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<title>Benchmarks — Quantum Package 2.0 documentation</title>
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<a href="../index.html" class="icon icon-home"> Quantum Package
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<div class="version">
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2.0
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<p class="caption"><span class="caption-text">Introduction</span></p>
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<p class="caption"><span class="caption-text">Appendix</span></p>
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<ul class="current">
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<li class="toctree-l1 current"><a class="current reference internal" href="#">Benchmarks</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="#convergence-of-the-energy">Convergence of the energy</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="#variational-energy">Variational energy</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#variational-energy-pt2-correction">Variational energy + PT2 correction</a></li>
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</ul>
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</li>
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<li class="toctree-l2"><a class="reference internal" href="#davidson-s-diagonalization">Davidson’s diagonalization</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="#olympe">Olympe</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#irene">Irene</a></li>
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</ul>
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</li>
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<li class="toctree-l2"><a class="reference internal" href="#pt2-correction">PT2 correction</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="#id1">Olympe</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#id2">Irene</a></li>
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</ul>
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</ul>
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</li>
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<li class="toctree-l1"><a class="reference internal" href="research.html">Some research made with the <em>Quantum Package</em></a></li>
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<li><a href="../index.html">Docs</a> »</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div itemprop="articleBody">
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<div class="section" id="benchmarks">
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<h1>Benchmarks<a class="headerlink" href="#benchmarks" title="Permalink to this headline">¶</a></h1>
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<p>The determinant selection, MR-PT2 and diagonalization are parallelized with
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distributed parallelism. Benchmarks for the [NH2-CH-NH2]+ molecule in the
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aug-cc-pVDZ basis set are presented with up to 50 nodes (1800 cores) on
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CALMIP’s <a class="reference external" href="https://www.calmip.univ-toulouse.fr/spip.php?article582&lang=fr">Olympe</a> supercomputer, and 200 nodes (9600 cores) on GENCI’s
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<a class="reference external" href="http://www-hpc.cea.fr/en/complexe/tgcc-Irene.htm">Irene</a> supercomputer. This represents an active space of 18 electrons
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in 111 MOs.</p>
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<ul class="simple">
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<li>Nodes of Olympe have two Skylake sockets, 2x18 cores @ 2.3GHz.</li>
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<li>Nodes of Irene have two Skylake sockets, 2x24 cores @ 2.7GHz.</li>
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</ul>
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<div class="section" id="convergence-of-the-energy">
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<h2>Convergence of the energy<a class="headerlink" href="#convergence-of-the-energy" title="Permalink to this headline">¶</a></h2>
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<div class="figure" id="id5">
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<img alt="Convergence of the energy." src="../_images/cn3_energy.png" />
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<p class="caption"><span class="caption-text">Convergence of the variational energy, with and without the PT2 correction.
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Both energies converge to the (frozen core) FCI energy.
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The plot is displayed for the ground state and for the 1st excited state.</span></p>
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</div>
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<div class="section" id="variational-energy">
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<h3>Variational energy<a class="headerlink" href="#variational-energy" title="Permalink to this headline">¶</a></h3>
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<table border="1" class="docutils">
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<colgroup>
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<thead valign="bottom">
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<tr class="row-odd"><th class="head">Number of dets</th>
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<th class="head">Ground state</th>
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<th class="head">Excited state</th>
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<th class="head">Excitation (eV)</th>
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</thead>
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<tbody valign="top">
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<tr class="row-even"><td>7</td>
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<td>-149.489 186</td>
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<td>-149.207 354</td>
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<td>7.67</td>
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</tr>
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<tr class="row-odd"><td>123</td>
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<td>-149.536 265</td>
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<td>-149.261 860</td>
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<td>7.47</td>
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</tr>
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<tr class="row-even"><td>3 083</td>
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<td>-149.685 606</td>
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<td>-149.404 450</td>
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<td>7.65</td>
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</tr>
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<tr class="row-odd"><td>29 409</td>
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<td>-149.826 151</td>
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<td>-149.547 275</td>
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<td>7.59</td>
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</tr>
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<tr class="row-even"><td>168 595</td>
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<td>-149.900 352</td>
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<td>-149.626 058</td>
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<td>7.46</td>
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</tr>
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<tr class="row-odd"><td>1 322 537</td>
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<td>-149.946 655</td>
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<td>-149.675 032</td>
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<td>7.39</td>
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</tr>
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<tr class="row-even"><td>8 495 334</td>
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<td>-149.972 032</td>
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<td>-149.704 145</td>
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<td>7.29</td>
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</tr>
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<tr class="row-odd"><td>9 356 952</td>
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<td>-149.973 375</td>
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<td>-149.706 822</td>
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<td>7.25</td>
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</tr>
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<tr class="row-even"><td>42 779 636</td>
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<td>-149.987 370</td>
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<td>-149.721 470</td>
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<td>7.24</td>
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</tr>
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<tr class="row-odd"><td>186 978 487</td>
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<td>-149.998 582</td>
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<td>-149.733 039</td>
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<td>7.23</td>
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</tr>
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</tbody>
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</table>
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</div>
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<div class="section" id="variational-energy-pt2-correction">
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<h3>Variational energy + PT2 correction<a class="headerlink" href="#variational-energy-pt2-correction" title="Permalink to this headline">¶</a></h3>
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<table border="1" class="docutils">
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<colgroup>
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<col width="25%" />
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<thead valign="bottom">
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<tr class="row-odd"><th class="head">Number of dets</th>
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<th class="head">Ground state</th>
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<th class="head">Excited state</th>
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<th class="head">Excitation (eV)</th>
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</tr>
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</thead>
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<tbody valign="top">
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<tr class="row-even"><td>7</td>
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<td>-150.161 107</td>
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<td>-149.904 883</td>
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<td>6.97</td>
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</tr>
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<tr class="row-odd"><td>123</td>
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<td>-150.116 958</td>
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<td>-149.849 465</td>
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<td>7.28</td>
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</tr>
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<tr class="row-even"><td>3 083</td>
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<td>-150.043 5(2)</td>
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<td>-149.780 8(2)</td>
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<td>7.15</td>
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</tr>
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<tr class="row-odd"><td>29 409</td>
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<td>-150.022 2(2)</td>
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<td>-149.758 3(2)</td>
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<td>7.18</td>
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</tr>
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<tr class="row-even"><td>168 595</td>
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|
<td>-150.019 9(1)</td>
|
|||
|
|
<td>-149.754 5(1)</td>
|
|||
|
|
<td>7.22</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>1 322 537</td>
|
|||
|
|
<td>-150.017 89(7)</td>
|
|||
|
|
<td>-149.752 55(7)</td>
|
|||
|
|
<td>7.22</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>8 495 334</td>
|
|||
|
|
<td>-150.015 97(4)</td>
|
|||
|
|
<td>-149.750 87(5)</td>
|
|||
|
|
<td>7.21</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>9 356 952</td>
|
|||
|
|
<td>-150.015 89(3)</td>
|
|||
|
|
<td>-149.750 66(3)</td>
|
|||
|
|
<td>7.22</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>42 959 496</td>
|
|||
|
|
<td>-150.016 75(2)</td>
|
|||
|
|
<td>-149.751 88(2)</td>
|
|||
|
|
<td>7.21</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>186 978 487</td>
|
|||
|
|
<td>-150.017 51(2)</td>
|
|||
|
|
<td>-149.752 90(2)</td>
|
|||
|
|
<td>7.20</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<div class="section" id="davidson-s-diagonalization">
|
|||
|
|
<h2>Davidson’s diagonalization<a class="headerlink" href="#davidson-s-diagonalization" title="Permalink to this headline">¶</a></h2>
|
|||
|
|
<p>We present the parallel speedup curve, and the wall-clock time in seconds
|
|||
|
|
required to compute one iteration for two wave functions measured on Olympe
|
|||
|
|
and Irene.</p>
|
|||
|
|
<div class="figure" id="id6">
|
|||
|
|
<img alt="Parallel speedup of Davidson's diagonalization." src="../_images/speedup_davidson.png" />
|
|||
|
|
<p class="caption"><span class="caption-text">Parallel speedup of Davidson’s diagonalization measured on Olympe and Irene.</span></p>
|
|||
|
|
</div>
|
|||
|
|
<div class="section" id="olympe">
|
|||
|
|
<h3>Olympe<a class="headerlink" href="#olympe" title="Permalink to this headline">¶</a></h3>
|
|||
|
|
<table border="1" class="docutils">
|
|||
|
|
<colgroup>
|
|||
|
|
<col width="34%" />
|
|||
|
|
<col width="32%" />
|
|||
|
|
<col width="34%" />
|
|||
|
|
</colgroup>
|
|||
|
|
<thead valign="bottom">
|
|||
|
|
<tr class="row-odd"><th class="head">Number of 36-core Nodes</th>
|
|||
|
|
<th class="head">9 356 952 determinants</th>
|
|||
|
|
<th class="head">42 959 496 determinants</th>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody valign="top">
|
|||
|
|
<tr class="row-even"><td>1</td>
|
|||
|
|
<td>775.55</td>
|
|||
|
|
<td>11 198.70</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>5</td>
|
|||
|
|
<td>169.88</td>
|
|||
|
|
<td>2 288.58</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>10</td>
|
|||
|
|
<td>93.22</td>
|
|||
|
|
<td>1 213.95</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>20</td>
|
|||
|
|
<td>56.86</td>
|
|||
|
|
<td>626.41</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>30</td>
|
|||
|
|
<td>43.76</td>
|
|||
|
|
<td>445.65</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>40</td>
|
|||
|
|
<td>36.18</td>
|
|||
|
|
<td>350.25</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>50</td>
|
|||
|
|
<td>33.67</td>
|
|||
|
|
<td>295.25</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
<div class="section" id="irene">
|
|||
|
|
<h3>Irene<a class="headerlink" href="#irene" title="Permalink to this headline">¶</a></h3>
|
|||
|
|
<table border="1" class="docutils">
|
|||
|
|
<colgroup>
|
|||
|
|
<col width="34%" />
|
|||
|
|
<col width="32%" />
|
|||
|
|
<col width="34%" />
|
|||
|
|
</colgroup>
|
|||
|
|
<thead valign="bottom">
|
|||
|
|
<tr class="row-odd"><th class="head">Number of 48-core Nodes</th>
|
|||
|
|
<th class="head">9 356 952 determinants</th>
|
|||
|
|
<th class="head">42 959 496 determinants</th>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody valign="top">
|
|||
|
|
<tr class="row-even"><td>1</td>
|
|||
|
|
<td>572.98</td>
|
|||
|
|
<td>9 154.30 *</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>10</td>
|
|||
|
|
<td>72.55</td>
|
|||
|
|
<td>922.07</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>25</td>
|
|||
|
|
<td>38.88</td>
|
|||
|
|
<td>412.34</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>50</td>
|
|||
|
|
<td>27.95</td>
|
|||
|
|
<td>241.35</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>75</td>
|
|||
|
|
<td>27.54</td>
|
|||
|
|
<td>183.63</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>100</td>
|
|||
|
|
<td>27.86</td>
|
|||
|
|
<td>165.68</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>150</td>
|
|||
|
|
<td>28.14</td>
|
|||
|
|
<td>134.05</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>200</td>
|
|||
|
|
<td>27.77</td>
|
|||
|
|
<td>134.64</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<div class="section" id="pt2-correction">
|
|||
|
|
<h2>PT2 correction<a class="headerlink" href="#pt2-correction" title="Permalink to this headline">¶</a></h2>
|
|||
|
|
<p>We present the parallel speedup curve, and the wall-clock time in seconds
|
|||
|
|
required to compute the PT2 correction for two wave functions measured on
|
|||
|
|
Olympe and Irene.</p>
|
|||
|
|
<div class="figure" id="id7">
|
|||
|
|
<img alt="Parallel speedup of the PT2 computation of the ground state." src="../_images/speedup_pt2.png" />
|
|||
|
|
<p class="caption"><span class="caption-text">Parallel speedup of the PT2 computation of the ground state measured
|
|||
|
|
on Olympe and Irene.</span></p>
|
|||
|
|
</div>
|
|||
|
|
<div class="section" id="id1">
|
|||
|
|
<h3>Olympe<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3>
|
|||
|
|
<table border="1" class="docutils">
|
|||
|
|
<colgroup>
|
|||
|
|
<col width="34%" />
|
|||
|
|
<col width="32%" />
|
|||
|
|
<col width="34%" />
|
|||
|
|
</colgroup>
|
|||
|
|
<thead valign="bottom">
|
|||
|
|
<tr class="row-odd"><th class="head">Number of 36-core Nodes</th>
|
|||
|
|
<th class="head">Ground state (9.3M)</th>
|
|||
|
|
<th class="head">Excited state (9.3M)</th>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody valign="top">
|
|||
|
|
<tr class="row-even"><td>1</td>
|
|||
|
|
<td>7 883.74</td>
|
|||
|
|
<td>9 829.19</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>5</td>
|
|||
|
|
<td>1 629.06</td>
|
|||
|
|
<td>2 022.36</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>10</td>
|
|||
|
|
<td>832.89</td>
|
|||
|
|
<td>1 029.91</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>20</td>
|
|||
|
|
<td>440.76</td>
|
|||
|
|
<td>537.37</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>30</td>
|
|||
|
|
<td>303.31</td>
|
|||
|
|
<td>378.69</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>40</td>
|
|||
|
|
<td>246.12</td>
|
|||
|
|
<td>296.31</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>50</td>
|
|||
|
|
<td>201.84</td>
|
|||
|
|
<td>241.55</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
<div class="section" id="id2">
|
|||
|
|
<h3>Irene<a class="headerlink" href="#id2" title="Permalink to this headline">¶</a></h3>
|
|||
|
|
<table border="1" class="docutils">
|
|||
|
|
<colgroup>
|
|||
|
|
<col width="20%" />
|
|||
|
|
<col width="19%" />
|
|||
|
|
<col width="20%" />
|
|||
|
|
<col width="19%" />
|
|||
|
|
<col width="20%" />
|
|||
|
|
</colgroup>
|
|||
|
|
<thead valign="bottom">
|
|||
|
|
<tr class="row-odd"><th class="head">Number of 48-core Nodes</th>
|
|||
|
|
<th class="head">Ground state (9.3M)</th>
|
|||
|
|
<th class="head">Excited state (9.3M)</th>
|
|||
|
|
<th class="head">Ground state (42.9M)</th>
|
|||
|
|
<th class="head">Excited state (42.9M)</th>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody valign="top">
|
|||
|
|
<tr class="row-even"><td>1</td>
|
|||
|
|
<td>4 935.81</td>
|
|||
|
|
<td>6 152.29</td>
|
|||
|
|
<td>24 586.62</td>
|
|||
|
|
<td>37 440.59</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>10</td>
|
|||
|
|
<td>525.95</td>
|
|||
|
|
<td>652.23</td>
|
|||
|
|
<td>2 458.66</td>
|
|||
|
|
<td>3 086.19</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>25</td>
|
|||
|
|
<td>237.47</td>
|
|||
|
|
<td>286.06</td>
|
|||
|
|
<td>1 041.69</td>
|
|||
|
|
<td>1 295.43</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>50</td>
|
|||
|
|
<td>144.39</td>
|
|||
|
|
<td>174.12</td>
|
|||
|
|
<td>588.35</td>
|
|||
|
|
<td>724.25</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>75</td>
|
|||
|
|
<td>109.13</td>
|
|||
|
|
<td>129.17</td>
|
|||
|
|
<td>446.74</td>
|
|||
|
|
<td>537.59</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>100</td>
|
|||
|
|
<td>100.75</td>
|
|||
|
|
<td>103.43</td>
|
|||
|
|
<td>367.21</td>
|
|||
|
|
<td>450.32</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td>150</td>
|
|||
|
|
<td>82.04</td>
|
|||
|
|
<td>91.77</td>
|
|||
|
|
<td>298.63</td>
|
|||
|
|
<td>358.25</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td>200</td>
|
|||
|
|
<td>75.62</td>
|
|||
|
|
<td>85.25</td>
|
|||
|
|
<td>268.96</td>
|
|||
|
|
<td>312.23</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
|
|||
|
|
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|
|||
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|
|||
|
|
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|||
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|||
|
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<a href="research.html" class="btn btn-neutral float-right" title="Some research made with the Quantum Package" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right"></span></a>
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|||
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|||
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|||
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<a href="../programmers_guide/conventions.html" class="btn btn-neutral" title="Coding conventions" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left"></span> Previous</a>
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|||
|
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<hr/>
|
|||
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|
|||
|
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<div role="contentinfo">
|
|||
|
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<p>
|
|||
|
|
© Copyright 2018, A. Scemama, E. Giner
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