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qp2/src/ao_two_e_ints/cholesky.irp.f

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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
BEGIN_PROVIDER [ integer, cholesky_ao_num ]
&BEGIN_PROVIDER [ double precision, cholesky_ao, (ao_num, ao_num, 1) ]
implicit none
BEGIN_DOC
! Cholesky vectors in AO basis: (ik|a):
! <ij|kl> = (ik|jl) = sum_a (ik|a).(a|jl)
!
! Last dimension of cholesky_ao is cholesky_ao_num
END_DOC
integer :: rank, ndim
double precision :: tau
double precision, pointer :: L(:,:), L_old(:,:)
double precision :: s
double precision, parameter :: dscale = 1.d0
double precision, allocatable :: D(:), Delta(:,:), Ltmp_p(:,:), Ltmp_q(:,:)
integer, allocatable :: Lset(:), Dset(:), addr(:,:)
logical, allocatable :: computed(:)
integer :: i,j,k,m,p,q, qj, dj, p2, q2
integer :: N, np, nq
double precision :: Dmax, Dmin, Qmax, f
double precision, external :: get_ao_two_e_integral
logical, external :: ao_two_e_integral_zero
double precision, external :: ao_two_e_integral
integer :: block_size, iblock, ierr
double precision :: mem
double precision, external :: memory_of_double, memory_of_int
integer, external :: getUnitAndOpen
integer :: iunit
ndim = ao_num*ao_num
deallocate(cholesky_ao)
if (read_ao_cholesky) then
print *, 'Reading Cholesky vectors from disk...'
iunit = getUnitAndOpen(trim(ezfio_work_dir)//'cholesky_ao', 'R')
read(iunit) rank
allocate(cholesky_ao(ao_num,ao_num,rank), stat=ierr)
read(iunit) cholesky_ao
close(iunit)
cholesky_ao_num = rank
else
PROVIDE nucl_coord ao_two_e_integral_schwartz
call set_multiple_levels_omp(.False.)
if (do_direct_integrals) then
if (ao_two_e_integral(1,1,1,1) < huge(1.d0)) then
! Trigger providers inside ao_two_e_integral
continue
endif
else
PROVIDE ao_two_e_integrals_in_map
endif
tau = ao_cholesky_threshold
mem = 6.d0 * memory_of_double(ndim) + 6.d0 * memory_of_int(ndim)
call check_mem(mem, irp_here)
call print_memory_usage()
allocate(L(ndim,1))
print *, ''
print *, 'Cholesky decomposition of AO integrals'
print *, '======================================'
print *, ''
print *, '============ ============='
print *, ' Rank Threshold'
print *, '============ ============='
rank = 0
allocate( D(ndim), Lset(ndim), Dset(ndim) )
allocate( addr(3,ndim) )
! 1.
k=0
do j=1,ao_num
do i=1,ao_num
k = k+1
addr(1,k) = i
addr(2,k) = j
addr(3,k) = (i-1)*ao_num + j
enddo
enddo
if (do_direct_integrals) then
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i) SCHEDULE(guided)
do i=1,ndim
D(i) = ao_two_e_integral(addr(1,i), addr(2,i), &
addr(1,i), addr(2,i))
enddo
!$OMP END PARALLEL DO
else
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i) SCHEDULE(guided)
do i=1,ndim
D(i) = get_ao_two_e_integral(addr(1,i), addr(1,i), &
addr(2,i), addr(2,i), &
ao_integrals_map)
enddo
!$OMP END PARALLEL DO
endif
Dmax = maxval(D)
! 2.
np=0
do p=1,ndim
if ( dscale*dscale*Dmax*D(p) > tau*tau ) then
np = np+1
Lset(np) = p
endif
enddo
! 3.
N = 0
! 4.
i = 0
! 5.
do while ( (Dmax > tau).and.(rank < ndim) )
! a.
i = i+1
s = 0.01d0
! Inrease s until the arrays fit in memory
do while (.True.)
! b.
Dmin = max(s*Dmax,tau)
! c.
nq=0
do p=1,np
if ( D(Lset(p)) > Dmin ) then
nq = nq+1
Dset(nq) = Lset(p)
endif
enddo
call total_memory(mem)
mem = mem &
+ np*memory_of_double(nq) &! Delta(np,nq)
+ (rank+nq)* memory_of_double(ndim) &! L(ndim,rank+nq)
+ (np+nq)*memory_of_double(block_size) ! Ltmp_p(np,block_size) + Ltmp_q(nq,block_size)
if (mem > qp_max_mem) then
s = s*2.d0
else
exit
endif
if ((s > 1.d0).or.(nq == 0)) then
call print_memory_usage()
print *, 'Not enough memory. Reduce cholesky threshold'
stop -1
endif
enddo
! d., e.
block_size = max(N,24)
L_old => L
allocate(L(ndim,rank+nq), stat=ierr)
if (ierr /= 0) then
call print_memory_usage()
print *, irp_here, ': allocation failed : (L(ndim,rank+nq))'
stop -1
endif
!$OMP PARALLEL DO PRIVATE(k,j)
do k=1,rank
do j=1,ndim
L(j,k) = L_old(j,k)
enddo
enddo
!$OMP END PARALLEL DO
deallocate(L_old)
allocate(Delta(np,nq), stat=ierr)
if (ierr /= 0) then
call print_memory_usage()
print *, irp_here, ': allocation failed : (Delta(np,nq))'
stop -1
endif
allocate(Ltmp_p(np,block_size), stat=ierr)
if (ierr /= 0) then
call print_memory_usage()
print *, irp_here, ': allocation failed : (Ltmp_p(np,block_size))'
stop -1
endif
allocate(Ltmp_q(nq,block_size), stat=ierr)
if (ierr /= 0) then
call print_memory_usage()
print *, irp_here, ': allocation failed : (Ltmp_q(nq,block_size))'
stop -1
endif
allocate(computed(nq))
!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(m,k,p,q,j)
!$OMP DO
do q=1,nq
do j=1,np
Delta(j,q) = 0.d0
enddo
computed(q) = .False.
enddo
!$OMP ENDDO NOWAIT
!$OMP DO
do k=1,N
do p=1,np
Ltmp_p(p,k) = L(Lset(p),k)
enddo
do q=1,nq
Ltmp_q(q,k) = L(Dset(q),k)
enddo
enddo
!$OMP END DO NOWAIT
!$OMP BARRIER
!$OMP END PARALLEL
if (N>0) then
call dgemm('N','T', np, nq, N, -1.d0, &
Ltmp_p, np, Ltmp_q, nq, 1.d0, Delta, np)
endif
! f.
Qmax = D(Dset(1))
do q=1,nq
Qmax = max(Qmax, D(Dset(q)))
enddo
! g.
iblock = 0
do j=1,nq
if ( (Qmax <= Dmin).or.(N+j > ndim) ) exit
! i.
rank = N+j
if (iblock == block_size) then
call dgemm('N','T',np,nq,block_size,-1.d0, &
Ltmp_p, np, Ltmp_q, nq, 1.d0, Delta, np)
iblock = 0
endif
! ii.
do dj=1,nq
qj = Dset(dj)
if (D(qj) == Qmax) then
exit
endif
enddo
L(1:ndim, rank) = 0.d0
if (.not.computed(dj)) then
m = dj
!$OMP PARALLEL DO PRIVATE(k) SCHEDULE(guided)
do k=np,1,-1
if (.not.ao_two_e_integral_zero( addr(1,Lset(k)), addr(1,Dset(m)),&
addr(2,Lset(k)), addr(2,Dset(m)) ) ) then
if (do_direct_integrals) then
Delta(k,m) = Delta(k,m) + &
ao_two_e_integral(addr(1,Lset(k)), addr(2,Lset(k)),&
addr(1,Dset(m)), addr(2,Dset(m)))
else
Delta(k,m) = Delta(k,m) + &
get_ao_two_e_integral( addr(1,Lset(k)), addr(1,Dset(m)),&
addr(2,Lset(k)), addr(2,Dset(m)), ao_integrals_map)
endif
endif
enddo
!$OMP END PARALLEL DO
computed(dj) = .True.
endif
iblock = iblock+1
do p=1,np
Ltmp_p(p,iblock) = Delta(p,dj)
enddo
! iv.
if (iblock > 1) then
call dgemv('N', np, iblock-1, -1.d0, Ltmp_p, np, Ltmp_q(dj,1), nq, 1.d0,&
Ltmp_p(1,iblock), 1)
endif
! iii.
f = 1.d0/dsqrt(Qmax)
!$OMP PARALLEL PRIVATE(m,p,q,k) DEFAULT(shared)
!$OMP DO
do p=1,np
Ltmp_p(p,iblock) = Ltmp_p(p,iblock) * f
L(Lset(p), rank) = Ltmp_p(p,iblock)
D(Lset(p)) = D(Lset(p)) - Ltmp_p(p,iblock) * Ltmp_p(p,iblock)
enddo
!$OMP END DO
!$OMP DO
do q=1,nq
Ltmp_q(q,iblock) = L(Dset(q), rank)
enddo
!$OMP END DO
!$OMP END PARALLEL
Qmax = D(Dset(1))
do q=1,nq
Qmax = max(Qmax, D(Dset(q)))
enddo
enddo
print '(I10, 4X, ES12.3)', rank, Qmax
deallocate(computed)
deallocate(Delta)
deallocate(Ltmp_p)
deallocate(Ltmp_q)
! i.
N = rank
! j.
Dmax = D(Lset(1))
do p=1,np
Dmax = max(Dmax, D(Lset(p)))
enddo
np=0
do p=1,ndim
if ( dscale*dscale*Dmax*D(p) > tau*tau ) then
np = np+1
Lset(np) = p
endif
enddo
enddo
allocate(cholesky_ao(ao_num,ao_num,rank), stat=ierr)
if (ierr /= 0) then
call print_memory_usage()
print *, irp_here, ': Allocation failed'
stop -1
endif
!$OMP PARALLEL DO PRIVATE(k)
do k=1,rank
call dcopy(ndim, L(1,k), 1, cholesky_ao(1,1,k), 1)
enddo
!$OMP END PARALLEL DO
deallocate(L)
cholesky_ao_num = rank
print *, '============ ============='
print *, ''
if (write_ao_cholesky) then
print *, 'Writing Cholesky vectors to disk...'
iunit = getUnitAndOpen(trim(ezfio_work_dir)//'cholesky_ao', 'W')
write(iunit) rank
write(iunit) cholesky_ao
close(iunit)
call ezfio_set_ao_two_e_ints_io_ao_cholesky('Read')
endif
endif
print *, 'Rank : ', cholesky_ao_num, '(', 100.d0*dble(cholesky_ao_num)/dble(ao_num*ao_num), ' %)'
print *, ''
END_PROVIDER
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