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https://github.com/LCPQ/quantum_package
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Davidson multistates works in a very standard version
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@ -30,7 +30,5 @@ Documentation
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Calls H_apply on the HF determinant and selects all connected single and double
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excitations (of the same symmetry).
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`cisd <http://github.com/LCPQ/quantum_package/tree/master/src/CISD/cisd.irp.f#L1>`_
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None
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@ -1,19 +1,18 @@
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program cisd
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implicit none
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integer :: i
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double precision, allocatable :: eigvalues(:),eigvectors(:,:)
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call H_apply_cisd
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double precision, allocatable :: eigvalues(:),eigvectors(:,:)
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allocate(eigvalues(n_det),eigvectors(n_det,n_det))
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print *, 'N_det = ', N_det
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call lapack_diag(eigvalues,eigvectors,H_matrix_all_dets,n_det,n_det)
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psi_coef = psi_coef - 1.d-4
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call davidson_diag(psi_det,psi_coef,eigvalues,size(psi_coef,1),N_det,N_states,N_int)
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! print *, H_matrix_all_dets
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print *, '---'
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print *, 'HF:', HF_energy
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print *, '---'
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do i = 1,3
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do i = 1,1
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print *, 'energy(i) = ',eigvalues(i) + nuclear_repulsion
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enddo
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! print *, eigvectors(:,1)
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deallocate(eigvalues,eigvectors)
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end
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259
src/DensityMatrix/density_matrix.irp.f
Normal file
259
src/DensityMatrix/density_matrix.irp.f
Normal file
@ -0,0 +1,259 @@
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use bitmasks
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BEGIN_PROVIDER [ integer, iunit_two_body_dm_aa ]
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&BEGIN_PROVIDER [ integer, iunit_two_body_dm_ab ]
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&BEGIN_PROVIDER [ integer, iunit_two_body_dm_bb ]
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implicit none
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use bitmasks
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BEGIN_DOC
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! Temporary files for 2-body dm calculation
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END_DOC
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integer :: getUnitAndOpen
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iunit_two_body_dm_aa = getUnitAndOpen(trim(ezfio_filename)//'/work/two_body_aa.tmp','w')
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iunit_two_body_dm_ab = getUnitAndOpen(trim(ezfio_filename)//'/work/two_body_ab.tmp','w')
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iunit_two_body_dm_bb = getUnitAndOpen(trim(ezfio_filename)//'/work/two_body_bb.tmp','w')
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! Compute two body DM in file
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integer :: k,l,degree, idx,i
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integer :: exc(0:2,2,2),n_occ_alpha
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double precision :: phase, coef
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integer :: h1,h2,p1,p2,s1,s2
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double precision :: ck, cl
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character*(128), parameter :: f = '(i8,4(x,i5),x,d16.8)'
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do k=1,det_num
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ck = (det_coef_provider(k)+det_coef_provider(k))
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do l=1,k-1
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cl = det_coef_provider(l)
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call get_excitation_degree(det_provider(1,1,k),det_provider(1,1,l),degree,N_int)
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if (degree == 2) then
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call get_double_excitation(det_provider(1,1,k),det_provider(1,1,l),exc,phase,N_int)
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call decode_exc(exc,degree,h1,p1,h2,p2,s1,s2)
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call bielec_integrals_index(h1,h2,p1,p2,idx)
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ckl = phase*ck*cl
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select case (s1+s2)
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case(2) ! alpha alpha
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write(iunit_two_body_dm_aa,f) idx, h1,h2,p1,p2, ckl
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call bielec_integrals_index(h1,h2,p2,p1,idx)
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write(iunit_two_body_dm_aa,f) idx, h1,h2,p2,p1, -ckl
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case(3) ! alpha beta
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write(iunit_two_body_dm_ab,f) idx, h1,h2,p1,p2, ckl
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case(4) ! beta beta
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write(iunit_two_body_dm_bb,f) idx, h1,h2,p1,p2, ckl
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call bielec_integrals_index(h1,h2,p2,p1,idx)
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write(iunit_two_body_dm_bb,f) idx, h1,h2,p2,p1, -ckl
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end select
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else if (degree == 1) then
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call get_mono_excitation(det_provider(1,1,k),det_provider(1,1,l),exc,phase,N_int)
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call decode_exc(exc,degree,h1,p1,h2,p2,s1,s2)
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double precision :: ckl
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ckl = phase*ck*cl
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call bitstring_to_list(det_provider(1,1,k), occ(1,1), n_occ_alpha, N_int)
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call bitstring_to_list(det_provider(1,2,k), occ(1,2), n_occ_alpha, N_int)
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select case (s1)
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case (1) ! Alpha single excitation
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integer :: occ(N_int*bit_kind_size,2)
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do i = 1, elec_alpha_num
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p2=occ(i,1)
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h2=p2
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call bielec_integrals_index(h1,h2,p1,p2,idx)
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write(iunit_two_body_dm_aa,f) idx, h1,h2,p1,p2, ckl
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call bielec_integrals_index(h1,h2,p2,p1,idx)
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write(iunit_two_body_dm_aa,f) idx, h1,h2,p2,p1, -ckl
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enddo
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do i = 1, elec_beta_num
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p2=occ(i,2)
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h2=p2
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call bielec_integrals_index(h1,h2,p1,p2,idx)
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write(iunit_two_body_dm_ab,f) idx, h1,h2,p1,p2, ckl
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enddo
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case (2) ! Beta single excitation
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do i = 1, elec_alpha_num
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p2=occ(i,1)
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h2=p2
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call bielec_integrals_index(h1,h2,p1,p2,idx)
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write(iunit_two_body_dm_ab,f) idx, h1,h2,p1,p2, ckl
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enddo
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do i = 1, elec_beta_num
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p2=occ(i,2)
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h2=p2
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call bielec_integrals_index(h1,h2,p1,p2,idx)
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write(iunit_two_body_dm_bb,f) idx, h1,h2,p1,p2, ckl
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call bielec_integrals_index(h1,h2,p2,p1,idx)
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write(iunit_two_body_dm_bb,f) idx, h1,h2,p2,p1, -ckl
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enddo
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end select
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endif
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enddo
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enddo
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! Sort file
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! Merge coefs
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close(iunit_two_body_dm_aa)
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close(iunit_two_body_dm_ab)
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close(iunit_two_body_dm_bb)
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character*(128) :: filename
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filename = trim(ezfio_filename)//'/work/two_body_aa.tmp'
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call system('sort -n '//trim(filename)//' > '//trim(filename)//'2 ; cp '//trim(filename)//'2 '//trim(filename))
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filename = trim(ezfio_filename)//'/work/two_body_ab.tmp'
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call system('sort -n '//trim(filename)//' > '//trim(filename)//'2 ; cp '//trim(filename)//'2 '//trim(filename))
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filename = trim(ezfio_filename)//'/work/two_body_bb.tmp'
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call system('sort -n '//trim(filename)//' > '//trim(filename)//'2 ; cp '//trim(filename)//'2 '//trim(filename))
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iunit_two_body_dm_aa = getUnitAndOpen(trim(ezfio_filename)//'/work/two_body_aa.tmp','r')
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iunit_two_body_dm_ab = getUnitAndOpen(trim(ezfio_filename)//'/work/two_body_ab.tmp','r')
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iunit_two_body_dm_bb = getUnitAndOpen(trim(ezfio_filename)//'/work/two_body_bb.tmp','r')
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END_PROVIDER
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BEGIN_TEMPLATE
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BEGIN_PROVIDER [ integer, size_two_body_dm_$AA ]
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implicit none
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use bitmasks
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BEGIN_DOC
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! Size of the two body $ALPHA density matrix
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END_DOC
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integer *8 :: key, key_old
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rewind(iunit_two_body_dm_$AA)
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size_two_body_dm_$AA = 0
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key = 0_8
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key_old = key
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do while (.True.)
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read(iunit_two_body_dm_$AA,*,END=99) key
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if (key /= key_old) then
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size_two_body_dm_$AA += 1
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key_old = key
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endif
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end do
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99 continue
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END_PROVIDER
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BEGIN_PROVIDER [ integer, two_body_dm_index_$AA, (4,size_two_body_dm_$AA) ]
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&BEGIN_PROVIDER [ double precision, two_body_dm_value_$AA, (size_two_body_dm_$AA) ]
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implicit none
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use bitmasks
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BEGIN_DOC
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! Two body $ALPHA density matrix
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END_DOC
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rewind(iunit_two_body_dm_$AA)
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integer *8 :: key, key_old
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integer :: ii, i,j,k,l
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double precision :: c
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key = 0_8
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key_old = key
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ii = 0
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do while (.True.)
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read(iunit_two_body_dm_$AA,*,END=99) key, i,j,k,l, c
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if (key /= key_old) then
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ii += 1
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two_body_dm_index_$AA(1,ii) = i
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two_body_dm_index_$AA(2,ii) = j
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two_body_dm_index_$AA(3,ii) = k
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two_body_dm_index_$AA(4,ii) = l
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two_body_dm_value_$AA(ii) = 0.d0
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key_old = key
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endif
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two_body_dm_value_$AA(ii) += c
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enddo
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99 continue
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close(iunit_two_body_dm_$AA, status='DELETE')
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END_PROVIDER
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SUBST [ AA, ALPHA ]
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aa ; alpha-alpha ;;
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ab ; alpha-beta ;;
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bb ; beta-beta ;;
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END_TEMPLATE
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BEGIN_PROVIDER [ double precision, two_body_dm_diag_aa, (mo_tot_num_align,mo_tot_num)]
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&BEGIN_PROVIDER [ double precision, two_body_dm_diag_bb, (mo_tot_num_align,mo_tot_num)]
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&BEGIN_PROVIDER [ double precision, two_body_dm_diag_ab, (mo_tot_num_align,mo_tot_num)]
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implicit none
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use bitmasks
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BEGIN_DOC
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! diagonal part of the two body density matrix
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END_DOC
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integer :: i,j,k,e1,e2
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integer :: occ(N_int*bit_kind_size,2)
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double precision :: ck
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integer :: n_occ_alpha
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two_body_dm_diag_aa=0.d0
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two_body_dm_diag_ab=0.d0
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two_body_dm_diag_bb=0.d0
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do k = 1, det_num
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call bitstring_to_list(det_provider(1,1,k), occ(1,1), n_occ_alpha, N_int)
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call bitstring_to_list(det_provider(1,2,k), occ(1,2), n_occ_alpha, N_int)
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ck = det_coef_provider(k) * det_coef_provider(k)
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do i = 1,elec_alpha_num
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e1=occ(i,1)
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do j = 1,elec_alpha_num
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e2=occ(j,1)
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! alpha-alpha
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two_body_dm_diag_aa(e1,e2) = two_body_dm_diag_aa(e1,e2) + ck
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enddo
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do j = 1,elec_beta_num
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e2=occ(j,2)
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! alpha-beta
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two_body_dm_diag_ab(e1,e2) = two_body_dm_diag_ab(e1,e2) + ck
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enddo
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enddo
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do i = 1,elec_beta_num
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e1=occ(i,2)
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do j = 1,elec_beta_num
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e2=occ(j,2)
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! beta-beta
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two_body_dm_diag_bb(e1,e2) = two_body_dm_diag_bb(e1,e2) + ck
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enddo
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, one_body_dm_a, (mo_tot_num_align,mo_tot_num) ]
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&BEGIN_PROVIDER [ double precision, one_body_dm_b, (mo_tot_num_align,mo_tot_num) ]
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implicit none
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BEGIN_DOC
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! Alpha and beta one-body density matrix
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END_DOC
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integer :: j,k,l
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integer :: occ(N_int*bit_kind_size,2)
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double precision :: ck, cl, ckl
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double precision :: phase
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integer :: h1,h2,p1,p2,s1,s2, degree
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integer :: exc(0:2,2,2),n_occ_alpha
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one_body_dm_a = 0.d0
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one_body_dm_b = 0.d0
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do k=1,det_num
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call bitstring_to_list(det_provider(1,1,k), occ(1,1), n_occ_alpha, N_int)
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call bitstring_to_list(det_provider(1,2,k), occ(1,2), n_occ_alpha, N_int)
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ck = det_coef_provider(k)
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do l=1,elec_alpha_num
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j = occ(l,1)
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one_body_dm_a(j,j) += ck*ck
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enddo
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do l=1,elec_beta_num
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j = occ(l,2)
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one_body_dm_b(j,j) += ck*ck
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enddo
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do l=1,k-1
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call get_excitation_degree(det_provider(1,1,k),det_provider(1,1,l),degree,N_int)
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if (degree /= 1) then
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cycle
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endif
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call get_mono_excitation(det_provider(1,1,k),det_provider(1,1,l),exc,phase,N_int)
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call decode_exc(exc,degree,h1,p1,h2,p2,s1,s2)
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ckl = ck * det_coef_provider(l) * phase
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if (s1==1) then
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one_body_dm_a(h1,p1) += ckl
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one_body_dm_a(p1,h1) += ckl
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else
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one_body_dm_b(h1,p1) += ckl
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one_body_dm_b(p1,h1) += ckl
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endif
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enddo
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enddo
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END_PROVIDER
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56
src/DensityMatrix/det_num.irp.f
Normal file
56
src/DensityMatrix/det_num.irp.f
Normal file
@ -0,0 +1,56 @@
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use bitmasks
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BEGIN_PROVIDER [integer, det_num]
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det_num = 10
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END_PROVIDER
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BEGIN_PROVIDER [ integer(bit_kind), det_provider, (N_int,2,det_num)]
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&BEGIN_PROVIDER [ double precision , det_coef_provider, (det_num) ]
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use bitmasks
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implicit none
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integer :: i
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det_provider = 0
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det_provider(1,1,1 ) = #001f ! 0000 0000 0001 1111
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det_provider(1,1,2 ) = #003b ! 0000 0000 0011 1011
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det_provider(1,1,3 ) = #008f ! 0000 0000 1000 1111
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det_provider(1,1,4 ) = #0057 ! 0000 0000 0101 0111
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det_provider(1,1,5 ) = #100f ! 0001 0000 0000 1111
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det_provider(1,1,6 ) = #001f ! 0000 0000 0001 1111
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det_provider(1,1,7 ) = #003b ! 0000 0000 0011 1011
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det_provider(1,1,8 ) = #00c7 ! 0000 0000 1100 0111
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det_provider(1,1,9 ) = #00ab ! 0000 0000 1010 1011
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det_provider(1,1,10) = #0073 ! 0000 0000 0111 0011
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det_provider(1,2,1 ) = #0007 ! 0000 0000 0001 0111
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det_provider(1,2,2 ) = #0023 ! 0000 0000 0010 0011
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det_provider(1,2,3 ) = #0023 ! 0000 0000 0010 0011
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det_provider(1,2,4 ) = #0023 ! 0000 0000 0010 0011
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det_provider(1,2,5 ) = #0015 ! 0000 0000 0001 0101
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det_provider(1,2,6 ) = #000d ! 0000 0000 0000 1101
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det_provider(1,2,7 ) = #0007 ! 0000 0000 0000 0111
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det_provider(1,2,8 ) = #0007 ! 0000 0000 0000 0111
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det_provider(1,2,9 ) = #0007 ! 0000 0000 0000 0111
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det_provider(1,2,10) = #0007 ! 0000 0000 0000 0111
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det_coef_provider = (/ &
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0.993536117982429D+00, &
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-0.556089064313864D-01, &
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0.403074722590178D-01, &
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0.403074717461626D-01, &
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-0.340290975461932D-01, &
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-0.340290958781670D-01, &
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-0.333949939765448D-01, &
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0.333418373363987D-01, &
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-0.316337211787351D-01, &
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-0.316337207748718D-01 &
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/)
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do i=1,10
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call write_bitstring( 6, det_provider(1,1,i), N_int )
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enddo
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print *, ''
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do i=1,10
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call write_bitstring( 6, det_provider(1,2,i), N_int )
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enddo
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print *, ''
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END_PROVIDER
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@ -120,6 +120,10 @@ subroutine copy_H_apply_buffer_to_wf
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N_det = N_det + H_apply_buffer_N_det
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TOUCH N_det
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if (psi_det_size < N_det) then
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psi_det_size = N_det
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TOUCH psi_det_size
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endif
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do i=1,N_det_old
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do k=1,N_int
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psi_det(k,1,i) = buffer_det(k,1,i)
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@ -51,7 +51,8 @@ Documentation
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.. NEEDED_MODULES file.
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`copy_h_apply_buffer_to_wf <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/H_apply.irp.f#L93>`_
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None
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Undocumented
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`h_apply_buffer_coef <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/H_apply.irp.f#L82>`_
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Buffer of determinants/coefficients for H_apply. Uninitialized. Filled by H_apply subroutines.
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@ -68,23 +69,49 @@ None
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Theshold on | <Di|H|Dj> |
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|
||||
`resize_h_apply_buffer_det <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/H_apply.irp.f#L31>`_
|
||||
None
|
||||
Undocumented
|
||||
|
||||
`davidson_diag <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/davidson.irp.f#L18>`_
|
||||
Davidson diagonalization.
|
||||
.br
|
||||
dets_in : bitmasks corresponding to determinants
|
||||
.br
|
||||
u_in : guess coefficients on the various states. Overwritten
|
||||
on exit
|
||||
.br
|
||||
dim_in : leftmost dimension of u_in
|
||||
.br
|
||||
sze : Number of determinants
|
||||
.br
|
||||
N_st : Number of eigenstates
|
||||
.br
|
||||
Initial guess vectors are not necessarily orthonormal
|
||||
|
||||
`davidson_iter_max <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/davidson.irp.f#L1>`_
|
||||
Max number of Davidson iterations
|
||||
|
||||
`davidson_sze_max <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/davidson.irp.f#L9>`_
|
||||
Max number of Davidson sizes
|
||||
|
||||
`n_det <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L11>`_
|
||||
Number of determinants in the wave function
|
||||
|
||||
`n_det_generators <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L47>`_
|
||||
`n_det_generators <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L55>`_
|
||||
Number of generator determinants in the wave function
|
||||
|
||||
`n_states <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L3>`_
|
||||
Number of states to consider
|
||||
|
||||
`psi_coef <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L20>`_
|
||||
`psi_coef <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L28>`_
|
||||
The wave function. Initialized with Hartree-Fock
|
||||
|
||||
`psi_det <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L19>`_
|
||||
`psi_det <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L27>`_
|
||||
The wave function. Initialized with Hartree-Fock
|
||||
|
||||
`psi_generators <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L55>`_
|
||||
`psi_det_size <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L19>`_
|
||||
Size of the psi_det/psi_coef arrays
|
||||
|
||||
`psi_generators <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants.irp.f#L63>`_
|
||||
Determinants on which H is applied
|
||||
|
||||
`double_exc_bitmask <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/determinants_bitmasks.irp.f#L40>`_
|
||||
@ -108,10 +135,10 @@ None
|
||||
`get_s2 <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/s2.irp.f#L1>`_
|
||||
Returns <S^2>
|
||||
|
||||
`a_operator <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L842>`_
|
||||
`a_operator <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L840>`_
|
||||
Needed for diag_H_mat_elem
|
||||
|
||||
`ac_operator <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L887>`_
|
||||
`ac_operator <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L885>`_
|
||||
Needed for diag_H_mat_elem
|
||||
|
||||
`decode_exc <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L76>`_
|
||||
@ -121,15 +148,16 @@ None
|
||||
s1,s2 : Spins (1:alpha, 2:beta)
|
||||
degree : Degree of excitation
|
||||
|
||||
`diag_h_mat_elem <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L779>`_
|
||||
`diag_h_mat_elem <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L778>`_
|
||||
Computes <i|H|i>
|
||||
|
||||
`filter_connected <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L602>`_
|
||||
`filter_connected <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L603>`_
|
||||
Filters out the determinants that are not connected by H
|
||||
|
||||
`filter_connected_i_h_psi0 <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L687>`_
|
||||
None
|
||||
`get_double_excitation <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L140>`_
|
||||
Undocumented
|
||||
|
||||
`get_double_excitation <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L141>`_
|
||||
Returns the two excitation operators between two doubly excited determinants and the phase
|
||||
|
||||
`get_excitation <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L30>`_
|
||||
@ -138,20 +166,28 @@ None
|
||||
`get_excitation_degree <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L1>`_
|
||||
Returns the excitation degree between two determinants
|
||||
|
||||
`get_excitation_degree_vector <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L518>`_
|
||||
`get_excitation_degree_vector <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L520>`_
|
||||
Applies get_excitation_degree to an array of determinants
|
||||
|
||||
`get_mono_excitation <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L273>`_
|
||||
`get_mono_excitation <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L274>`_
|
||||
Returns the excitation operator between two singly excited determinants and the phase
|
||||
|
||||
`get_occ_from_key <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L935>`_
|
||||
`get_occ_from_key <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L933>`_
|
||||
Returns a list of occupation numbers from a bitstring
|
||||
|
||||
`i_h_j <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L354>`_
|
||||
`h_u_0 <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L949>`_
|
||||
Computes v_0 = H|u_0>
|
||||
.br
|
||||
n : number of determinants
|
||||
.br
|
||||
H_jj : array of <j|H|j>
|
||||
|
||||
`i_h_j <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L355>`_
|
||||
Returns <i|H|j> where i and j are determinants
|
||||
|
||||
`i_h_psim <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L490>`_
|
||||
None
|
||||
`i_h_psim <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/slater_rules.irp.f#L491>`_
|
||||
Undocumented
|
||||
|
||||
`h_matrix_all_dets <http://github.com/LCPQ/quantum_package/tree/master/src/Dets/utils.irp.f#L1>`_
|
||||
H matrix on the basis of the slater deter;inants defined by psi_det
|
||||
|
||||
|
261
src/Dets/davidson.irp.f
Normal file
261
src/Dets/davidson.irp.f
Normal file
@ -0,0 +1,261 @@
|
||||
BEGIN_PROVIDER [ integer, davidson_iter_max]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Max number of Davidson iterations
|
||||
END_DOC
|
||||
davidson_iter_max = 100
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer, davidson_sze_max]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Max number of Davidson sizes
|
||||
END_DOC
|
||||
ASSERT (davidson_sze_max <= davidson_iter_max)
|
||||
davidson_sze_max = 10
|
||||
END_PROVIDER
|
||||
|
||||
subroutine davidson_diag(dets_in,u_in,energies,dim_in,sze,N_st,Nint)
|
||||
use bitmasks
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Davidson diagonalization.
|
||||
!
|
||||
! dets_in : bitmasks corresponding to determinants
|
||||
!
|
||||
! u_in : guess coefficients on the various states. Overwritten
|
||||
! on exit
|
||||
!
|
||||
! dim_in : leftmost dimension of u_in
|
||||
!
|
||||
! sze : Number of determinants
|
||||
!
|
||||
! N_st : Number of eigenstates
|
||||
!
|
||||
! Initial guess vectors are not necessarily orthonormal
|
||||
END_DOC
|
||||
integer, intent(in) :: dim_in, sze, N_st, Nint
|
||||
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
|
||||
double precision, intent(inout) :: u_in(dim_in,N_st)
|
||||
double precision, intent(out) :: energies(N_st)
|
||||
|
||||
integer :: iter
|
||||
integer :: i,j,k,l
|
||||
logical :: converged
|
||||
|
||||
double precision :: overlap(N_st,N_st)
|
||||
double precision :: u_dot_v, u_dot_u
|
||||
|
||||
integer, allocatable :: kl_pairs(:,:)
|
||||
integer :: k_pairs, kl
|
||||
|
||||
integer :: iter2
|
||||
double precision, allocatable :: W(:,:), H_jj(:), U(:,:,:), R(:,:)
|
||||
double precision, allocatable :: y(:,:,:,:), h(:,:,:,:), lambda(:)
|
||||
double precision :: diag_h_mat_elem
|
||||
double precision :: residual_norm(N_st)
|
||||
|
||||
allocate( &
|
||||
kl_pairs(2,N_st*(N_st+1)/2), &
|
||||
H_jj(sze), &
|
||||
W(sze,N_st), &
|
||||
U(sze,N_st,davidson_sze_max), &
|
||||
R(sze,N_st), &
|
||||
h(N_st,davidson_sze_max,N_st,davidson_sze_max), &
|
||||
y(N_st,davidson_sze_max,N_st,davidson_sze_max), &
|
||||
lambda(N_st*davidson_sze_max))
|
||||
|
||||
ASSERT (N_st > 0)
|
||||
ASSERT (sze > 0)
|
||||
ASSERT (Nint > 0)
|
||||
ASSERT (Nint == N_int)
|
||||
! Conventions:
|
||||
! i,j : 1,sze
|
||||
! k,l : 1,N_st
|
||||
|
||||
!$OMP PARALLEL DEFAULT(NONE) &
|
||||
!$OMP PRIVATE(k,i) SHARED(U,u_in,sze,N_st)
|
||||
do k=1,N_st
|
||||
!$OMP DO
|
||||
do i=1,sze
|
||||
U(i,k,1) = u_in(i,k)
|
||||
enddo
|
||||
!$OMP END DO NOWAIT
|
||||
enddo
|
||||
!$OMP END PARALLEL
|
||||
|
||||
! Orthonormalize initial guess
|
||||
! ============================
|
||||
|
||||
k_pairs=0
|
||||
do l=1,N_st
|
||||
do k=1,l
|
||||
k_pairs+=1
|
||||
kl_pairs(1,k_pairs) = k
|
||||
kl_pairs(2,k_pairs) = l
|
||||
enddo
|
||||
enddo
|
||||
!$OMP PARALLEL DO DEFAULT(NONE) &
|
||||
!$OMP SHARED(U,sze,N_st,overlap,kl_pairs,k_pairs) &
|
||||
!$OMP PRIVATE(k,l,kl)
|
||||
do kl=1,k_pairs
|
||||
k = kl_pairs(1,kl)
|
||||
l = kl_pairs(2,kl)
|
||||
if (k==l) then
|
||||
overlap(k,k) = u_dot_u(U(1,k,1),sze)
|
||||
endif
|
||||
overlap(k,l) = u_dot_v(U(1,k,1),U(1,l,1),sze)
|
||||
overlap(l,k) = overlap(k,l)
|
||||
enddo
|
||||
!$OMP END PARALLEL DO
|
||||
call ortho_lowdin(overlap,size(overlap,1),N_st,U,size(U,1),sze)
|
||||
|
||||
!$OMP PARALLEL DO DEFAULT(NONE) &
|
||||
!$OMP PRIVATE(i) &
|
||||
!$OMP SHARED(H_jj,Nint,dets_in,sze)
|
||||
do i=1,sze
|
||||
H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
|
||||
enddo
|
||||
!$OMP END PARALLEL DO
|
||||
|
||||
! Davidson iterations
|
||||
! ===================
|
||||
|
||||
converged = .False.
|
||||
|
||||
do iter=1,davidson_sze_max-1
|
||||
print *, 'iter = ',iter
|
||||
|
||||
! print *, '***************'
|
||||
! do i=1,iter
|
||||
! do k=1,N_st
|
||||
! do j=1,iter
|
||||
! do l=1,N_st
|
||||
! print '(4(I4,X),F16.8)', i,j,k,l, u_dot_v(U(1,k,i),U(1,l,j),sze)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! print *, '***************'
|
||||
|
||||
! Compute W_k = H |u_k>
|
||||
! ----------------------
|
||||
|
||||
do k=1,N_st
|
||||
call H_u_0(W(1,k),U(1,k,iter),H_jj,sze,dets_in,Nint)
|
||||
enddo
|
||||
|
||||
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
|
||||
! -------------------------------------------
|
||||
do l=1,N_st
|
||||
do iter2=1,iter-1
|
||||
do k=1,N_st
|
||||
h(k,iter2,l,iter) = u_dot_v(U(1,k,iter2),W(1,l),sze)
|
||||
h(k,iter,l,iter2) = h(k,iter2,l,iter)
|
||||
enddo
|
||||
enddo
|
||||
do k=1,l
|
||||
h(k,iter,l,iter) = u_dot_v(U(1,k,iter),W(1,l),sze)
|
||||
h(l,iter,k,iter) = h(k,iter,l,iter)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Diagonalize h
|
||||
! -------------
|
||||
call lapack_diag(lambda,y,h,N_st*davidson_sze_max,N_st*iter)
|
||||
|
||||
! Express eigenvectors of h in the determinant basis
|
||||
! --------------------------------------------------
|
||||
|
||||
!TODO dgemm
|
||||
do k=1,N_st
|
||||
do i=1,sze
|
||||
U(i,k,iter+1) = 0.d0
|
||||
do iter2=1,iter
|
||||
do l=1,N_st
|
||||
U(i,k,iter+1) += U(i,l,iter2)*y(l,iter2,k,1)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Compute residual vector
|
||||
! -----------------------
|
||||
|
||||
do k=1,N_st
|
||||
call H_u_0(W(1,k),U(1,k,iter+1),H_jj,sze,dets_in,Nint)
|
||||
enddo
|
||||
|
||||
do k=1,N_st
|
||||
do i=1,sze
|
||||
R(i,k) = lambda(k) * U(i,k,iter+1) - W(i,k)
|
||||
enddo
|
||||
residual_norm(k) = u_dot_u(R(1,k),sze)
|
||||
enddo
|
||||
print *, 'Lambda'
|
||||
print *, lambda(1:N_st) + nuclear_repulsion
|
||||
print *, 'Residual_norm'
|
||||
print *, residual_norm(1:N_st)
|
||||
print *, ''
|
||||
|
||||
converged = maxval(residual_norm) < 1.d-10
|
||||
if (converged) then
|
||||
exit
|
||||
endif
|
||||
|
||||
! Davidson step
|
||||
! -------------
|
||||
|
||||
do k=1,N_st
|
||||
do i=1,sze
|
||||
U(i,k,iter+1) = 1.d0/(lambda(k) - H_jj(i)) * R(i,k)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Gram-Schmidt
|
||||
! ------------
|
||||
|
||||
double precision :: c
|
||||
do k=1,N_st
|
||||
do iter2=1,iter
|
||||
do l=1,N_st
|
||||
c = u_dot_v(U(1,k,iter+1),U(1,l,iter2),sze)
|
||||
do i=1,sze
|
||||
U(i,k,iter+1) -= c * U(i,l,iter2)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
do l=1,k-1
|
||||
c = u_dot_v(U(1,k,iter+1),U(1,l,iter+1),sze)
|
||||
do i=1,sze
|
||||
U(i,k,iter+1) -= c * U(i,l,iter+1)
|
||||
enddo
|
||||
enddo
|
||||
call normalize( U(1,k,iter+1), sze )
|
||||
enddo
|
||||
|
||||
enddo
|
||||
do k=1,N_st
|
||||
energies(k) = lambda(k)
|
||||
do i=1,sze
|
||||
u_in(i,k) = 0.d0
|
||||
do iter2=1,iter
|
||||
do l=1,N_st
|
||||
u_in(i,k) += U(i,l,iter2)*y(l,iter2,k,1)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
deallocate ( &
|
||||
kl_pairs, &
|
||||
H_jj, &
|
||||
W, &
|
||||
U, &
|
||||
R, &
|
||||
h, &
|
||||
y, &
|
||||
lambda &
|
||||
)
|
||||
end
|
||||
|
@ -13,11 +13,19 @@ BEGIN_PROVIDER [ integer, N_det ]
|
||||
BEGIN_DOC
|
||||
! Number of determinants in the wave function
|
||||
END_DOC
|
||||
N_det = max(1,N_states)
|
||||
N_det = 1
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer(bit_kind), psi_det, (N_int,2,N_det) ]
|
||||
&BEGIN_PROVIDER [ double precision, psi_coef, (N_det,N_states) ]
|
||||
BEGIN_PROVIDER [ integer, psi_det_size ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Size of the psi_det/psi_coef arrays
|
||||
END_DOC
|
||||
psi_det_size = 1000
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer(bit_kind), psi_det, (N_int,2,psi_det_size) ]
|
||||
&BEGIN_PROVIDER [ double precision, psi_coef, (psi_det_size,N_states) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! The wave function. Initialized with Hartree-Fock
|
||||
@ -52,7 +60,7 @@ BEGIN_PROVIDER [ integer, N_det_generators ]
|
||||
N_det_generators = N_det
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer(bit_kind), psi_generators, (N_int,2,N_det) ]
|
||||
BEGIN_PROVIDER [ integer(bit_kind), psi_generators, (N_int,2,psi_det_size) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Determinants on which H is applied
|
||||
|
@ -74,6 +74,7 @@ subroutine get_excitation(det1,det2,exc,degree,phase,Nint)
|
||||
end
|
||||
|
||||
subroutine decode_exc(exc,degree,h1,p1,h2,p2,s1,s2)
|
||||
use bitmasks
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Decodes the exc arrays returned by get_excitation.
|
||||
@ -488,6 +489,7 @@ end
|
||||
|
||||
|
||||
subroutine i_H_psim(key,keys,coef,Nint,Ndet,Ndet_max,Nstate,i_H_psi_array)
|
||||
use bitmasks
|
||||
implicit none
|
||||
integer, intent(in) :: Nint, Ndet,Ndet_max,Nstate
|
||||
integer, intent(in) :: keys(Nint,2,Ndet_max)
|
||||
@ -515,14 +517,14 @@ end
|
||||
|
||||
|
||||
|
||||
subroutine get_excitation_degree_vector(key1,key2,degree,Nint,sze,sze_max,idx)
|
||||
subroutine get_excitation_degree_vector(key1,key2,degree,Nint,sze,idx)
|
||||
use bitmasks
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Applies get_excitation_degree to an array of determinants
|
||||
END_DOC
|
||||
integer, intent(in) :: Nint, sze,sze_max
|
||||
integer(bit_kind), intent(in) :: key1(Nint,2,sze_max)
|
||||
integer, intent(in) :: Nint, sze
|
||||
integer(bit_kind), intent(in) :: key1(Nint,2,sze)
|
||||
integer(bit_kind), intent(in) :: key2(Nint,2)
|
||||
integer, intent(out) :: degree(sze)
|
||||
integer, intent(out) :: idx(0:sze)
|
||||
@ -531,7 +533,6 @@ subroutine get_excitation_degree_vector(key1,key2,degree,Nint,sze,sze_max,idx)
|
||||
|
||||
ASSERT (Nint > 0)
|
||||
ASSERT (sze > 0)
|
||||
ASSERT (sze_max >= sze)
|
||||
|
||||
l=1
|
||||
if (Nint==1) then
|
||||
@ -599,14 +600,14 @@ end
|
||||
|
||||
|
||||
|
||||
subroutine filter_connected(key1,key2,Nint,sze,sze_max,idx)
|
||||
subroutine filter_connected(key1,key2,Nint,sze,idx)
|
||||
use bitmasks
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Filters out the determinants that are not connected by H
|
||||
END_DOC
|
||||
integer, intent(in) :: Nint, sze,sze_max
|
||||
integer(bit_kind), intent(in) :: key1(Nint,2,sze_max)
|
||||
integer, intent(in) :: Nint, sze
|
||||
integer(bit_kind), intent(in) :: key1(Nint,2,sze)
|
||||
integer(bit_kind), intent(in) :: key2(Nint,2)
|
||||
integer, intent(out) :: idx(0:sze)
|
||||
|
||||
@ -615,7 +616,6 @@ subroutine filter_connected(key1,key2,Nint,sze,sze_max,idx)
|
||||
|
||||
ASSERT (Nint > 0)
|
||||
ASSERT (sze > 0)
|
||||
ASSERT (sze_max >= sze)
|
||||
|
||||
l=1
|
||||
|
||||
@ -684,11 +684,11 @@ subroutine filter_connected(key1,key2,Nint,sze,sze_max,idx)
|
||||
idx(0) = l-1
|
||||
end
|
||||
|
||||
subroutine filter_connected_i_H_psi0(key1,key2,Nint,sze,sze_max,idx)
|
||||
subroutine filter_connected_i_H_psi0(key1,key2,Nint,sze,idx)
|
||||
use bitmasks
|
||||
implicit none
|
||||
integer, intent(in) :: Nint, sze,sze_max
|
||||
integer(bit_kind), intent(in) :: key1(Nint,2,sze_max)
|
||||
integer, intent(in) :: Nint, sze
|
||||
integer(bit_kind), intent(in) :: key1(Nint,2,sze)
|
||||
integer(bit_kind), intent(in) :: key2(Nint,2)
|
||||
integer, intent(out) :: idx(0:sze)
|
||||
|
||||
@ -697,7 +697,6 @@ subroutine filter_connected_i_H_psi0(key1,key2,Nint,sze,sze_max,idx)
|
||||
|
||||
ASSERT (Nint > 0)
|
||||
ASSERT (sze > 0)
|
||||
ASSERT (sze_max >= sze)
|
||||
|
||||
l=1
|
||||
|
||||
@ -777,7 +776,6 @@ end
|
||||
|
||||
|
||||
double precision function diag_H_mat_elem(det_in,Nint)
|
||||
use bitmasks
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Computes <i|H|i>
|
||||
@ -947,3 +945,46 @@ subroutine get_occ_from_key(key,occ,Nint)
|
||||
call bitstring_to_list(key(1,2), occ(1,2), tmp, Nint)
|
||||
|
||||
end
|
||||
|
||||
subroutine H_u_0(v_0,u_0,H_jj,n,keys_tmp,Nint)
|
||||
use bitmasks
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Computes v_0 = H|u_0>
|
||||
!
|
||||
! n : number of determinants
|
||||
!
|
||||
! H_jj : array of <j|H|j>
|
||||
END_DOC
|
||||
integer, intent(in) :: n,Nint
|
||||
double precision, intent(out) :: v_0(n)
|
||||
double precision, intent(in) :: u_0(n)
|
||||
double precision, intent(in) :: H_jj(n)
|
||||
integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
|
||||
integer, allocatable :: idx(:)
|
||||
double precision :: hij
|
||||
integer :: i,j,k,l, jj
|
||||
ASSERT (Nint > 0)
|
||||
ASSERT (Nint == N_int)
|
||||
ASSERT (n>0)
|
||||
!$OMP PARALLEL DEFAULT(NONE) &
|
||||
!$OMP PRIVATE(i,hij,j,k,idx,jj) SHARED(n,H_jj,u_0,keys_tmp,Nint)&
|
||||
!$OMP SHARED(v_0)
|
||||
allocate(idx(0:n))
|
||||
!$OMP DO SCHEDULE(dynamic)
|
||||
do i=1,n
|
||||
v_0(i) = H_jj(i) * u_0(i)
|
||||
call filter_connected(keys_tmp,keys_tmp(1,1,i),Nint,n,idx)
|
||||
do jj=1,idx(0)
|
||||
j = idx(jj)
|
||||
if (j/=i) then
|
||||
call i_H_j(keys_tmp(1,1,j),keys_tmp(1,1,i),Nint,hij)
|
||||
v_0(i) = v_0(i) + hij*u_0(j)
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
deallocate(idx)
|
||||
!$OMP END PARALLEL
|
||||
end
|
||||
|
||||
|
@ -1,10 +1,24 @@
|
||||
subroutine ortho_lowdin(overlap,lda,n,C,ldc,m)
|
||||
subroutine ortho_lowdin(overlap,LDA,N,C,LDC,m)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Compute U.S^-1/2 canonical orthogonalization
|
||||
! Compute C_new=C_old.S^-1/2 canonical orthogonalization.
|
||||
!
|
||||
! overlap : overlap matrix
|
||||
!
|
||||
! LDA : leftmost dimension of overlap array
|
||||
!
|
||||
! N : Overlap matrix is NxN (array is (LDA,N) )
|
||||
!
|
||||
! C : Coefficients of the vectors to orthogonalize. On exit,
|
||||
! orthogonal vectors
|
||||
!
|
||||
! LDC : leftmost dimension of C
|
||||
!
|
||||
! m : Coefficients matrix is MxN, ( array is (LDC,N) )
|
||||
!
|
||||
END_DOC
|
||||
|
||||
integer, intent(in) :: lda, ldc, n, m
|
||||
integer, intent(in) :: LDA, ldc, n, m
|
||||
double precision, intent(in) :: overlap(lda,n)
|
||||
double precision, intent(inout) :: C(ldc,n)
|
||||
double precision :: U(ldc,n)
|
||||
@ -34,37 +48,45 @@ subroutine ortho_lowdin(overlap,lda,n,C,ldc,m)
|
||||
stop
|
||||
endif
|
||||
|
||||
|
||||
!$OMP PARALLEL DEFAULT(NONE) &
|
||||
!$OMP SHARED(S_half,U,D,Vt,n,C,m) &
|
||||
!$OMP PRIVATE(i,j,k)
|
||||
|
||||
!$OMP DO
|
||||
do i=1,n
|
||||
if ( D(i) < 1.d-6 ) then
|
||||
D(i) = 0.d0
|
||||
else
|
||||
D(i) = 1.d0/dsqrt(D(i))
|
||||
endif
|
||||
enddo
|
||||
|
||||
S_half = 0.d0
|
||||
do k=1,n
|
||||
do j=1,n
|
||||
do i=1,n
|
||||
S_half(i,j) += U(i,k)*D(k)*Vt(k,j)
|
||||
enddo
|
||||
S_half(j,i) = 0.d0
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
do k=1,n
|
||||
!$OMP DO
|
||||
do j=1,n
|
||||
do i=1,n
|
||||
S_half(i,j) = S_half(i,j) + U(i,k)*D(k)*Vt(k,j)
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO NOWAIT
|
||||
enddo
|
||||
|
||||
!$OMP DO
|
||||
do j=1,n
|
||||
do i=1,m
|
||||
U(i,j) = C(i,j)
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
C = 0.d0
|
||||
do j=1,n
|
||||
do i=1,m
|
||||
do k=1,n
|
||||
C(i,j) += U(i,k)*S_half(k,j)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END PARALLEL
|
||||
|
||||
call dgemm('N','N',m,n,n,1.d0,U,size(U,1),S_half,size(S_half,1),0.d0,C,size(C,1))
|
||||
|
||||
end
|
||||
|
||||
@ -171,6 +193,17 @@ subroutine lapack_diag(eigvalues,eigvectors,H,nmax,n)
|
||||
allocate(A(nmax,n),eigenvalues(nmax),work(4*nmax))
|
||||
integer :: LWORK, info, i,j,l,k
|
||||
A=H
|
||||
|
||||
! if (n<30) then
|
||||
! do i=1,n
|
||||
! do j=1,n
|
||||
! print *, j,i, H(j,i)
|
||||
! enddo
|
||||
! print *, '---'
|
||||
! enddo
|
||||
! print *, '---'
|
||||
! endif
|
||||
|
||||
LWORK = 4*nmax
|
||||
call dsyev( 'V', 'U', n, A, nmax, eigenvalues, work, LWORK, info )
|
||||
if (info < 0) then
|
||||
|
@ -214,7 +214,6 @@ double precision function u_dot_v(u,v,sze)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Compute <u|v>
|
||||
! u and v are expected to be aligned in memory.
|
||||
END_DOC
|
||||
integer, intent(in) :: sze
|
||||
double precision, intent(in) :: u(sze),v(sze)
|
||||
@ -227,14 +226,10 @@ double precision function u_dot_v(u,v,sze)
|
||||
t3 = t2+t2
|
||||
t4 = t3+t2
|
||||
u_dot_v = 0.d0
|
||||
!DIR$ VECTOR ALWAYS
|
||||
!DIR$ VECTOR ALIGNED
|
||||
do i=1,t2
|
||||
u_dot_v = u_dot_v + u(t1+i)*v(t1+i) + u(t2+i)*v(t2+i) + &
|
||||
u(t3+i)*v(t3+i) + u(t4+i)*v(t4+i)
|
||||
enddo
|
||||
!DIR$ VECTOR ALWAYS
|
||||
!DIR$ VECTOR ALIGNED
|
||||
do i=t4+t2+1,sze
|
||||
u_dot_v = u_dot_v + u(i)*v(i)
|
||||
enddo
|
||||
@ -245,7 +240,6 @@ double precision function u_dot_u(u,sze)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Compute <u|u>
|
||||
! u is expected to be aligned in memory.
|
||||
END_DOC
|
||||
integer, intent(in) :: sze
|
||||
double precision, intent(in) :: u(sze)
|
||||
|
Loading…
Reference in New Issue
Block a user