LCCD correction Rodrigo - #218
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…ms, include test_biorthogonality
…els for a fixed spatial 'i'
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This Pull request introduces fixes applied relative to the original "first implementation":
A_mu_nu accumulator was being reset inside the 'for m in pspace' loop,
so only the last pspace determinant ever contributed. Fixed by
accumulating over m before applying the diagonal correction.
Parameters were enumerated over ALL ordered (i,j,a,b), even though
tau_(i,j,a,b) == tau_(j,i,b,a) (E_ai and E_bj commute). See the conditions
set in the paper. This produced exact duplicate rows/columns in A -> singular
matrix -> needed lstsq.
Fixed by enumerating only unique, unordered occ-virt pairs (P<Q).
The excluded pair-excitation case (i=j, a=b, t_ii^aa=0) was still
being created as a parameter with an all-zero row/column (since
_generate_sub_exops strips all its sub-excitations). This is now
automatically excluded by the P<Q parameterization.
Solve with np.linalg.solve instead of scipy.linalg.lstsq now that A
should be square and (generically) non-singular.
Energy formula: corrected to properly sum both index orderings of each unique amplitude (see note in compute_correction).