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qp2/src/utils/linear_algebra.irp.f

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subroutine svd(A,LDA,U,LDU,D,Vt,LDVt,m,n)
implicit none
BEGIN_DOC
! Compute A = U.D.Vt
!
! LDx : leftmost dimension of x
!
! Dimsneion of A is m x n
!
END_DOC
integer, intent(in) :: LDA, LDU, LDVt, m, n
double precision, intent(in) :: A(LDA,n)
double precision, intent(out) :: U(LDU,m)
double precision,intent(out) :: Vt(LDVt,n)
double precision,intent(out) :: D(min(m,n))
double precision,allocatable :: work(:)
integer :: info, lwork, i, j, k
double precision,allocatable :: A_tmp(:,:)
allocate (A_tmp(LDA,n))
A_tmp = A
! Find optimal size for temp arrays
allocate(work(1))
lwork = -1
call dgesvd('A','A', m, n, A_tmp, LDA, &
D, U, LDU, Vt, LDVt, work, lwork, info)
! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
lwork = max(int(work(1)), 5*MIN(M,N))
deallocate(work)
allocate(work(lwork))
call dgesvd('A','A', m, n, A_tmp, LDA, &
D, U, LDU, Vt, LDVt, work, lwork, info)
deallocate(work,A_tmp)
if (info /= 0) then
print *, info, ': SVD failed'
stop
endif
end
subroutine svd_complex(A,LDA,U,LDU,D,Vt,LDVt,m,n)
implicit none
BEGIN_DOC
! Compute A = U.D.Vt
!
! LDx : leftmost dimension of x
!
! Dimension of A is m x n
! A,U,Vt are complex*16
! D is double precision
END_DOC
integer, intent(in) :: LDA, LDU, LDVt, m, n
complex*16, intent(in) :: A(LDA,n)
complex*16, intent(out) :: U(LDU,m)
complex*16, intent(out) :: Vt(LDVt,n)
double precision,intent(out) :: D(min(m,n))
complex*16,allocatable :: work(:)
double precision,allocatable :: rwork(:)
integer :: info, lwork, i, j, k, lrwork
complex*16,allocatable :: A_tmp(:,:)
allocate (A_tmp(LDA,n))
A_tmp = A
lrwork = 5*min(m,n)
! Find optimal size for temp arrays
allocate(work(1),rwork(lrwork))
lwork = -1
call zgesvd('A','A', m, n, A_tmp, LDA, &
D, U, LDU, Vt, LDVt, work, lwork, rwork, info)
lwork = int(work(1))
deallocate(work)
allocate(work(lwork))
call zgesvd('A','A', m, n, A_tmp, LDA, &
D, U, LDU, Vt, LDVt, work, lwork, rwork, info)
deallocate(work,rwork,A_tmp)
if (info /= 0) then
print *, info, ': SVD failed'
stop
endif
end
subroutine ortho_canonical_complex(overlap,LDA,N,C,LDC,m,cutoff)
implicit none
BEGIN_DOC
! Compute C_new=C_old.U.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
integer, intent(out) :: m
complex*16, intent(in) :: overlap(lda,n)
double precision, intent(in) :: cutoff
complex*16, intent(inout) :: C(ldc,n)
complex*16, allocatable :: U(:,:)
complex*16, allocatable :: Vt(:,:)
double precision, allocatable :: D(:)
complex*16, allocatable :: S(:,:)
!DIR$ ATTRIBUTES ALIGN : 64 :: U, Vt, D
integer :: info, i, j
if (n < 2) then
return
endif
allocate (U(ldc,n), Vt(lda,n), D(n), S(lda,n))
call svd_complex(overlap,lda,U,ldc,D,Vt,lda,n,n)
D(:) = dsqrt(D(:))
m=n
do i=1,n
if ( D(i) >= cutoff ) then
D(i) = 1.d0/D(i)
else
m = i-1
print *, 'Removed Linear dependencies below:', 1.d0/D(m)
exit
endif
enddo
do i=m+1,n
D(i) = 0.d0
enddo
do i=1,m
if ( D(i) >= 1.d5 ) then
print *, 'Warning: Basis set may have linear dependence problems'
endif
enddo
do j=1,n
do i=1,n
S(i,j) = U(i,j)*D(j)
enddo
enddo
do j=1,n
do i=1,n
U(i,j) = C(i,j)
enddo
enddo
call zgemm('N','N',n,n,n,(1.d0,0.d0),U,size(U,1),S,size(S,1),(0.d0,0.d0),C,size(C,1))
deallocate (U, Vt, D, S)
end
subroutine ortho_qr_complex(A,LDA,m,n)
implicit none
BEGIN_DOC
! Orthogonalization using Q.R factorization
!
! A : matrix to orthogonalize
!
! LDA : leftmost dimension of A
!
! n : Number of rows of A
!
! m : Number of columns of A
!
END_DOC
integer, intent(in) :: m,n, LDA
complex*16, intent(inout) :: A(LDA,n)
integer :: lwork, info
integer, allocatable :: jpvt(:)
complex*16, allocatable :: tau(:), work(:)
allocate (jpvt(n), tau(n), work(1))
LWORK=-1
call zgeqrf( m, n, A, LDA, TAU, WORK, LWORK, INFO )
LWORK=2*int(WORK(1))
deallocate(WORK)
allocate(WORK(LWORK))
call zgeqrf(m, n, A, LDA, TAU, WORK, LWORK, INFO )
call zungqr(m, n, n, A, LDA, tau, WORK, LWORK, INFO)
deallocate(WORK,jpvt,tau)
end
subroutine ortho_qr_unblocked_complex(A,LDA,m,n)
implicit none
BEGIN_DOC
! Orthogonalization using Q.R factorization
!
! A : matrix to orthogonalize
!
! LDA : leftmost dimension of A
!
! n : Number of rows of A
!
! m : Number of columns of A
!
END_DOC
integer, intent(in) :: m,n, LDA
double precision, intent(inout) :: A(LDA,n)
integer :: info
integer, allocatable :: jpvt(:)
double precision, allocatable :: tau(:), work(:)
print *, irp_here, ': TO DO'
stop -1
! allocate (jpvt(n), tau(n), work(n))
! call dgeqr2( m, n, A, LDA, TAU, WORK, INFO )
! call dorg2r(m, n, n, A, LDA, tau, WORK, INFO)
! deallocate(WORK,jpvt,tau)
end
subroutine ortho_lowdin_complex(overlap,LDA,N,C,LDC,m,cutoff)
implicit none
BEGIN_DOC
! Compute C_new=C_old.S^-1/2 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
complex*16, intent(in) :: overlap(lda,n)
complex*16, intent(inout) :: C(ldc,n)
complex*16, allocatable :: U(:,:)
complex*16, allocatable :: Vt(:,:)
double precision, allocatable :: D(:)
complex*16, allocatable :: S(:,:)
double precision, intent(in) :: cutoff
integer :: info, i, j, k
if (n < 2) then
return
endif
allocate(U(ldc,n),Vt(lda,n),S(lda,n),D(n))
call svd_complex(overlap,lda,U,ldc,D,Vt,lda,n,n)
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(S,U,D,Vt,n,C,m,cutoff) &
!$OMP PRIVATE(i,j,k)
!$OMP DO
do i=1,n
if ( D(i) < cutoff) then
print *, 'Removed Linear dependencies :', 1.d0/D(i)
D(i) = 0.d0
else
D(i) = 1.d0/dsqrt(D(i))
endif
do j=1,n
S(j,i) = (0.d0,0.d0)
enddo
enddo
!$OMP END DO
do k=1,n
if (D(k) /= 0.d0) then
!$OMP DO
do j=1,n
do i=1,n
S(i,j) = S(i,j) + U(i,k)*D(k)*Vt(k,j)
enddo
enddo
!$OMP END DO NOWAIT
endif
enddo
!$OMP BARRIER
!$OMP DO
do j=1,n
do i=1,m
U(i,j) = C(i,j)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call zgemm('N','N',m,n,n,(1.d0,0.d0),U,size(U,1),S,size(S,1),(0.d0,0.d0),C,size(C,1))
deallocate(U,Vt,S,D)
end
subroutine get_inverse_complex(A,LDA,m,C,LDC)
implicit none
BEGIN_DOC
! Returns the inverse of the square matrix A
END_DOC
integer, intent(in) :: m, LDA, LDC
complex*16, intent(in) :: A(LDA,m)
complex*16, intent(out) :: C(LDC,m)
integer :: info,lwork
integer, allocatable :: ipiv(:)
complex*16,allocatable :: work(:)
allocate (ipiv(m), work(m*m))
lwork = size(work)
C(1:m,1:m) = A(1:m,1:m)
call zgetrf(m,m,C,size(C,1),ipiv,info)
if (info /= 0) then
print *, info
stop 'error in inverse (zgetrf)'
endif
call zgetri(m,C,size(C,1),ipiv,work,lwork,info)
if (info /= 0) then
print *, info
stop 'error in inverse (zgetri)'
endif
deallocate(ipiv,work)
end
subroutine get_pseudo_inverse_complex(A,LDA,m,n,C,LDC,cutoff)
implicit none
BEGIN_DOC
! Find C = A^-1
END_DOC
integer, intent(in) :: m,n, LDA, LDC
complex*16, intent(in) :: A(LDA,n)
double precision, intent(in) :: cutoff
complex*16, intent(out) :: C(LDC,m)
double precision, allocatable :: D(:), rwork(:)
complex*16, allocatable :: U(:,:), Vt(:,:), work(:), A_tmp(:,:)
integer :: info, lwork
integer :: i,j,k
allocate (D(n),U(m,n),Vt(n,n),work(1),A_tmp(m,n),rwork(5*n))
do j=1,n
do i=1,m
A_tmp(i,j) = A(i,j)
enddo
enddo
lwork = -1
call zgesvd('S','A', m, n, A_tmp, m,D,U,m,Vt,n,work,lwork,rwork,info)
if (info /= 0) then
print *, info, ': SVD failed'
stop
endif
lwork = int(real(work(1)))
deallocate(work)
allocate(work(lwork))
call zgesvd('S','A', m, n, A_tmp, m,D,U,m,Vt,n,work,lwork,rwork,info)
if (info /= 0) then
print *, info, ':: SVD failed'
stop 1
endif
do i=1,n
if (D(i)/D(1) > cutoff) then
D(i) = 1.d0/D(i)
else
D(i) = 0.d0
endif
enddo
C = (0.d0,0.d0)
do i=1,m
do j=1,n
do k=1,n
C(j,i) = C(j,i) + U(i,k) * D(k) * Vt(k,j)
enddo
enddo
enddo
deallocate(U,D,Vt,work,A_tmp,rwork)
end
subroutine lapack_diagd_diag_in_place_complex(eigvalues,eigvectors,nmax,n)
implicit none
BEGIN_DOC
! Diagonalize matrix H(complex)
!
! H is untouched between input and ouptut
!
! eigevalues(i) = ith lowest eigenvalue of the H matrix
!
! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
!
END_DOC
integer, intent(in) :: n,nmax
! double precision, intent(out) :: eigvectors(nmax,n)
complex*16, intent(inout) :: eigvectors(nmax,n)
double precision, intent(out) :: eigvalues(n)
! double precision, intent(in) :: H(nmax,n)
complex*16,allocatable :: work(:)
integer ,allocatable :: iwork(:)
! complex*16,allocatable :: A(:,:)
double precision, allocatable :: rwork(:)
integer :: lrwork, lwork, info, i,j,l,k, liwork
! print*,'Diagonalization by jacobi'
! print*,'n = ',n
lwork = 2*n*n + 2*n
lrwork = 2*n*n + 5*n+ 1
liwork = 5*n + 3
allocate (work(lwork),iwork(liwork),rwork(lrwork))
lwork = -1
liwork = -1
lrwork = -1
! get optimal work size
call ZHEEVD( 'V', 'U', n, eigvectors, nmax, eigvalues, work, lwork, &
rwork, lrwork, iwork, liwork, info )
if (info < 0) then
print *, irp_here, ': ZHEEVD: the ',-info,'-th argument had an illegal value'
stop 2
endif
lwork = int( real(work(1)))
liwork = iwork(1)
lrwork = int(rwork(1))
deallocate (work,iwork,rwork)
allocate (work(lwork),iwork(liwork),rwork(lrwork))
call ZHEEVD( 'V', 'U', n, eigvectors, nmax, eigvalues, work, lwork, &
rwork, lrwork, iwork, liwork, info )
deallocate(work,iwork,rwork)
if (info < 0) then
print *, irp_here, ': ZHEEVD: the ',-info,'-th argument had an illegal value'
stop 2
else if( info > 0 ) then
write(*,*)'ZHEEVD Failed; calling ZHEEV'
lwork = 2*n - 1
lrwork = 3*n - 2
allocate(work(lwork),rwork(lrwork))
lwork = -1
call ZHEEV('V','L',n,eigvectors,nmax,eigvalues,work,lwork,rwork,info)
if (info < 0) then
print *, irp_here, ': ZHEEV: the ',-info,'-th argument had an illegal value'
stop 2
endif
lwork = int(work(1))
deallocate(work)
allocate(work(lwork))
call ZHEEV('V','L',n,eigvectors,nmax,eigvalues,work,lwork,rwork,info)
if (info /= 0 ) then
write(*,*)'ZHEEV Failed'
stop 1
endif
deallocate(work,rwork)
end if
end
subroutine lapack_diagd_diag_complex(eigvalues,eigvectors,H,nmax,n)
implicit none
BEGIN_DOC
! Diagonalize matrix H(complex)
!
! H is untouched between input and ouptut
!
! eigevalues(i) = ith lowest eigenvalue of the H matrix
!
! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
!
END_DOC
integer, intent(in) :: n,nmax
! double precision, intent(out) :: eigvectors(nmax,n)
complex*16, intent(out) :: eigvectors(nmax,n)
double precision, intent(out) :: eigvalues(n)
! double precision, intent(in) :: H(nmax,n)
complex*16, intent(in) :: H(nmax,n)
double precision, allocatable :: eigenvalues(:)
complex*16,allocatable :: work(:)
integer ,allocatable :: iwork(:)
complex*16,allocatable :: A(:,:)
double precision, allocatable :: rwork(:)
integer :: lrwork, lwork, info, i,j,l,k, liwork
allocate(A(nmax,n),eigenvalues(n))
! print*,'Diagonalization by jacobi'
! print*,'n = ',n
A=H
lwork = 2*n*n + 2*n
lrwork = 2*n*n + 5*n+ 1
liwork = 5*n + 3
allocate (work(lwork),iwork(liwork),rwork(lrwork))
lwork = -1
liwork = -1
lrwork = -1
! get optimal work size
call ZHEEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
rwork, lrwork, iwork, liwork, info )
if (info < 0) then
print *, irp_here, ': ZHEEVD: the ',-info,'-th argument had an illegal value'
stop 2
endif
lwork = int( real(work(1)))
liwork = iwork(1)
lrwork = int(rwork(1))
deallocate (work,iwork,rwork)
allocate (work(lwork),iwork(liwork),rwork(lrwork))
call ZHEEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
rwork, lrwork, iwork, liwork, info )
deallocate(work,iwork,rwork)
if (info < 0) then
print *, irp_here, ': ZHEEVD: the ',-info,'-th argument had an illegal value'
stop 2
else if( info > 0 ) then
write(*,*)'ZHEEVD Failed; calling ZHEEV'
lwork = 2*n - 1
lrwork = 3*n - 2
allocate(work(lwork),rwork(lrwork))
lwork = -1
call ZHEEV('V','L',n,A,nmax,eigenvalues,work,lwork,rwork,info)
if (info < 0) then
print *, irp_here, ': ZHEEV: the ',-info,'-th argument had an illegal value'
stop 2
endif
lwork = int(work(1))
deallocate(work)
allocate(work(lwork))
call ZHEEV('V','L',n,A,nmax,eigenvalues,work,lwork,rwork,info)
if (info /= 0 ) then
write(*,*)'ZHEEV Failed'
stop 1
endif
deallocate(work,rwork)
end if
eigvectors = (0.d0,0.d0)
eigvalues = 0.d0
do j = 1, n
eigvalues(j) = eigenvalues(j)
do i = 1, n
eigvectors(i,j) = A(i,j)
enddo
enddo
deallocate(A,eigenvalues)
end
subroutine lapack_diagd_complex(eigvalues,eigvectors,H,nmax,n)
implicit none
BEGIN_DOC
! Diagonalize matrix H(complex)
!
! H is untouched between input and ouptut
!
! eigevalues(i) = ith lowest eigenvalue of the H matrix
!
! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
!
END_DOC
integer, intent(in) :: n,nmax
! double precision, intent(out) :: eigvectors(nmax,n)
complex*16, intent(out) :: eigvectors(nmax,n)
double precision, intent(out) :: eigvalues(n)
! double precision, intent(in) :: H(nmax,n)
complex*16, intent(in) :: H(nmax,n)
double precision, allocatable :: eigenvalues(:)
complex*16,allocatable :: work(:)
integer ,allocatable :: iwork(:)
complex*16,allocatable :: A(:,:)
double precision, allocatable :: rwork(:)
integer :: lrwork, lwork, info, i,j,l,k, liwork
allocate(A(nmax,n),eigenvalues(n))
! print*,'Diagonalization by jacobi'
! print*,'n = ',n
A=H
lwork = 2*n*n + 2*n
lrwork = 2*n*n + 5*n+ 1
liwork = 5*n + 3
allocate (work(lwork),iwork(liwork),rwork(lrwork))
lwork = -1
liwork = -1
lrwork = -1
call ZHEEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
rwork, lrwork, iwork, liwork, info )
if (info < 0) then
print *, irp_here, ': ZHEEVD: the ',-info,'-th argument had an illegal value'
stop 2
endif
lwork = max(int( work( 1 ) ),lwork)
liwork = iwork(1)
lrwork = max(int(rwork(1),4),lrwork)
deallocate (work,iwork,rwork)
allocate (work(lwork),iwork(liwork),rwork(lrwork))
call ZHEEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
rwork, lrwork, iwork, liwork, info )
deallocate(work,iwork,rwork)
if (info < 0) then
print *, irp_here, ': ZHEEVD: the ',-info,'-th argument had an illegal value'
stop 2
else if( info > 0 ) then
write(*,*)'ZHEEVD Failed'
stop 1
end if
eigvectors = (0.d0,0.d0)
eigvalues = 0.d0
do j = 1, n
eigvalues(j) = eigenvalues(j)
do i = 1, n
eigvectors(i,j) = A(i,j)
enddo
enddo
deallocate(A,eigenvalues)
end
subroutine lapack_diag_complex(eigvalues,eigvectors,H,nmax,n)
implicit none
BEGIN_DOC
! Diagonalize matrix H (complex)
!
! H is untouched between input and ouptut
!
! eigevalues(i) = ith lowest eigenvalue of the H matrix
!
! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
!
END_DOC
integer, intent(in) :: n,nmax
complex*16, intent(out) :: eigvectors(nmax,n)
double precision, intent(out) :: eigvalues(n)
complex*16, intent(in) :: H(nmax,n)
double precision,allocatable :: eigenvalues(:)
complex*16,allocatable :: work(:)
complex*16,allocatable :: A(:,:)
double precision,allocatable :: rwork(:)
integer :: lwork, info, i,j,l,k,lrwork
allocate(A(nmax,n),eigenvalues(n))
! print*,'Diagonalization by jacobi'
! print*,'n = ',n
A=H
!lwork = 2*n*n + 6*n+ 1
lwork = 2*n - 1
lrwork = 3*n - 2
allocate (work(lwork),rwork(lrwork))
lwork = -1
call ZHEEV( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
rwork, info )
if (info < 0) then
print *, irp_here, ': ZHEEV: the ',-info,'-th argument had an illegal value'
stop 2
endif
lwork = int( work( 1 ) )
deallocate (work)
allocate (work(lwork))
call ZHEEV( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
rwork, info )
deallocate(work,rwork)
if (info < 0) then
print *, irp_here, ': ZHEEV: the ',-info,'-th argument had an illegal value'
stop 2
else if( info > 0 ) then
write(*,*)'ZHEEV Failed : ', info
do i=1,n
do j=1,n
print *, H(i,j)
enddo
enddo
stop 1
end if
eigvectors = (0.d0,0.d0)
eigvalues = 0.d0
do j = 1, n
eigvalues(j) = eigenvalues(j)
do i = 1, n
eigvectors(i,j) = A(i,j)
enddo
enddo
deallocate(A,eigenvalues)
end
subroutine matrix_vector_product_complex(u0,u1,matrix,sze,lda)
implicit none
BEGIN_DOC
! performs u1 += u0 * matrix
END_DOC
integer, intent(in) :: sze,lda
complex*16, intent(in) :: u0(sze)
complex*16, intent(inout) :: u1(sze)
complex*16, intent(in) :: matrix(lda,sze)
integer :: i,j
integer :: incx,incy
incx = 1
incy = 1
!call dsymv('U', sze, 1.d0, matrix, lda, u0, incx, 1.d0, u1, incy)
call zhemv('U', sze, (1.d0,0.d0), matrix, lda, u0, incx, (1.d0,0.d0), u1, incy)
end
subroutine ortho_canonical(overlap,LDA,N,C,LDC,m,cutoff)
implicit none
BEGIN_DOC
! Compute C_new=C_old.U.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
integer, intent(out) :: m
double precision, intent(in) :: overlap(lda,n)
double precision, intent(in) :: cutoff
double precision, intent(inout) :: C(ldc,n)
double precision, allocatable :: U(:,:)
double precision, allocatable :: Vt(:,:)
double precision, allocatable :: D(:)
double precision, allocatable :: S(:,:)
!DIR$ ATTRIBUTES ALIGN : 64 :: U, Vt, D
integer :: info, i, j
if (n < 2) then
return
endif
allocate (U(ldc,n), Vt(lda,n), D(n), S(lda,n))
call svd(overlap,lda,U,ldc,D,Vt,lda,n,n)
D(:) = dsqrt(D(:))
m=n
do i=1,n
if ( D(i) >= cutoff ) then
D(i) = 1.d0/D(i)
else
m = i-1
print *, 'Removed Linear dependencies below:', 1.d0/D(m)
exit
endif
enddo
do i=m+1,n
D(i) = 0.d0
enddo
do i=1,m
if ( D(i) >= 1.d5 ) then
print *, 'Warning: Basis set may have linear dependence problems'
endif
enddo
do j=1,n
do i=1,n
S(i,j) = U(i,j)*D(j)
enddo
enddo
do j=1,n
do i=1,n
U(i,j) = C(i,j)
enddo
enddo
call dgemm('N','N',n,n,n,1.d0,U,size(U,1),S,size(S,1),0.d0,C,size(C,1))
deallocate (U, Vt, D, S)
end
subroutine ortho_qr(A,LDA,m,n)
implicit none
BEGIN_DOC
! Orthogonalization using Q.R factorization
!
! A : matrix to orthogonalize
!
! LDA : leftmost dimension of A
!
! m : Number of rows of A
!
! n : Number of columns of A
!
END_DOC
integer, intent(in) :: m,n, LDA
double precision, intent(inout) :: A(LDA,n)
integer :: LWORK, INFO
double precision, allocatable :: TAU(:), WORK(:)
allocate (TAU(min(m,n)), WORK(1))
LWORK=-1
call dgeqrf( m, n, A, LDA, TAU, WORK, LWORK, INFO )
! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
LWORK=max(n,int(WORK(1)))
deallocate(WORK)
allocate(WORK(LWORK))
call dgeqrf(m, n, A, LDA, TAU, WORK, LWORK, INFO )
LWORK=-1
call dorgqr(m, n, n, A, LDA, TAU, WORK, LWORK, INFO)
! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
LWORK=max(n,int(WORK(1)))
deallocate(WORK)
allocate(WORK(LWORK))
call dorgqr(m, n, n, A, LDA, TAU, WORK, LWORK, INFO)
deallocate(WORK,TAU)
end
subroutine ortho_qr_unblocked(A,LDA,m,n)
implicit none
BEGIN_DOC
! Orthogonalization using Q.R factorization
!
! A : matrix to orthogonalize
!
! LDA : leftmost dimension of A
!
! n : Number of rows of A
!
! m : Number of columns of A
!
END_DOC
integer, intent(in) :: m,n, LDA
double precision, intent(inout) :: A(LDA,n)
integer :: info
double precision, allocatable :: TAU(:), WORK(:)
allocate (TAU(n), WORK(n))
call dgeqr2( m, n, A, LDA, TAU, WORK, INFO )
call dorg2r(m, n, n, A, LDA, TAU, WORK, INFO)
deallocate(WORK,TAU)
end
subroutine ortho_lowdin(overlap,LDA,N,C,LDC,m,cutoff)
implicit none
BEGIN_DOC
! Compute C_new=C_old.S^-1/2 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
double precision, intent(in) :: overlap(lda,n)
double precision, intent(in) :: cutoff
double precision, intent(inout) :: C(ldc,n)
double precision, allocatable :: U(:,:)
double precision, allocatable :: Vt(:,:)
double precision, allocatable :: D(:)
double precision, allocatable :: S(:,:)
integer :: info, i, j, k
if (n < 2) then
return
endif
allocate(U(ldc,n),Vt(lda,n),S(lda,n),D(n))
call svd(overlap,lda,U,ldc,D,Vt,lda,n,n)
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(S,U,D,Vt,n,C,m,cutoff) &
!$OMP PRIVATE(i,j,k)
!$OMP DO
do i=1,n
if ( D(i) < cutoff ) then
print *, 'Removed Linear dependencies :', 1.d0/D(i)
D(i) = 0.d0
else
D(i) = 1.d0/dsqrt(D(i))
endif
do j=1,n
S(j,i) = 0.d0
enddo
enddo
!$OMP END DO
do k=1,n
if (D(k) /= 0.d0) then
!$OMP DO
do j=1,n
do i=1,n
S(i,j) = S(i,j) + U(i,k)*D(k)*Vt(k,j)
enddo
enddo
!$OMP END DO NOWAIT
endif
enddo
!$OMP BARRIER
!$OMP DO
do j=1,n
do i=1,m
U(i,j) = C(i,j)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call dgemm('N','N',m,n,n,1.d0,U,size(U,1),S,size(S,1),0.d0,C,size(C,1))
deallocate(U,Vt,S,D)
end
subroutine get_inverse(A,LDA,m,C,LDC)
implicit none
BEGIN_DOC
! Returns the inverse of the square matrix A
END_DOC
integer, intent(in) :: m, LDA, LDC
double precision, intent(in) :: A(LDA,m)
double precision, intent(out) :: C(LDC,m)
integer :: info,lwork
integer, allocatable :: ipiv(:)
double precision,allocatable :: work(:)
allocate (ipiv(m), work(m*m))
lwork = size(work)
C(1:m,1:m) = A(1:m,1:m)
call dgetrf(m,m,C,size(C,1),ipiv,info)
if (info /= 0) then
print *, info
stop 'error in inverse (dgetrf)'
endif
call dgetri(m,C,size(C,1),ipiv,work,lwork,info)
if (info /= 0) then
print *, info
stop 'error in inverse (dgetri)'
endif
deallocate(ipiv,work)
end
subroutine get_pseudo_inverse(A,LDA,m,n,C,LDC,cutoff)
implicit none
BEGIN_DOC
! Find C = A^-1
END_DOC
integer, intent(in) :: m,n, LDA, LDC
double precision, intent(in) :: A(LDA,n)
double precision, intent(in) :: cutoff
double precision, intent(out) :: C(LDC,m)
double precision, allocatable :: U(:,:), D(:), Vt(:,:), work(:), A_tmp(:,:)
integer :: info, lwork
integer :: i,j,k
allocate (D(n),U(m,n),Vt(n,n),work(1),A_tmp(m,n))
do j=1,n
do i=1,m
A_tmp(i,j) = A(i,j)
enddo
enddo
lwork = -1
call dgesvd('S','A', m, n, A_tmp, m,D,U,m,Vt,n,work,lwork,info)
if (info /= 0) then
print *, info, ': SVD failed'
stop
endif
LWORK=max(5*min(m,n),int(WORK(1)))
deallocate(work)
allocate(work(lwork))
call dgesvd('S','A', m, n, A_tmp, m,D,U,m,Vt,n,work,lwork,info)
if (info /= 0) then
print *, info, ':: SVD failed'
stop 1
endif
do i=1,n
if (D(i)/D(1) > cutoff) then
D(i) = 1.d0/D(i)
else
D(i) = 0.d0
endif
enddo
C = 0.d0
do i=1,m
do j=1,n
do k=1,n
C(j,i) = C(j,i) + U(i,k) * D(k) * Vt(k,j)
enddo
enddo
enddo
deallocate(U,D,Vt,work,A_tmp)
end
subroutine find_rotation(A,LDA,B,m,C,n)
implicit none
BEGIN_DOC
! Find A.C = B
END_DOC
integer, intent(in) :: m,n, LDA
double precision, intent(in) :: A(LDA,n), B(LDA,n)
double precision, intent(out) :: C(n,n)
double precision, allocatable :: A_inv(:,:)
allocate(A_inv(LDA,n))
call get_pseudo_inverse(A,LDA,m,n,A_inv,LDA,1.d-10)
integer :: i,j,k
call dgemm('N','N',n,n,m,1.d0,A_inv,n,B,LDA,0.d0,C,n)
deallocate(A_inv)
end
subroutine apply_rotation(A,LDA,R,LDR,B,LDB,m,n)
implicit none
BEGIN_DOC
! Apply the rotation found by find_rotation
END_DOC
integer, intent(in) :: m,n, LDA, LDB, LDR
double precision, intent(in) :: R(LDR,n)
double precision, intent(in) :: A(LDA,n)
double precision, intent(out) :: B(LDB,n)
call dgemm('N','N',m,n,n,1.d0,A,LDA,R,LDR,0.d0,B,LDB)
end
subroutine lapack_diagd(eigvalues,eigvectors,H,nmax,n)
implicit none
BEGIN_DOC
! Diagonalize matrix H
!
! H is untouched between input and ouptut
!
! eigevalues(i) = ith lowest eigenvalue of the H matrix
!
! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
!
END_DOC
integer, intent(in) :: n,nmax
double precision, intent(out) :: eigvectors(nmax,n)
double precision, intent(out) :: eigvalues(n)
double precision, intent(in) :: H(nmax,n)
double precision,allocatable :: eigenvalues(:)
double precision,allocatable :: work(:)
integer ,allocatable :: iwork(:)
double precision,allocatable :: A(:,:)
integer :: lwork, info, i,j,l,k, liwork
allocate(A(nmax,n),eigenvalues(n))
! print*,'Diagonalization by jacobi'
! print*,'n = ',n
A=H
lwork = 1
liwork = 1
allocate (work(lwork),iwork(liwork))
lwork = -1
liwork = -1
call DSYEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
iwork, liwork, info )
if (info < 0) then
print *, irp_here, ': DSYEVD: the ',-info,'-th argument had an illegal value'
stop 2
endif
! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
LWORK = max(int(work(1)), 2*n*n + 6*n+ 1)
liwork = max(iwork(1), 5*n + 3)
deallocate (work,iwork)
allocate (work(lwork),iwork(liwork))
call DSYEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
iwork, liwork, info )
deallocate(work,iwork)
if (info < 0) then
print *, irp_here, ': DSYEVD: the ',-info,'-th argument had an illegal value'
stop 2
else if( info > 0 ) then
write(*,*)'DSYEVD Failed'
stop 1
end if
eigvectors = 0.d0
eigvalues = 0.d0
do j = 1, n
eigvalues(j) = eigenvalues(j)
do i = 1, n
eigvectors(i,j) = A(i,j)
enddo
enddo
deallocate(A,eigenvalues)
end
subroutine lapack_diag(eigvalues,eigvectors,H,nmax,n)
implicit none
BEGIN_DOC
! Diagonalize matrix H
!
! H is untouched between input and ouptut
!
! eigevalues(i) = ith lowest eigenvalue of the H matrix
!
! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
!
END_DOC
integer, intent(in) :: n,nmax
double precision, intent(out) :: eigvectors(nmax,n)
double precision, intent(out) :: eigvalues(n)
double precision, intent(in) :: H(nmax,n)
double precision,allocatable :: eigenvalues(:)
double precision,allocatable :: work(:)
double precision,allocatable :: A(:,:)
integer :: lwork, info, i,j,l,k, liwork
allocate(A(nmax,n),eigenvalues(n))
A=H
lwork = 1
allocate (work(lwork))
lwork = -1
call DSYEV( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
info )
if (info < 0) then
print *, irp_here, ': DSYEV: the ',-info,'-th argument had an illegal value'
stop 2
endif
! /!\ int(WORK(1)) becomes negative when WORK(1) > 2147483648
LWORK = max(int(work(1)), 2*n*n + 6*n+ 1)
deallocate (work)
allocate (work(lwork))
call DSYEV( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
info )
deallocate(work)
if (info < 0) then
print *, irp_here, ': DSYEV: the ',-info,'-th argument had an illegal value'
stop 2
else if( info > 0 ) then
write(*,*)'DSYEV Failed : ', info
do i=1,n
do j=1,n
print *, H(i,j)
enddo
enddo
stop 1
end if
eigvectors = 0.d0
eigvalues = 0.d0
do j = 1, n
eigvalues(j) = eigenvalues(j)
do i = 1, n
eigvectors(i,j) = A(i,j)
enddo
enddo
deallocate(A,eigenvalues)
end
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