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NLESC-JCER / Fortran_Davidson

Davidson eigensolver implemented in Fortran
Apache License 2.0
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Davidson free version can be speed-up in the calculation of the residues #33

Closed lopeztarifa closed 4 years ago

lopeztarifa commented 5 years ago

The calculation of the residues in the free version: https://github.com/NLESC-JCER/Fortran_Davidson/blob/1ad27484ab09d8ff9dc69f16be62abed27a218d7/src/davidson.f90#L388-L392

can be vectorised to avoid the callings to fun_mtx_gemv and fun_stx_gemv. The trick was inspired by Votca lines:

https://github.com/votca/xtp/blob/0b1252f2f0e18d22b2eeba8428afd59c87490425/include/votca/xtp/davidsonsolver.h#L118-L122

And consists in constructing a squere matrix with the eingevalues in the diagonal first, e.g.:

! 6. Construction of lambda matrix 
lambda= eye( size( V, 2), size( V, 2))
do j= 1, size(V,2) 
 lambda( j, j)= eigenvalues_sub( j)
enddo

then followed by the residue calculation: 

! 7. Residue calculation
rs = lapack_matmul('N', 'N', stxV, eigenvectors_sub)
guess =  lapack_matmul('N', 'N', rs, lambda)  
deallocate(rs)
rs =  lapack_matmul('N', 'N', mtxV, eigenvectors_sub) - guess 
do j=1,lowest
  errors(j) = norm(reshape(rs,(/parameters%nparm/)))
end do