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Cholesky OK
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Anthony Scemama 2023-07-03 18:19:31 +02:00
parent d911f4eee8
commit 487e85c6ae

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@ -34,106 +34,11 @@ END_PROVIDER
! <ij|kl> = (ik|jl) = sum_a (ik|a).(a|jl)
END_DOC
type(c_ptr) :: ptr
integer :: fd, i,j,k,l,m,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/))
print*, 'Providing the AO integrals (Cholesky)'
call wall_time(wall_1)
call cpu_time(cpu_1)
ao_integrals = 0.d0
double precision :: integral, cpu_1, cpu_2, wall_1, wall_2
logical, external :: ao_two_e_integral_zero
double precision, external :: get_ao_two_e_integral
if (read_ao_two_e_integrals) then
PROVIDE ao_two_e_integrals_in_map
!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l, integral, wall_2)
do m=0,9
do l=1+m,ao_num,10
!$OMP DO SCHEDULE(dynamic)
do j=1,ao_num
do k=1,ao_num
do i=1,ao_num
if (ao_two_e_integral_zero(i,j,k,l)) cycle
integral = get_ao_two_e_integral(i,j,k,l, ao_integrals_map)
ao_integrals(i,k,j,l) = integral
enddo
enddo
enddo
!$OMP END DO NOWAIT
enddo
!$OMP MASTER
call wall_time(wall_2)
print '(I10,'' % in'', 4X, F10.2, '' s.'')', (m+1) * 10, wall_2-wall_1
!$OMP END MASTER
enddo
!$OMP END PARALLEL
else
!$OMP PARALLEL DEFAULT(SHARED) PRIVATE(i,j,k,l, integral, wall_2)
do m=0,9
do l=1+m,ao_num,10
!$OMP DO SCHEDULE(dynamic)
do j=1,l
do k=1,ao_num
do i=1,min(k,j)
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
ao_integrals(j,l,i,k) = integral
ao_integrals(j,l,k,i) = integral
ao_integrals(l,j,i,k) = integral
ao_integrals(l,j,k,i) = integral
enddo
enddo
enddo
!$OMP END DO NOWAIT
enddo
!$OMP MASTER
call wall_time(wall_2)
print '(I10,'' % in'', 4X, F10.2, '' s.'')', (m+1) * 10, wall_2-wall_1
!$OMP END MASTER
enddo
!$OMP END PARALLEL
call wall_time(wall_2)
call cpu_time(cpu_2)
print*, 'AO integrals provided:'
print*, ' cpu time :',cpu_2 - cpu_1, 's'
print*, ' wall time :',wall_2 - wall_1, 's ( x ', (cpu_2-cpu_1)/(wall_2-wall_1+tiny(1.d0)), ' )'
endif
! Call Lapack
cholesky_ao_num = cholesky_ao_num_guess
! call pivoted_cholesky(ao_integrals, cholesky_ao_num, ao_cholesky_threshold, ao_num*ao_num, cholesky_ao)
call direct_cholesky(ao_integrals, cholesky_ao_num, ao_cholesky_threshold, ao_num*ao_num, cholesky_ao)
call direct_cholesky(cholesky_ao, ao_num*ao_num, cholesky_ao_num, ao_cholesky_threshold)
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) ]
@ -152,35 +57,53 @@ BEGIN_PROVIDER [ double precision, cholesky_ao_transp, (cholesky_ao_num, ao_num,
END_PROVIDER
subroutine direct_cholesky( A, rank, tau, ndim, L)
subroutine direct_cholesky(L, ndim, rank, tau)
implicit none
BEGIN_DOC
! Cholesky-decomposed AOs.
!
! https://www.diva-portal.org/smash/get/diva2:396223/FULLTEXT01.pdf :
! Page 32, section 13.5
END_DOC
integer :: ndim
integer, intent(inout) :: rank
double precision, intent(inout) :: A(ndim, ndim)
double precision, intent(out) :: L(ndim, rank)
integer, intent(out) :: rank
double precision, intent(out) :: L(ndim, ndim)
double precision, intent(in) :: tau
double precision, parameter :: s = 1.d-2
double precision, parameter :: dscale = 1.d0
double precision, allocatable :: D(:), Delta(:,:)
integer, allocatable :: Lset(:), Dset(:)
integer, allocatable :: Lset(:), Dset(:), addr(:,:)
integer :: i,j,k,m,p,q, qj, dj
integer :: N, np, nq
double precision :: Dmax, Dmin, Qmax, f
allocate( D(ndim), Lset(ndim), Dset(ndim) )
double precision, external :: get_ao_two_e_integral
L = 0.d0
allocate( D(ndim), Lset(ndim), Dset(ndim) )
allocate( addr(2,ndim) )
! 1.
do i=1,ndim
D(i) = A(i,i)
k=0
do i=1,ao_num
do j=1,ao_num
k = k+1
addr(1,k) = i
addr(2,k) = j
enddo
enddo
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i)
do i=1,ndim
D(i) = get_ao_two_e_integral(addr(1,i), addr(1,i), &
addr(2,i), addr(2,i), &
ao_integrals_map)
enddo
!$OMP END PARALLEL DO
Dmax = maxval(D)
! print *, '# 1. ', D
! print *, '# 1. ', Dmax
! 2.
np=0
@ -190,25 +113,20 @@ subroutine direct_cholesky( A, rank, tau, ndim, L)
Lset(np) = p
endif
enddo
! print *, '# 2. ', Lset(:np)
! 3.
N = 0
! print *, '# 3. ', N
! 4.
! 4.
i = 0
! print *, '# 4. ', i
! 5.
! 5.
do while (Dmax > tau)
! a.
i = i+1
! print *, '# 5.a ', i
! b.
Dmin = max(s*Dmax, tau)
! print *, '# 5.b ', Dmin
! c.
nq=0
@ -218,43 +136,42 @@ subroutine direct_cholesky( A, rank, tau, ndim, L)
Dset(nq) = Lset(q)
endif
enddo
! print *, '# 5.c ', Dset(:nq)
! d.
! d., e.
allocate(Delta(np,nq))
!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(m,k)
do m=1,nq
do k=1,np
Delta(k,m) = A(Lset(k), Dset(m))
Delta(k,m) = get_ao_two_e_integral( &
addr(1,Lset(k)), &
addr(1,Dset(m)), &
addr(2,Lset(k)), &
addr(2,Dset(m)), &
ao_integrals_map)
enddo
enddo
! print *, '# 5.d ', Delta
! e.
do m=1,nq
do k=1,np
do p=1,N
Delta(k,m) = Delta(k,m) - L(Lset(k),p) * L(Dset(m),p)
do p=1,N
f = L(Dset(m),p)
do k=1,np
Delta(k,m) = Delta(k,m) - L(Lset(k),p) * f
enddo
enddo
enddo
! print *, '# 5.e ', Delta
!$OMP END PARALLEL DO
! f.
Qmax = D(Dset(1))
do q=1,nq
Qmax = max(Qmax, D(Dset(q)))
enddo
! print *, '# 5.f ', Qmax
! g.
j = 0
! print *, '# 5.g ', j
do while ( (j <= nq).and.(Qmax > Dmin) )
! i.
j = j+1
rank = N+j
! print *, '# 5.h.i ', j, rank
! ii.
do dj=1,nq
@ -263,22 +180,18 @@ subroutine direct_cholesky( A, rank, tau, ndim, L)
exit
endif
enddo
! print *, ' # 5.h.ii ', qj, dj
! iii.
f = 1.d0/dsqrt(Qmax)
do p=1,np
L(Lset(p), rank) = Delta(p,dj) * f
enddo
! print *, ' # 5.h.iii '
! do k=1,20
! print *, L(k,1:rank)
! enddo
! iv.
do m=1, nq
f = L(Dset(m),rank)
do k=1, np
Delta(k,m) = Delta(k,m) - L(Lset(k),rank) * L(Dset(m),rank)
Delta(k,m) = Delta(k,m) - L(Lset(k),rank) * f
enddo
enddo
@ -290,9 +203,6 @@ subroutine direct_cholesky( A, rank, tau, ndim, L)
do q=1,np
Qmax = max(Qmax, D(Lset(q)))
enddo
! print *, '# 5.h.iv ', Delta
! print *, '# 5.h.iv ', D
! print *, '# 5.h.iv ', Qmax
enddo
@ -300,14 +210,12 @@ subroutine direct_cholesky( A, rank, tau, ndim, L)
! i.
N = N+j
! print *, '# 5.i ', N
! j.
Dmax = D(Lset(1))
do p=1,np
Dmax = max(Dmax, D(Lset(p)))
enddo
! print *, '# 5.j ', Dmax
np=0
do p=1,ndim
@ -316,7 +224,7 @@ subroutine direct_cholesky( A, rank, tau, ndim, L)
Lset(np) = p
endif
enddo
! print *, '# k. ', Lset(:np)
enddo
end