IRPJAST

CHAMP’s Jastrow factor computation using the IRPF90 method

Original equation:

$$\sum i=2Ne\sum j=1^i\sum pkl{\sum }_{a}Nncapklri{j}^k(Ri{a}^l+Rj{a}^l)(RiaRja{)}^m$$

Expanding, one obtains:

$$\sum i=2Ne\sum j=1^i\sum pkl{\sum }_{a}NncapklRiap-k-lri{j}^{k}Rjap-k+l+capklRiap-k+lri{j}^{k}Rjap-k-l$$

The equation is symmetric if we exchange $i$ and $j$, so we can rewrite

$$\sum i=1Ne\sum j=1Ne\sum pkl{\sum }_{a}NncapklRiap-k-lri{j}^{k}Rjap-k+l$$

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

$$ C_i,al^k = ∑_j r_ij^k\, R_i,al $$ which can be computed efficiently with BLAS. We can express the total Jastrow as:

$$\sum i=1Ne\sum pkl{\sum }_{a}NncapklRiap-k-lCi,a(p-k+l{)}^k$$

Running

python ./generateData.py -a $Natoms -r $Ratio

Cela genere les trois fichiers: geometry.txt elec_coords.txt jast_coeffs.txt

./codelet_factor_een_blas $Natoms