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56 lines
1.2 KiB
Org Mode
56 lines
1.2 KiB
Org Mode
* IRPJAST
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CHAMP's Jastrow factor computation using the IRPF90 method
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Original equation:
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$$
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\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m
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$$
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Expanding, one obtains:
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$$
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\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l}
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$$
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The equation is symmetric if we exchange $i$ and $j$, so we can rewrite
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$$
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\sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l}
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$$
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If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size
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$N_e \times N_n(N_c+1)$,
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for every $k$, we can pre-compute the matrix product
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$$
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C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al}
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$$
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which can be computed efficiently with BLAS.
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We can express the total Jastrow as:
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$$
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\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
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c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
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$$
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* Running
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#+begin_src bash :var Ratio=5 Natoms=500
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python ./generateData.py -a $Natoms -r $Ratio
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#+end_src
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Cela genere les trois fichiers:
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geometry.txt
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elec_coords.txt
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jast_coeffs.txt
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#+begin_src bash :var Natoms=500
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./codelet_factor_een_blas $Natoms
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#+end_src
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