Introducing Cholesky-decomposed SCF

src/ao_two_e_ints/cholesky.irp.f

@@ -0,0 +1,100 @@
+BEGIN_PROVIDER [ integer, cholesky_ao_num_guess ]
+ implicit none
+ BEGIN_DOC
+ ! Number of Cholesky vectors in AO basis
+ END_DOC
+
+ integer :: i,j,k,l
+ double precision :: xnorm0, x, integral
+ double precision, external :: ao_two_e_integral
+
+ cholesky_ao_num_guess = 0
+ xnorm0 = 0.d0
+ x = 0.d0
+ do j=1,ao_num
+   do i=1,ao_num
+     integral = ao_two_e_integral(i,i,j,j)
+     if (integral > ao_integrals_threshold) then
+       cholesky_ao_num_guess += 1
+     else
+       x += integral
+     endif
+   enddo
+ enddo
+ print *, 'Cholesky decomposition of AO integrals'
+ print *, '--------------------------------------'
+ print *, ''
+ print *, 'Estimated Error: ', x
+ print *, 'Guess size: ', cholesky_ao_num_guess, '(', 100.d0*dble(cholesky_ao_num_guess)/dble(ao_num*ao_num), ' %)'
+
+END_PROVIDER
+
+ BEGIN_PROVIDER [ integer, cholesky_ao_num ]
+&BEGIN_PROVIDER [ double precision, cholesky_ao, (ao_num, ao_num, cholesky_ao_num_guess) ]
+ use mmap_module
+ implicit none
+ BEGIN_DOC
+ ! Cholesky vectors in AO basis: (ik|a):
+ ! <ij|kl> = (ik|jl) = sum_a (ik|a).(a|jl)
+ END_DOC
+
+ type(c_ptr) :: ptr
+ integer :: fd, i,j,k,l, rank
+ double precision, pointer :: ao_integrals(:,:,:,:)
+ double precision, external :: ao_two_e_integral
+
+ ! Store AO integrals in a memory mapped file
+ call mmap(trim(ezfio_work_dir)//'ao_integrals', &
+   (/ int(ao_num,8), int(ao_num,8), int(ao_num,8), int(ao_num,8) /), &
+   8, fd, .False., ptr)
+ call c_f_pointer(ptr, ao_integrals, (/ao_num, ao_num, ao_num, ao_num/))
+
+ double precision :: integral
+ logical, external :: ao_two_e_integral_zero
+ !$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,j,k,l, integral) SCHEDULE(dynamic)
+ do l=1,ao_num
+  do j=1,l
+   do k=1,ao_num
+    do i=1,k
+     if (ao_two_e_integral_zero(i,j,k,l)) cycle
+     integral = ao_two_e_integral(i,k,j,l)
+     ao_integrals(i,k,j,l) = integral
+     ao_integrals(k,i,j,l) = integral
+     ao_integrals(i,k,l,j) = integral
+     ao_integrals(k,i,l,j) = integral
+    enddo
+   enddo
+  enddo
+ enddo
+ !$OMP END PARALLEL DO
+
+ ! Call Lapack
+ cholesky_ao_num = cholesky_ao_num_guess
+ call pivoted_cholesky(ao_integrals, cholesky_ao_num, ao_integrals_threshold, ao_num*ao_num, cholesky_ao)
+ print *, 'Rank: ', cholesky_ao_num, '(', 100.d0*dble(cholesky_ao_num)/dble(ao_num*ao_num), ' %)'
+
+ ! Remove mmap
+ double precision, external :: getUnitAndOpen
+ call munmap( &
+   (/ int(ao_num,8), int(ao_num,8), int(ao_num,8), int(ao_num,8) /), &
+   8, fd, ptr)
+ open(unit=99,file=trim(ezfio_work_dir)//'ao_integrals')
+ close(99, status='delete')
+
+END_PROVIDER
+
+BEGIN_PROVIDER [ double precision, cholesky_ao_transp, (cholesky_ao_num, ao_num, ao_num) ]
+ implicit none
+ BEGIN_DOC
+! Transposed of the Cholesky vectors in AO basis set
+ END_DOC
+ integer :: i,j,k
+ do j=1,ao_num
+  do i=1,ao_num
+   do k=1,ao_num
+    cholesky_ao_transp(k,i,j) = cholesky_ao(i,j,k)
+   enddo
+  enddo
+ enddo
+END_PROVIDER
+

src/ao_two_e_ints/map_integrals.irp.f

@@ -486,7 +486,7 @@ subroutine get_ao_two_e_integrals(j,k,l,sze,out_val)
   PROVIDE ao_two_e_integrals_in_map ao_integrals_map
 
   if (ao_one_e_integral_zero(j,l)) then
-    out_val = 0.d0
+    out_val(1:sze) = 0.d0
     return
   endif
 

src/hartree_fock/fock_matrix_hf.irp.f

@@ -15,115 +15,59 @@
  double precision, allocatable  :: ao_two_e_integral_alpha_tmp(:,:)
  double precision, allocatable  :: ao_two_e_integral_beta_tmp(:,:)
 
- ao_two_e_integral_alpha = 0.d0
+ if (.True.) then   ! Use Cholesky-decomposed integrals
- ao_two_e_integral_beta  = 0.d0
+   ao_two_e_integral_alpha(:,:) = ao_two_e_integral_alpha_chol(:,:)
- if (do_direct_integrals) then
+   ao_two_e_integral_beta (:,:) = ao_two_e_integral_beta_chol (:,:)
 
-   !$OMP PARALLEL DEFAULT(NONE)                                      &
+ else ! Use integrals in AO basis set
-       !$OMP PRIVATE(i,j,l,k1,k,integral,ii,jj,kk,ll,keys,values,p,q,r,s,i0,j0,k0,l0, &
-       !$OMP ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp, c0, c1, c2, &
-       !$OMP local_threshold)&
-       !$OMP SHARED(ao_num,SCF_density_matrix_ao_alpha,SCF_density_matrix_ao_beta,&
-       !$OMP ao_integrals_map,ao_integrals_threshold, ao_two_e_integral_schwartz, &
-       !$OMP ao_two_e_integral_alpha, ao_two_e_integral_beta)
 
-   allocate(keys(1), values(1))
+   ao_two_e_integral_alpha = 0.d0
-   allocate(ao_two_e_integral_alpha_tmp(ao_num,ao_num), &
+   ao_two_e_integral_beta  = 0.d0
-            ao_two_e_integral_beta_tmp(ao_num,ao_num))
+   if (do_direct_integrals) then
-   ao_two_e_integral_alpha_tmp = 0.d0
-   ao_two_e_integral_beta_tmp  = 0.d0
 
-   q = ao_num*ao_num*ao_num*ao_num
+     !$OMP PARALLEL DEFAULT(NONE)                                    &
-   !$OMP DO SCHEDULE(static,64)
+         !$OMP PRIVATE(i,j,l,k1,k,integral,ii,jj,kk,ll,keys,values,p,q,r,s,i0,j0,k0,l0,&
-   do p=1_8,q
+         !$OMP ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp, c0, c1, c2,&
-           call two_e_integrals_index_reverse(kk,ii,ll,jj,p)
+         !$OMP local_threshold)                                      &
-           if ( (kk(1)>ao_num).or. &
+         !$OMP SHARED(ao_num,SCF_density_matrix_ao_alpha,SCF_density_matrix_ao_beta,&
-                (ii(1)>ao_num).or. &
+         !$OMP ao_integrals_map,ao_integrals_threshold, ao_two_e_integral_schwartz,&
-                (jj(1)>ao_num).or. &
+         !$OMP ao_two_e_integral_alpha, ao_two_e_integral_beta)
-                (ll(1)>ao_num) ) then
-                cycle
-           endif
-           k = kk(1)
-           i = ii(1)
-           l = ll(1)
-           j = jj(1)
 
-           logical, external :: ao_two_e_integral_zero
+     allocate(keys(1), values(1))
-           if (ao_two_e_integral_zero(i,k,j,l)) then
+     allocate(ao_two_e_integral_alpha_tmp(ao_num,ao_num),            &
-             cycle
+         ao_two_e_integral_beta_tmp(ao_num,ao_num))
-           endif
+     ao_two_e_integral_alpha_tmp = 0.d0
-           local_threshold = ao_two_e_integral_schwartz(k,l)*ao_two_e_integral_schwartz(i,j)
+     ao_two_e_integral_beta_tmp  = 0.d0
-           if (local_threshold < ao_integrals_threshold) then
-             cycle
-           endif
-           i0 = i
-           j0 = j
-           k0 = k
-           l0 = l
-           values(1) = 0.d0
-           local_threshold = ao_integrals_threshold/local_threshold
-           do k2=1,8
-             if (kk(k2)==0) then
-               cycle
-             endif
-             i = ii(k2)
-             j = jj(k2)
-             k = kk(k2)
-             l = ll(k2)
-             c0 = SCF_density_matrix_ao_alpha(k,l)+SCF_density_matrix_ao_beta(k,l)
-             c1 = SCF_density_matrix_ao_alpha(k,i)
-             c2 = SCF_density_matrix_ao_beta(k,i)
-             if ( dabs(c0)+dabs(c1)+dabs(c2) < local_threshold) then
-               cycle
-             endif
-             if (values(1) == 0.d0) then
-               values(1) = ao_two_e_integral(k0,l0,i0,j0)
-             endif
-             integral = c0 * values(1)
-             ao_two_e_integral_alpha_tmp(i,j) += integral
-             ao_two_e_integral_beta_tmp (i,j) += integral
-             integral = values(1)
-             ao_two_e_integral_alpha_tmp(l,j) -= c1 * integral
-             ao_two_e_integral_beta_tmp (l,j) -= c2 * integral
-           enddo
-   enddo
-   !$OMP END DO NOWAIT
-   !$OMP CRITICAL
-   ao_two_e_integral_alpha += ao_two_e_integral_alpha_tmp
-   ao_two_e_integral_beta  += ao_two_e_integral_beta_tmp
-   !$OMP END CRITICAL
-   deallocate(keys,values,ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp)
-   !$OMP END PARALLEL
- else
-   PROVIDE ao_two_e_integrals_in_map
 
-   integer(omp_lock_kind) :: lck(ao_num)
+     q = ao_num*ao_num*ao_num*ao_num
-   integer(map_size_kind)     :: i8
+     !$OMP DO SCHEDULE(static,64)
-   integer                        :: ii(8), jj(8), kk(8), ll(8), k2
+     do p=1_8,q
-   integer(cache_map_size_kind)   :: n_elements_max, n_elements
+       call two_e_integrals_index_reverse(kk,ii,ll,jj,p)
-   integer(key_kind), allocatable :: keys(:)
+       if ( (kk(1)>ao_num).or.                                       &
-   double precision, allocatable  :: values(:)
+             (ii(1)>ao_num).or.                                      &
-
+             (jj(1)>ao_num).or.                                      &
-   !$OMP PARALLEL DEFAULT(NONE)                                      &
+             (ll(1)>ao_num) ) then
-       !$OMP PRIVATE(i,j,l,k1,k,integral,ii,jj,kk,ll,i8,keys,values,n_elements_max, &
+         cycle
-       !$OMP  n_elements,ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp)&
+       endif
-       !$OMP SHARED(ao_num,SCF_density_matrix_ao_alpha,SCF_density_matrix_ao_beta,&
+       k = kk(1)
-       !$OMP  ao_integrals_map, ao_two_e_integral_alpha, ao_two_e_integral_beta)
+       i = ii(1)
-
+       l = ll(1)
-   call get_cache_map_n_elements_max(ao_integrals_map,n_elements_max)
+       j = jj(1)
-   allocate(keys(n_elements_max), values(n_elements_max))
-   allocate(ao_two_e_integral_alpha_tmp(ao_num,ao_num), &
-            ao_two_e_integral_beta_tmp(ao_num,ao_num))
-   ao_two_e_integral_alpha_tmp = 0.d0
-   ao_two_e_integral_beta_tmp  = 0.d0
-
-   !$OMP DO SCHEDULE(static,1)
-   do i8=0_8,ao_integrals_map%map_size
-     n_elements = n_elements_max
-     call get_cache_map(ao_integrals_map,i8,keys,values,n_elements)
-     do k1=1,n_elements
-       call two_e_integrals_index_reverse(kk,ii,ll,jj,keys(k1))
 
+       logical, external              :: ao_two_e_integral_zero
+       if (ao_two_e_integral_zero(i,k,j,l)) then
+         cycle
+       endif
+       local_threshold = ao_two_e_integral_schwartz(k,l)*ao_two_e_integral_schwartz(i,j)
+       if (local_threshold < ao_integrals_threshold) then
+         cycle
+       endif
+       i0 = i
+       j0 = j
+       k0 = k
+       l0 = l
+       values(1) = 0.d0
+       local_threshold = ao_integrals_threshold/local_threshold
        do k2=1,8
          if (kk(k2)==0) then
            cycle
@@ -132,25 +76,162 @@
          j = jj(k2)
          k = kk(k2)
          l = ll(k2)
-         integral = (SCF_density_matrix_ao_alpha(k,l)+SCF_density_matrix_ao_beta(k,l)) * values(k1)
+         c0 = SCF_density_matrix_ao_alpha(k,l)+SCF_density_matrix_ao_beta(k,l)
+         c1 = SCF_density_matrix_ao_alpha(k,i)
+         c2 = SCF_density_matrix_ao_beta(k,i)
+         if ( dabs(c0)+dabs(c1)+dabs(c2) < local_threshold) then
+           cycle
+         endif
+         if (values(1) == 0.d0) then
+           values(1) = ao_two_e_integral(k0,l0,i0,j0)
+         endif
+         integral = c0 * values(1)
          ao_two_e_integral_alpha_tmp(i,j) += integral
          ao_two_e_integral_beta_tmp (i,j) += integral
-         integral = values(k1)
+         integral = values(1)
-         ao_two_e_integral_alpha_tmp(l,j) -= SCF_density_matrix_ao_alpha(k,i) * integral
+         ao_two_e_integral_alpha_tmp(l,j) -= c1 * integral
-         ao_two_e_integral_beta_tmp (l,j) -= SCF_density_matrix_ao_beta (k,i) * integral
+         ao_two_e_integral_beta_tmp (l,j) -= c2 * integral
        enddo
      enddo
-   enddo
+     !$OMP END DO NOWAIT
-   !$OMP END DO NOWAIT
+     !$OMP CRITICAL
-   !$OMP CRITICAL
+     ao_two_e_integral_alpha += ao_two_e_integral_alpha_tmp
-   ao_two_e_integral_alpha += ao_two_e_integral_alpha_tmp
+     ao_two_e_integral_beta  += ao_two_e_integral_beta_tmp
-   ao_two_e_integral_beta  += ao_two_e_integral_beta_tmp
+     !$OMP END CRITICAL
-   !$OMP END CRITICAL
+     deallocate(keys,values,ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp)
-   deallocate(keys,values,ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp)
+     !$OMP END PARALLEL
-   !$OMP END PARALLEL
+   else
+     PROVIDE ao_two_e_integrals_in_map
 
+     integer(omp_lock_kind)         :: lck(ao_num)
+     integer(map_size_kind)         :: i8
+     integer                        :: ii(8), jj(8), kk(8), ll(8), k2
+     integer(cache_map_size_kind)   :: n_elements_max, n_elements
+     integer(key_kind), allocatable :: keys(:)
+     double precision, allocatable  :: values(:)
+
+     !$OMP PARALLEL DEFAULT(NONE)                                    &
+         !$OMP PRIVATE(i,j,l,k1,k,integral,ii,jj,kk,ll,i8,keys,values,n_elements_max,&
+         !$OMP  n_elements,ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp)&
+         !$OMP SHARED(ao_num,SCF_density_matrix_ao_alpha,SCF_density_matrix_ao_beta,&
+         !$OMP  ao_integrals_map, ao_two_e_integral_alpha, ao_two_e_integral_beta)
+
+     call get_cache_map_n_elements_max(ao_integrals_map,n_elements_max)
+     allocate(keys(n_elements_max), values(n_elements_max))
+     allocate(ao_two_e_integral_alpha_tmp(ao_num,ao_num),            &
+         ao_two_e_integral_beta_tmp(ao_num,ao_num))
+     ao_two_e_integral_alpha_tmp = 0.d0
+     ao_two_e_integral_beta_tmp  = 0.d0
+
+     !$OMP DO SCHEDULE(static,1)
+     do i8=0_8,ao_integrals_map%map_size
+       n_elements = n_elements_max
+       call get_cache_map(ao_integrals_map,i8,keys,values,n_elements)
+       do k1=1,n_elements
+         call two_e_integrals_index_reverse(kk,ii,ll,jj,keys(k1))
+
+         do k2=1,8
+           if (kk(k2)==0) then
+             cycle
+           endif
+           i = ii(k2)
+           j = jj(k2)
+           k = kk(k2)
+           l = ll(k2)
+           integral = (SCF_density_matrix_ao_alpha(k,l)+SCF_density_matrix_ao_beta(k,l)) * values(k1)
+           ao_two_e_integral_alpha_tmp(i,j) += integral
+           ao_two_e_integral_beta_tmp (i,j) += integral
+           integral = values(k1)
+           ao_two_e_integral_alpha_tmp(l,j) -= SCF_density_matrix_ao_alpha(k,i) * integral
+           ao_two_e_integral_beta_tmp (l,j) -= SCF_density_matrix_ao_beta (k,i) * integral
+         enddo
+       enddo
+     enddo
+     !$OMP END DO NOWAIT
+     !$OMP CRITICAL
+     ao_two_e_integral_alpha += ao_two_e_integral_alpha_tmp
+     ao_two_e_integral_beta  += ao_two_e_integral_beta_tmp
+     !$OMP END CRITICAL
+     deallocate(keys,values,ao_two_e_integral_alpha_tmp,ao_two_e_integral_beta_tmp)
+     !$OMP END PARALLEL
+
+   endif
  endif
 
+END_PROVIDER
+
+ BEGIN_PROVIDER [ double precision, ao_two_e_integral_alpha_chol, (ao_num, ao_num) ]
+&BEGIN_PROVIDER [ double precision, ao_two_e_integral_beta_chol ,  (ao_num, ao_num) ]
+ use map_module
+ implicit none
+ BEGIN_DOC
+ ! Alpha and Beta Fock matrices in AO basis set
+ END_DOC
+
+ integer :: m,n,l,s,j
+ double precision :: integral
+ double precision, allocatable :: X(:), X2(:,:,:,:), X3(:,:,:,:)
+
+ allocate (X(cholesky_ao_num))
+
+
+ ! X(j) = \sum_{mn} SCF_density_matrix_ao(m,n) * cholesky_ao(m,n,j)
+ call dgemm('T','N',cholesky_ao_num,1,ao_num*ao_num,1.d0,            &
+     cholesky_ao, ao_num*ao_num,                                     &
+     SCF_density_matrix_ao, ao_num*ao_num,0.d0,                      &
+     X, cholesky_ao_num)
+!
+
+ ! ao_two_e_integral_alpha(m,n) = \sum_{j} cholesky_ao(m,n,j) * X(j)
+ call dgemm('N','N',ao_num*ao_num,1,cholesky_ao_num, 1.d0,           &
+     cholesky_ao, ao_num*ao_num,                                     &
+     X, cholesky_ao_num, 0.d0,                                       &
+     ao_two_e_integral_alpha_chol, ao_num*ao_num)
+
+ deallocate(X)
+
+ ao_two_e_integral_beta_chol = ao_two_e_integral_alpha_chol
+
+
+ allocate(X2(ao_num,ao_num,cholesky_ao_num,2))
+
+! ao_two_e_integral_alpha_chol (l,s) -= cholesky_ao(l,m,j) * SCF_density_matrix_ao_beta (m,n) * cholesky_ao(n,s,j)
+
+ call dgemm('N','N',ao_num,ao_num*cholesky_ao_num,ao_num, 1.d0,      &
+     SCF_density_matrix_ao_alpha, ao_num,                            &
+     cholesky_ao, ao_num, 0.d0,                                      &
+     X2(1,1,1,1), ao_num)
+
+ call dgemm('N','N',ao_num,ao_num*cholesky_ao_num,ao_num, 1.d0,      &
+     SCF_density_matrix_ao_beta, ao_num,                             &
+     cholesky_ao, ao_num, 0.d0,                                      &
+     X2(1,1,1,2), ao_num)
+
+ allocate(X3(ao_num,cholesky_ao_num,ao_num,2))
+
+ do s=1,ao_num
+  do j=1,cholesky_ao_num
+   do m=1,ao_num
+    X3(m,j,s,1) = X2(m,s,j,1)
+    X3(m,j,s,2) = X2(m,s,j,2)
+   enddo
+  enddo
+ enddo
+
+ deallocate(X2)
+
+ call dgemm('N','N',ao_num,ao_num,ao_num*cholesky_ao_num, -1.d0,     &
+     cholesky_ao, ao_num,                                            &
+     X3(1,1,1,1), ao_num*cholesky_ao_num, 1.d0,                      &
+     ao_two_e_integral_alpha_chol, ao_num)
+
+ call dgemm('N','N',ao_num,ao_num,ao_num*cholesky_ao_num, -1.d0,     &
+     cholesky_ao, ao_num,                                            &
+     X3(1,1,1,2), ao_num*cholesky_ao_num, 1.d0,                      &
+     ao_two_e_integral_beta_chol, ao_num)
+
+ deallocate(X3)
+
 END_PROVIDER
 
  BEGIN_PROVIDER [ double precision, Fock_matrix_ao_alpha, (ao_num, ao_num) ]

src/utils/linear_algebra.irp.f

@@ -1854,7 +1854,7 @@ do k = 1, N
 end do
 ! TODO: It should be possible to use only one vector of size (1:rank) as a buffer
 ! to do the swapping in-place
-U = 0.00D+0
+U(:,:) = 0.00D+0
 do k = 1, N
   l = piv(k)
   U(l, :) = A(1:rank, k)