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mirror of https://github.com/TREX-CoE/irpjast.git synced 2024-11-03 20:54:10 +01:00
This commit is contained in:
Anthony Scemama 2021-01-19 16:22:12 +01:00
parent 7b9db3808b
commit c1a4638886
4 changed files with 25 additions and 24 deletions

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IRPF90 = irpf90 --codelet=factor_een:100000 #-a -d
IRPF90 = irpf90 -s nelec:10 -s nnuc:2 -s ncord:5 #-a -d
FC = ifort -xHost -g -mkl=sequential
FCFLAGS= -O2 -ffree-line-length-none -I .
NINJA = ninja

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Original equation:
$$
\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m
$$
$$
\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m
$$
Expanding, one obtains:
Expanding, one obtains:
$$
\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l}
$$
$$
\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l}
$$
The equation is symmetric if we exchange $i$ and $j$, so we can rewrite
The equation is symmetric if we exchange $i$ and $j$, so we can rewrite
$$
\sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l}
$$
$$
\sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l}
$$
If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size
$N_e \times N_n(N_c+1)$,
for every $k$, we can pre-compute the matrix product
If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size
$N_e \times N_n(N_c+1)$,
for every $k$, we can pre-compute the matrix product
$$
C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al}
$$
which can be computed efficiently with BLAS.
We can express the total Jastrow as:
$$
C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al}
$$
which can be computed efficiently with BLAS.
We can express the total Jastrow as:
$$
\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
$$
$$
\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
$$

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