CHAMP’s Jastrow factor computation using the IRPF90 method

Original equation:

$$ ∑i=2Ne ∑j=1^i ∑pkl ∑_aNn capkl\, rij^k\, ( Ria^l + Rja^l) ( Ria Rja)^m $$

Expanding, one obtains:

$$ ∑i=2Ne ∑j=1^i ∑pkl ∑_aNn capkl Riap-k-l\, rij^k\, Rjap-k+l + capkl Riap-k+l\, rij^k\, Rjap-k-l $$

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

$$ ∑i=1Ne ∑j=1Ne ∑pkl ∑_aNn capkl Riap-k-l\, rij^k\, Rjap-k+l $$

If we reshape $R_ja^p$ as a matrix $R_j,al$ of size $N_e × N_n(N_c+1)$, 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:

$$ ∑i=1Ne ∑pkl ∑_aNn capkl Riap-k-l\, Ci,a(p-k+l)^k $$

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