
}
|
|
|
|
}
|
|
|
|
|
|
rc = qmckl_set_mo_basis_r_cusp(context, &(r_cusp[0]), nucl_num);
|
|
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error setting r_cusp:\n%s\n"</span>, qmckl_string_of_error(rc));
|
|
exit(1);
|
|
}
|
|
|
|
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<p>
|
|
We now define the grid points \(\mathbf{r}_k\) as a regular grid around the
|
|
molecule.
|
|
We fetch the nuclear coordinates from the context,
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span> <span style="color: #a0522d;">nucl_coord</span>[nucl_num][3];
|
|
|
|
rc = qmckl_get_nucleus_coord(context, <span style="color: #8b2252;">'N'</span>, &(nucl_coord[0][0]), nucl_num*3);
|
|
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error getting nucl_coord:\n%s\n"</span>, qmckl_string_of_error(rc));
|
|
exit(1);
|
|
}
|
|
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">i</span>=0 ; i<nucl_num ; ++i) {
|
|
printf(<span style="color: #8b2252;">"%d %+f %+f %+f\n"</span>,
|
|
(<span style="color: #228b22;">int32_t</span>) nucl_charge[i],
|
|
nucl_coord[i][0],
|
|
nucl_coord[i][1],
|
|
nucl_coord[i][2]);
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
8 +0.000000 +0.000000 +0.000000
|
|
1 -1.430429 +0.000000 -1.107157
|
|
1 +1.430429 +0.000000 -1.107157
|
|
</pre>
|
|
|
|
<p>
|
|
and compute the coordinates of the grid points:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">nx</span>[3] = { 120, 120, 120 };
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">shift</span>[3] = {5.,5.,5.};
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">point_num</span> = nx[0] * nx[1] * nx[2];
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">rmin</span>[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">rmax</span>[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
|
|
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">i</span>=0 ; i<nucl_num ; ++i) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">int</span> <span style="color: #a0522d;">j</span>=0 ; j<3 ; ++j) {
|
|
rmin[j] = nucl_coord[i][j] < rmin[j] ? nucl_coord[i][j] : rmin[j];
|
|
rmax[j] = nucl_coord[i][j] > rmax[j] ? nucl_coord[i][j] : rmax[j];
|
|
}
|
|
}
|
|
|
|
<span style="color: #228b22;">rmin</span>[0] -= shift[0]; <span style="color: #228b22;">rmin</span>[1] -= shift[1]; <span style="color: #228b22;">rmin</span>[2] -= shift[2];
|
|
<span style="color: #228b22;">rmax</span>[0] += shift[0]; <span style="color: #228b22;">rmax</span>[1] += shift[1]; <span style="color: #228b22;">rmax</span>[2] += shift[2];
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">step</span>[3];
|
|
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">linspace</span>[3];
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">int</span> <span style="color: #a0522d;">i</span>=0 ; i<3 ; ++i) {
|
|
|
|
linspace[i] = (<span style="color: #228b22;">double</span>*) calloc( <span style="color: #a020f0;">sizeof</span>(<span style="color: #228b22;">double</span>), nx[i] );
|
|
|
|
<span style="color: #a020f0;">if</span> (linspace[i] == <span style="color: #008b8b;">NULL</span>) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Allocation failed (linspace)\n"</span>);
|
|
exit(1);
|
|
}
|
|
|
|
step[i] = (rmax[i] - rmin[i]) / ((<span style="color: #228b22;">double</span>) (nx[i]-1));
|
|
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">j</span>=0 ; j<nx[i] ; ++j) {
|
|
linspace[i][j] = rmin[i] + j*step[i];
|
|
}
|
|
|
|
}
|
|
|
|
<span style="color: #228b22;">double</span> <span style="color: #a0522d;">dr</span> = step[0] * step[1] * step[2];
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Now the grid is ready, we can create the list of grid points
|
|
\(\mathbf{r}_k\) on which the MOs \(\phi_i\) will be evaluated, and
|
|
transfer them to the QMCkl context:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">double</span>* <span style="color: #a0522d;">point</span> = (<span style="color: #228b22;">double</span>*) calloc(<span style="color: #a020f0;">sizeof</span>(<span style="color: #228b22;">double</span>), 3*point_num);
|
|
|
|
<span style="color: #a020f0;">if</span> (point == <span style="color: #008b8b;">NULL</span>) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Allocation failed (point)\n"</span>);
|
|
exit(1);
|
|
}
|
|
|
|
<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">m</span> = 0;
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">i</span>=0 ; i<nx[0] ; ++i) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">j</span>=0 ; j<nx[1] ; ++j) {
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">k</span>=0 ; k<nx[2] ; ++k) {
|
|
|
|
point[m] = linspace[0][i];
|
|
m++;
|
|
|
|
point[m] = linspace[1][j];
|
|
m++;
|
|
|
|
point[m] = linspace[2][k];
|
|
m++;
|
|
|
|
}
|
|
}
|
|
}
|
|
|
|
rc = qmckl_set_point(context, <span style="color: #8b2252;">'N'</span>, point_num, point, (point_num*3));
|
|
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error setting points:\n%s\n"</span>, qmckl_string_of_error(rc));
|
|
exit(1);
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then, we evaluate all the MOs at the grid points (and time the execution),
|
|
and thus obtain the matrix \(M_{ki} = \langle \mathbf{r}_k | \phi_i
|
|
\rangle = \phi_i(\mathbf{r}_k)\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c">
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">mo_num</span>;
|
|
rc = qmckl_get_mo_basis_mo_num(context, &mo_num);
|
|
|
|
<span style="color: #228b22;">long</span> <span style="color: #a0522d;">before</span>, <span style="color: #a0522d;">after</span>;
|
|
<span style="color: #a020f0;">struct</span> <span style="color: #228b22;">timeval</span> <span style="color: #a0522d;">timecheck</span>;
|
|
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a0522d;">mo_value</span> = (<span style="color: #228b22;">double</span>*) calloc(<span style="color: #a020f0;">sizeof</span>(<span style="color: #228b22;">double</span>), point_num*mo_num);
|
|
<span style="color: #a020f0;">if</span> (mo_value == <span style="color: #008b8b;">NULL</span>) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Allocation failed (mo_value)\n"</span>);
|
|
exit(1);
|
|
}
|
|
|
|
gettimeofday(&timecheck, <span style="color: #008b8b;">NULL</span>);
|
|
before = (<span style="color: #228b22;">long</span>)timecheck.tv_sec * 1000 + (<span style="color: #228b22;">long</span>)timecheck.tv_usec / 1000;
|
|
|
|
rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num*mo_num);
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error getting mo_value)\n"</span>);
|
|
exit(1);
|
|
}
|
|
|
|
gettimeofday(&timecheck, <span style="color: #008b8b;">NULL</span>);
|
|
after = (<span style="color: #228b22;">long</span>)timecheck.tv_sec * 1000 + (<span style="color: #228b22;">long</span>)timecheck.tv_usec / 1000;
|
|
|
|
printf(<span style="color: #8b2252;">"Number of MOs: %ld\n"</span>, (<span style="color: #228b22;">long</span>) mo_num);
|
|
printf(<span style="color: #8b2252;">"Number of grid points: %ld\n"</span>, (<span style="color: #228b22;">long</span>) point_num);
|
|
printf(<span style="color: #8b2252;">"Execution time : %f seconds\n"</span>, (after - before)*1.e-3);
|
|
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
Number of MOs: 201
|
|
Number of grid points: 1728000
|
|
Execution time : 5.608000 seconds
|
|
</pre>
|
|
|
|
<p>
|
|
and finally we compute the overlap between all the MOs as
|
|
\(M.M^\dagger\).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">overlap</span> = (<span style="color: #228b22;">double</span>*) <span style="color: #0000ff;">malloc</span> (<span style="color: #228b22;">mo_num</span>*<span style="color: #0000ff;">mo_num</span>*<span style="color: #a020f0;">sizeof</span>(<span style="color: #228b22;">double</span>));
|
|
|
|
rc = qmckl_dgemm(context, <span style="color: #8b2252;">'N'</span>, <span style="color: #8b2252;">'T'</span>, mo_num, mo_num, point_num, dr,
|
|
mo_value, mo_num, mo_value, mo_num, 0.0,
|
|
overlap, mo_num);
|
|
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">i</span>=0 ; i<mo_num ; ++i) {
|
|
printf(<span style="color: #8b2252;">"%4ld"</span>, i);
|
|
<span style="color: #a020f0;">for</span> (<span style="color: #228b22;">size_t</span> <span style="color: #a0522d;">j</span>=0 ; j<mo_num ; ++j) {
|
|
printf(<span style="color: #8b2252;">" %f"</span>, overlap[i*mo_num+j]);
|
|
}
|
|
printf(<span style="color: #8b2252;">"\n"</span>);
|
|
}
|
|
|
|
// <span style="color: #b22222;">Clean-up and exit</span>
|
|
<span style="color: #0000ff;">free</span>(mo_value);
|
|
<span style="color: #0000ff;">free</span>(overlap);
|
|
|
|
rc = qmckl_context_destroy(context);
|
|
<span style="color: #a020f0;">if</span> (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, <span style="color: #8b2252;">"Error destroying context)\n"</span>);
|
|
exit(1);
|
|
}
|
|
|
|
<span style="color: #a020f0;">return</span> 0;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
0 0.988765 0.002336 0.000000 -0.000734 0.000000 0.000530 0.000000 0.000446 0.000000 -0.000000 -0.000511 -0.000000 -0.000267 0.000000 0.000000 0.001007 0.000000 0.000168 -0.000000 -0.000000 -0.000670 -0.000000 0.000000 -0.000251 -0.000261 -0.000000 -0.000000 -0.000000 -0.000397 -0.000000 -0.000810 0.000000 0.000231 -0.000000 -0.000000 0.000000 -0.000000
|
|
...
|
|
200 0.039017 -0.013066 -0.000000 -0.001935 -0.000000 -0.003829 -0.000000 0.000996 -0.000000 0.000000 -0.003733 0.000000 0.000065 -0.000000 -0.000000 -0.002220 -0.000000 -0.001961 0.000000 0.000000 -0.004182 0.000000 -0.000000 -0.000165 -0.002445 0.000000 -0.000000 0.000000 0.001985 0.000000 0.001685 -0.000000 -0.002899 0.000000 0.000000 0.000000 -0.000000 0.002591 0.000000 -0.000000 0.000000 0.002385 0.000000 -0.011086 0.000000 -0.003885 0.000000 -0.000000 0.003602 -0.000000 0.000000 -0.003241 0.000000 0.000000 0.002613 -0.007344 -0.000000 -0.000000 0.000000 0.000017 0.000000 0.000000 0.000000 -0.008719 0.000000 -0.001358 -0.003233 0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.003778 0.000000 0.000000 -0.000000 0.000000 0.000000 -0.001190 0.000000 0.000000 -0.000000 0.005578 -0.000000 -0.001502 0.003899 -0.000000 -0.000000 0.000000 -0.003291 -0.001775 -0.000000 -0.002374 0.000000 -0.000000 -0.000000 -0.000000 -0.001290 -0.000000 0.002178 0.000000 0.000000 0.000000 -0.001252 0.000000 -0.000000 -0.000926 0.000000 -0.000000 -0.013130 -0.000000 0.012124 0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.025194 0.000343 -0.000000 0.000000 -0.000000 -0.004421 0.000000 0.000000 -0.000599 -0.000000 0.005289 0.000000 -0.000000 0.012826 -0.000000 0.000000 0.006190 0.000000 0.000000 -0.000000 0.000000 -0.000321 0.000000 -0.000000 -0.000000 0.000000 -0.000000 0.001499 -0.006629 0.000000 0.000000 0.000000 -0.000000 0.008737 -0.000000 0.006880 0.000000 -0.001851 -0.000000 -0.000000 0.000000 -0.007464 0.000000 0.010298 -0.000000 -0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.000540 0.000000 -0.006616 -0.000000 0.000000 -0.002927 -0.000000 0.000000 0.010352 0.000000 -0.003103 -0.000000 -0.007640 -0.000000 -0.000000 0.005302 0.000000 0.000000 -0.000000 -0.000000 -0.010181 0.000000 -0.001108 0.000000 0.000000 -0.000000 0.000000 0.000000 -0.000998 -0.009754 0.013562 0.000000 -0.000000 0.887510
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org95d497b" class="outline-3">
|
|
<h3 id="org95d497b"><span class="section-number-3">1.3</span> Fortran</h3>
|
|
<div class="outline-text-3" id="text-1-3">
|
|
<p>
|
|
Here is the same piece of code translated in Fortran
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #483d8b;">#include</span> <span style="color: #8b2252;"><qmckl_f.F90></span>
|
|
|
|
<span style="color: #a020f0;">program</span> <span style="color: #0000ff;">main</span>
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">iso_c_binding</span>
|
|
<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: #b22222;">Declare variables</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> argc</span>
|
|
<span style="color: #228b22;">character</span>(128) ::<span style="color: #a0522d;"> trexio_filename, err_msg</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> rc</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_context) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> nucl_num, mo_num, point_num</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> nucl_coord(:,:)</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> nx(3)</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">dimension</span>(3) ::<span style="color: #a0522d;"> shift, step, rmin, rmax</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> mo_value(:,:), overlap(:,:), point(:), linspace(:,:)</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> before, after, dr</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j,k,m</span>
|
|
|
|
! <span style="color: #b22222;">Initialize variables</span>
|
|
err_msg = <span style="color: #8b2252;">' '</span>
|
|
argc = <span style="color: #a020f0;">command_argument_count</span>()
|
|
<span style="color: #a020f0;">if</span> (argc /= 1) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">"Usage: ./program <TREXIO filename>"</span>
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">get_command_argument</span>(1, trexio_filename)
|
|
rc = QMCKL_SUCCESS
|
|
|
|
! <span style="color: #b22222;">Create a QMCkl context</span>
|
|
context = qmckl_context_create()
|
|
|
|
! <span style="color: #b22222;">Read the TREXIO file into the context</span>
|
|
rc = qmckl_trexio_read(context, <span style="color: #a020f0;">trim</span>(trexio_filename), <span style="color: #a020f0;">len</span>(trexio_filename)*1_8)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error reading TREXIO file:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
! <span style="color: #b22222;">Retrieve the number of nuclei</span>
|
|
rc = qmckl_get_nucleus_num(context, nucl_num)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error getting nucl_num:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
! <span style="color: #b22222;">Retrieve the nuclear coordinates</span>
|
|
<span style="color: #a020f0;">allocate</span>(nucl_coord(3, nucl_num))
|
|
rc = qmckl_get_nucleus_coord(context, <span style="color: #8b2252;">'N'</span>, nucl_coord, nucl_num * 3_8)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error getting nucl_coord:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
! <span style="color: #b22222;">Retrieve the number of MOs</span>
|
|
rc = qmckl_get_mo_basis_mo_num(context, mo_num)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error getting mo_num:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
! <span style="color: #b22222;">Initialize grid points for the calculation</span>
|
|
nx = (/ 120, 120, 120 /)
|
|
shift = (/ 5.d0, 5.d0, 5.d0 /)
|
|
point_num = nx(1) * nx(2) * nx(3)
|
|
|
|
! <span style="color: #b22222;">Initialize rmin and rmax</span>
|
|
rmin = nucl_coord(:,1)
|
|
rmax = nucl_coord(:,1)
|
|
|
|
! <span style="color: #b22222;">Update rmin and rmax based on nucl_coord</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, 3
|
|
<span style="color: #a020f0;">do</span> j = 1, nucl_num
|
|
rmin(i) = <span style="color: #a020f0;">min</span>(nucl_coord(i,j), rmin(i))
|
|
rmax(i) = <span style="color: #a020f0;">max</span>(nucl_coord(i,j), rmax(i))
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Apply shift</span>
|
|
rmin = rmin - shift
|
|
rmax = rmax + shift
|
|
|
|
! <span style="color: #b22222;">Initialize linspace and step</span>
|
|
<span style="color: #a020f0;">allocate</span>(linspace(3, <span style="color: #a020f0;">maxval</span>(nx)))
|
|
|
|
<span style="color: #a020f0;">do</span> i = 1, 3
|
|
step(i) = (rmax(i) - rmin(i)) / <span style="color: #a020f0;">real</span>(nx(i) - 1, 8)
|
|
<span style="color: #a020f0;">do</span> j = 1, nx(i)
|
|
linspace(i, j) = rmin(i) + (j - 1) * step(i)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Initialize point array</span>
|
|
<span style="color: #a020f0;">allocate</span>(point(3 * point_num))
|
|
m = 1
|
|
<span style="color: #a020f0;">do</span> i = 1, nx(1)
|
|
<span style="color: #a020f0;">do</span> j = 1, nx(2)
|
|
<span style="color: #a020f0;">do</span> k = 1, nx(3)
|
|
point(m) = linspace(1, i); m = m + 1
|
|
point(m) = linspace(2, j); m = m + 1
|
|
point(m) = linspace(3, k); m = m + 1
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">deallocate</span>(linspace)
|
|
|
|
|
|
! <span style="color: #b22222;">Set points in QMCKL context</span>
|
|
rc = qmckl_set_point(context, <span style="color: #8b2252;">'N'</span>, point_num, point, point_num * 3)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error setting point:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
|
|
|
|
|
! <span style="color: #b22222;">Perform the actual calculation and measure the time taken</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">cpu_time</span>(before)
|
|
<span style="color: #a020f0;">allocate</span>(mo_value(point_num, mo_num))
|
|
rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num * mo_num)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error getting mo_value:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">cpu_time</span>(after)
|
|
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Number of MOs:"</span>, mo_num
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Number of grid points:"</span>, point_num
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Execution time:"</span>, (after - before), <span style="color: #8b2252;">"seconds"</span>
|
|
|
|
! <span style="color: #b22222;">Compute the overlap matrix</span>
|
|
dr = step(1) * step(2) * step(3)
|
|
|
|
<span style="color: #a020f0;">allocate</span>(overlap(mo_num, mo_num))
|
|
rc = qmckl_dgemm(context, <span style="color: #8b2252;">'N'</span>, <span style="color: #8b2252;">'T'</span>, mo_num, mo_num, point_num, dr, <span style="color: #a020f0;">&</span>
|
|
mo_value, mo_num, mo_value, mo_num, 0.d0, overlap, mo_num)
|
|
|
|
! <span style="color: #b22222;">Print the overlap matrix</span>
|
|
<span style="color: #a020f0;">do</span> i = 1, mo_num
|
|
<span style="color: #a020f0;">write</span>(*,<span style="color: #8b2252;">'(i4)'</span>, advance=<span style="color: #8b2252;">'no'</span>) i
|
|
<span style="color: #a020f0;">do</span> j = 1, mo_num
|
|
<span style="color: #a020f0;">write</span>(*,<span style="color: #8b2252;">'(f8.4)'</span>, advance=<span style="color: #8b2252;">'no'</span>) overlap(i, j)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">write</span>(*,*)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
! <span style="color: #b22222;">Clean-up and exit</span>
|
|
<span style="color: #a020f0;">deallocate</span>(mo_value, overlap)
|
|
rc = qmckl_context_destroy(context)
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, err_msg)
|
|
<span style="color: #a020f0;">write</span>(*,*) <span style="color: #8b2252;">"Error destroying context:"</span>, err_msg
|
|
<span style="color: #a020f0;">stop</span> -1
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
<span style="color: #a020f0;">end program</span> <span style="color: #0000ff;">main</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgfab8044" class="outline-2">
|
|
<h2 id="orgfab8044"><span class="section-number-2">2</span> Fortran</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
<div id="outline-container-org4a8436e" class="outline-3">
|
|
<h3 id="org4a8436e"><span class="section-number-3">2.1</span> Checking errors</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
All QMCkl functions return an error code. A convenient way to handle
|
|
errors is to write an error-checking function that displays the
|
|
error in text format and exits the program.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90" id="orgc3bcf40"><span style="color: #a020f0;">subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, message)
|
|
<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_exit_code), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> rc</span>
|
|
<span style="color: #228b22;">character</span>(len=*) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> message</span>
|
|
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> str_buffer</span>
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">print</span> *, message
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, str_buffer)
|
|
<span style="color: #a020f0;">print</span> *, str_buffer
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(rc)
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">end subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6e86986" class="outline-3">
|
|
<h3 id="org6e86986"><span class="section-number-3">2.2</span> Computing an atomic orbital on a grid</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
The following program, in Fortran, computes the values of an atomic
|
|
orbital on a regular 3-dimensional grid. The 100<sup>3</sup> grid points are
|
|
automatically defined, such that the molecule fits in a box with 5
|
|
atomic units in the borders.
|
|
</p>
|
|
|
|
<p>
|
|
This program uses the <code>qmckl_check_error</code> function defined above.
|
|
</p>
|
|
|
|
<p>
|
|
To use this program, run
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-bash">$ ao_grid <trexio_file> <AO_id> <point_num>
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, message)
|
|
<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_exit_code), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> rc</span>
|
|
<span style="color: #228b22;">character</span>(len=*) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> message</span>
|
|
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> str_buffer</span>
|
|
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">print</span> *, message
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, str_buffer)
|
|
<span style="color: #a020f0;">print</span> *, str_buffer
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(rc)
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">end subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>
|
|
|
|
<span style="color: #a020f0;">program</span> <span style="color: #0000ff;">ao_grid</span>
|
|
<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: #a0522d;"> qmckl_ctx </span>! <span style="color: #b22222;">QMCkl context</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> rc </span>! <span style="color: #b22222;">Exit code of QMCkl functions</span>
|
|
|
|
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> trexio_filename</span>
|
|
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> str_buffer</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> ao_id</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> point_num_x</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> nucl_num</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> nucl_coord(:,:)</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> point_num</span>
|
|
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> ao_num</span>
|
|
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> ipoint, i, j, k</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> x, y, z, dr(3)</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> rmin(3), rmax(3)</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> points(:,:)</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> ao_vgl(:,:,:)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Start by fetching the command-line arguments:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">if</span> (iargc() /= 3) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Syntax: ao_grid <trexio_file> <AO_id> <point_num>'</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(-1)
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(1, trexio_filename)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(2, str_buffer)
|
|
<span style="color: #a020f0;">read</span>(str_buffer, *) ao_id
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(3, str_buffer)
|
|
<span style="color: #a020f0;">read</span>(str_buffer, *) point_num_x
|
|
|
|
<span style="color: #a020f0;">if</span> (point_num_x < 0 <span style="color: #a020f0;">.or.</span> point_num_x > 300) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error: 0 < point_num < 300'</span>
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(-1)
|
|
<span style="color: #a020f0;">end if</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Create the QMCkl context and initialize it with the wave function
|
|
present in the TREXIO file:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">qmckl_ctx = qmckl_context_create()
|
|
rc = qmckl_trexio_read(qmckl_ctx, trexio_filename, 1_8*<span style="color: #a020f0;">len</span>(<span style="color: #a020f0;">trim</span>(trexio_filename)))
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Read TREXIO'</span>)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We need to check that <code>ao_id</code> is in the range, so we get the total
|
|
number of AOs from QMCkl:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = qmckl_get_ao_basis_ao_num(qmckl_ctx, ao_num)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Getting ao_num'</span>)
|
|
|
|
<span style="color: #a020f0;">if</span> (ao_id < 0 <span style="color: #a020f0;">.or.</span> ao_id > ao_num) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error: 0 < ao_id < '</span>, ao_num
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(-1)
|
|
<span style="color: #a020f0;">end if</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Now we will compute the limits of the box in which the molecule fits.
|
|
For that, we first need to ask QMCkl the coordinates of nuclei.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = qmckl_get_nucleus_num(qmckl_ctx, nucl_num)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Get nucleus num'</span>)
|
|
|
|
<span style="color: #a020f0;">allocate</span>( nucl_coord(3, nucl_num) )
|
|
rc = qmckl_get_nucleus_coord(qmckl_ctx, <span style="color: #8b2252;">'N'</span>, nucl_coord, 3_8*nucl_num)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Get nucleus coord'</span>)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We now compute the coordinates of opposite points of the box, and
|
|
the distance between points along the 3 directions:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rmin(1) = <span style="color: #a020f0;">minval</span>( nucl_coord(1,:) ) - 5.d0
|
|
rmin(2) = <span style="color: #a020f0;">minval</span>( nucl_coord(2,:) ) - 5.d0
|
|
rmin(3) = <span style="color: #a020f0;">minval</span>( nucl_coord(3,:) ) - 5.d0
|
|
|
|
rmax(1) = <span style="color: #a020f0;">maxval</span>( nucl_coord(1,:) ) + 5.d0
|
|
rmax(2) = <span style="color: #a020f0;">maxval</span>( nucl_coord(2,:) ) + 5.d0
|
|
rmax(3) = <span style="color: #a020f0;">maxval</span>( nucl_coord(3,:) ) + 5.d0
|
|
|
|
dr(1:3) = (rmax(1:3) - rmin(1:3)) / <span style="color: #a020f0;">dble</span>(point_num_x-1)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We now produce the list of point coordinates where the AO will be
|
|
evaluated:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">point_num = point_num_x**3
|
|
<span style="color: #a020f0;">allocate</span>( points(point_num, 3) )
|
|
ipoint=0
|
|
z = rmin(3)
|
|
<span style="color: #a020f0;">do</span> k=1,point_num_x
|
|
y = rmin(2)
|
|
<span style="color: #a020f0;">do</span> j=1,point_num_x
|
|
x = rmin(1)
|
|
<span style="color: #a020f0;">do</span> i=1,point_num_x
|
|
ipoint = ipoint+1
|
|
points(ipoint,1) = x
|
|
points(ipoint,2) = y
|
|
points(ipoint,3) = z
|
|
x = x + dr(1)
|
|
<span style="color: #a020f0;">end do</span>
|
|
y = y + dr(2)
|
|
<span style="color: #a020f0;">end do</span>
|
|
z = z + dr(3)
|
|
<span style="color: #a020f0;">end do</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We give the points to QMCkl:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90">rc = qmckl_set_point(qmckl_ctx, <span style="color: #8b2252;">'T'</span>, point_num, points, <span style="color: #a020f0;">size</span>(points)*1_8 )
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Setting points'</span>)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We allocate the space required to retrieve the values, gradients and
|
|
Laplacian of all AOs, and ask to retrieve the values of the
|
|
AOs computed at the point positions.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #a020f0;">allocate</span>( ao_vgl(ao_num, 5, point_num) )
|
|
rc = qmckl_get_ao_basis_ao_vgl(qmckl_ctx, ao_vgl, ao_num*5_8*point_num)
|
|
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Setting points'</span>)
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We finally print the value and Laplacian of the AO:
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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;">do</span> ipoint=1, point_num
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<span style="color: #a020f0;">print</span> <span style="color: #8b2252;">'(3(F10.6,X),2(E20.10,X))'</span>, points(ipoint, 1:3), ao_vgl(ao_id,1,ipoint), ao_vgl(ao_id,5,ipoint)
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<span style="color: #a020f0;">end do</span>
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-f90"> <span style="color: #a020f0;">deallocate</span>( nucl_coord, points, ao_vgl )
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<span style="color: #a020f0;">end program</span> <span style="color: #0000ff;">ao_grid</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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</div>
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<div id="postamble" class="status">
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<p class="author">Author: TREX CoE</p>
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<p class="date">Created: 2024-02-26 Mon 08:24</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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