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https://github.com/QuantumPackage/qp2.git
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512 lines
12 KiB
Fortran
512 lines
12 KiB
Fortran
subroutine svd(A,LDA,U,LDU,D,Vt,LDVt,m,n)
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implicit none
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BEGIN_DOC
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! Compute A = U.D.Vt
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!
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! LDx : leftmost dimension of x
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!
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! Dimsneion of A is m x n
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!
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END_DOC
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integer, intent(in) :: LDA, LDU, LDVt, m, n
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double precision, intent(in) :: A(LDA,n)
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double precision, intent(out) :: U(LDU,m)
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double precision,intent(out) :: Vt(LDVt,n)
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double precision,intent(out) :: D(min(m,n))
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double precision,allocatable :: work(:)
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integer :: info, lwork, i, j, k
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double precision,allocatable :: A_tmp(:,:)
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allocate (A_tmp(LDA,n))
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A_tmp = A
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! Find optimal size for temp arrays
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allocate(work(1))
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lwork = -1
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call dgesvd('A','A', m, n, A_tmp, LDA, &
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D, U, LDU, Vt, LDVt, work, lwork, info)
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lwork = int(work(1))
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deallocate(work)
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allocate(work(lwork))
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call dgesvd('A','A', m, n, A_tmp, LDA, &
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D, U, LDU, Vt, LDVt, work, lwork, info)
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deallocate(work,A_tmp)
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if (info /= 0) then
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print *, info, ': SVD failed'
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stop
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endif
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end
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subroutine ortho_canonical(overlap,LDA,N,C,LDC,m)
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implicit none
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BEGIN_DOC
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! Compute C_new=C_old.U.s^-1/2 canonical orthogonalization.
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!
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! overlap : overlap matrix
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!
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! LDA : leftmost dimension of overlap array
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!
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! N : Overlap matrix is NxN (array is (LDA,N) )
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!
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! C : Coefficients of the vectors to orthogonalize. On exit,
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! orthogonal vectors
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!
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! LDC : leftmost dimension of C
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!
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! m : Coefficients matrix is MxN, ( array is (LDC,N) )
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!
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END_DOC
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integer, intent(in) :: lda, ldc, n
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integer, intent(out) :: m
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double precision, intent(in) :: overlap(lda,n)
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double precision, intent(inout) :: C(ldc,n)
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double precision, allocatable :: U(:,:)
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double precision, allocatable :: Vt(:,:)
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double precision, allocatable :: D(:)
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double precision, allocatable :: S(:,:)
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!DIR$ ATTRIBUTES ALIGN : 64 :: U, Vt, D
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integer :: info, i, j
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if (n < 2) then
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return
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endif
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allocate (U(ldc,n), Vt(lda,n), D(n), S(lda,n))
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call svd(overlap,lda,U,ldc,D,Vt,lda,n,n)
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D(:) = dsqrt(D(:))
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m=n
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do i=1,n
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if ( D(i) >= 1.d-6 ) then
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D(i) = 1.d0/D(i)
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else
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m = i-1
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print *, 'Removed Linear dependencies below:', 1.d0/D(m)
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exit
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endif
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enddo
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do i=m+1,n
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D(i) = 0.d0
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enddo
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do i=1,m
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if ( D(i) >= 1.d5 ) then
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print *, 'Warning: Basis set may have linear dependence problems'
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endif
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enddo
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do j=1,n
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do i=1,n
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S(i,j) = U(i,j)*D(j)
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enddo
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enddo
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do j=1,n
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do i=1,n
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U(i,j) = C(i,j)
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enddo
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enddo
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call dgemm('N','N',n,n,n,1.d0,U,size(U,1),S,size(S,1),0.d0,C,size(C,1))
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deallocate (U, Vt, D, S)
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end
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subroutine ortho_qr(A,LDA,m,n)
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implicit none
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BEGIN_DOC
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! Orthogonalization using Q.R factorization
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!
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! A : matrix to orthogonalize
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!
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! LDA : leftmost dimension of A
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!
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! n : Number of rows of A
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!
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! m : Number of columns of A
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!
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END_DOC
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integer, intent(in) :: m,n, LDA
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double precision, intent(inout) :: A(LDA,n)
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integer :: lwork, info
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integer, allocatable :: jpvt(:)
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double precision, allocatable :: tau(:), work(:)
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allocate (jpvt(n), tau(n), work(1))
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LWORK=-1
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call dgeqrf( m, n, A, LDA, TAU, WORK, LWORK, INFO )
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LWORK=2*int(WORK(1))
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deallocate(WORK)
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allocate(WORK(LWORK))
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call dgeqrf(m, n, A, LDA, TAU, WORK, LWORK, INFO )
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call dorgqr(m, n, n, A, LDA, tau, WORK, LWORK, INFO)
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deallocate(WORK,jpvt,tau)
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end
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subroutine ortho_qr_unblocked(A,LDA,m,n)
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implicit none
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BEGIN_DOC
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! Orthogonalization using Q.R factorization
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!
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! A : matrix to orthogonalize
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!
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! LDA : leftmost dimension of A
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!
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! n : Number of rows of A
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!
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! m : Number of columns of A
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!
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END_DOC
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integer, intent(in) :: m,n, LDA
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double precision, intent(inout) :: A(LDA,n)
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integer :: info
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integer, allocatable :: jpvt(:)
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double precision, allocatable :: tau(:), work(:)
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allocate (jpvt(n), tau(n), work(n))
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call dgeqr2( m, n, A, LDA, TAU, WORK, INFO )
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call dorg2r(m, n, n, A, LDA, tau, WORK, INFO)
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deallocate(WORK,jpvt,tau)
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end
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subroutine ortho_lowdin(overlap,LDA,N,C,LDC,m)
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implicit none
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BEGIN_DOC
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! Compute C_new=C_old.S^-1/2 orthogonalization.
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!
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! overlap : overlap matrix
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!
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! LDA : leftmost dimension of overlap array
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!
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! N : Overlap matrix is NxN (array is (LDA,N) )
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!
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! C : Coefficients of the vectors to orthogonalize. On exit,
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! orthogonal vectors
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!
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! LDC : leftmost dimension of C
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!
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! M : Coefficients matrix is MxN, ( array is (LDC,N) )
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!
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END_DOC
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integer, intent(in) :: LDA, ldc, n, m
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double precision, intent(in) :: overlap(lda,n)
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double precision, intent(inout) :: C(ldc,n)
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double precision, allocatable :: U(:,:)
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double precision, allocatable :: Vt(:,:)
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double precision, allocatable :: D(:)
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double precision, allocatable :: S(:,:)
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integer :: info, i, j, k
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if (n < 2) then
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return
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endif
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allocate(U(ldc,n),Vt(lda,n),S(lda,n),D(n))
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call svd(overlap,lda,U,ldc,D,Vt,lda,n,n)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(S,U,D,Vt,n,C,m) &
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!$OMP PRIVATE(i,j,k)
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!$OMP DO
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do i=1,n
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if ( D(i) < 1.d-6 ) then
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D(i) = 0.d0
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else
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D(i) = 1.d0/dsqrt(D(i))
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endif
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do j=1,n
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S(j,i) = 0.d0
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enddo
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enddo
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!$OMP END DO
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do k=1,n
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if (D(k) /= 0.d0) then
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!$OMP DO
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do j=1,n
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do i=1,n
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S(i,j) = S(i,j) + U(i,k)*D(k)*Vt(k,j)
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enddo
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enddo
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!$OMP END DO NOWAIT
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endif
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enddo
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!$OMP BARRIER
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!$OMP DO
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do j=1,n
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do i=1,m
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U(i,j) = C(i,j)
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call dgemm('N','N',m,n,n,1.d0,U,size(U,1),S,size(S,1),0.d0,C,size(C,1))
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deallocate(U,Vt,S,D)
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end
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subroutine get_inverse(A,LDA,m,C,LDC)
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implicit none
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BEGIN_DOC
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! Returns the inverse of the square matrix A
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END_DOC
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integer, intent(in) :: m, LDA, LDC
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double precision, intent(in) :: A(LDA,m)
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double precision, intent(out) :: C(LDC,m)
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integer :: info,lwork
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integer, allocatable :: ipiv(:)
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double precision,allocatable :: work(:)
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allocate (ipiv(m), work(m*m))
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lwork = size(work)
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C(1:m,1:m) = A(1:m,1:m)
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call dgetrf(m,m,C,size(C,1),ipiv,info)
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if (info /= 0) then
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print *, info
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stop 'error in inverse (dgetrf)'
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endif
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call dgetri(m,C,size(C,1),ipiv,work,lwork,info)
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if (info /= 0) then
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print *, info
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stop 'error in inverse (dgetri)'
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endif
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deallocate(ipiv,work)
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end
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subroutine get_pseudo_inverse(A,LDA,m,n,C,LDC)
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implicit none
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BEGIN_DOC
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! Find C = A^-1
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END_DOC
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integer, intent(in) :: m,n, LDA, LDC
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double precision, intent(in) :: A(LDA,n)
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double precision, intent(out) :: C(LDC,m)
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double precision, allocatable :: U(:,:), D(:), Vt(:,:), work(:), A_tmp(:,:)
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integer :: info, lwork
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integer :: i,j,k
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allocate (D(n),U(m,n),Vt(n,n),work(1),A_tmp(m,n))
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do j=1,n
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do i=1,m
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A_tmp(i,j) = A(i,j)
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enddo
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enddo
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lwork = -1
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call dgesvd('S','A', m, n, A_tmp, m,D,U,m,Vt,n,work,lwork,info)
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if (info /= 0) then
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print *, info, ': SVD failed'
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stop
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endif
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lwork = int(work(1))
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deallocate(work)
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allocate(work(lwork))
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call dgesvd('S','A', m, n, A_tmp, m,D,U,m,Vt,n,work,lwork,info)
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if (info /= 0) then
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print *, info, ':: SVD failed'
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stop 1
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endif
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do i=1,n
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if (D(i)/D(1) > 1.d-10) then
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D(i) = 1.d0/D(i)
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else
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D(i) = 0.d0
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endif
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enddo
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C = 0.d0
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do i=1,m
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do j=1,n
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do k=1,n
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C(j,i) = C(j,i) + U(i,k) * D(k) * Vt(k,j)
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enddo
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enddo
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enddo
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deallocate(U,D,Vt,work,A_tmp)
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end
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subroutine find_rotation(A,LDA,B,m,C,n)
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implicit none
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BEGIN_DOC
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! Find A.C = B
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END_DOC
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integer, intent(in) :: m,n, LDA
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double precision, intent(in) :: A(LDA,n), B(LDA,n)
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double precision, intent(out) :: C(n,n)
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double precision, allocatable :: A_inv(:,:)
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allocate(A_inv(LDA,n))
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call get_pseudo_inverse(A,LDA,m,n,A_inv,LDA)
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integer :: i,j,k
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call dgemm('N','N',n,n,m,1.d0,A_inv,n,B,LDA,0.d0,C,n)
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deallocate(A_inv)
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end
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subroutine apply_rotation(A,LDA,R,LDR,B,LDB,m,n)
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implicit none
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BEGIN_DOC
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! Apply the rotation found by find_rotation
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END_DOC
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integer, intent(in) :: m,n, LDA, LDB, LDR
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double precision, intent(in) :: R(LDR,n)
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double precision, intent(in) :: A(LDA,n)
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double precision, intent(out) :: B(LDB,n)
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call dgemm('N','N',m,n,n,1.d0,A,LDA,R,LDR,0.d0,B,LDB)
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end
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subroutine lapack_diagd(eigvalues,eigvectors,H,nmax,n)
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implicit none
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BEGIN_DOC
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! Diagonalize matrix H
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!
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! H is untouched between input and ouptut
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!
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! eigevalues(i) = ith lowest eigenvalue of the H matrix
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!
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! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
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!
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END_DOC
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integer, intent(in) :: n,nmax
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double precision, intent(out) :: eigvectors(nmax,n)
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double precision, intent(out) :: eigvalues(n)
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double precision, intent(in) :: H(nmax,n)
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double precision,allocatable :: eigenvalues(:)
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double precision,allocatable :: work(:)
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integer ,allocatable :: iwork(:)
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double precision,allocatable :: A(:,:)
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integer :: lwork, info, i,j,l,k, liwork
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allocate(A(nmax,n),eigenvalues(n))
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! print*,'Diagonalization by jacobi'
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! print*,'n = ',n
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A=H
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lwork = max(1000,2*n*n + 6*n+ 1)
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liwork = max(5*n + 3,1000)
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allocate (work(lwork),iwork(liwork))
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lwork = -1
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liwork = -1
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call DSYEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
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iwork, liwork, info )
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if (info < 0) then
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print *, irp_here, ': DSYEVD: the ',-info,'-th argument had an illegal value'
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stop 2
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endif
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lwork = int( work( 1 ) )
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liwork = iwork(1)
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deallocate (work,iwork)
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allocate (work(lwork),iwork(liwork))
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call DSYEVD( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
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iwork, liwork, info )
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deallocate(work,iwork)
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if (info < 0) then
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print *, irp_here, ': DSYEVD: the ',-info,'-th argument had an illegal value'
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stop 2
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else if( info > 0 ) then
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write(*,*)'DSYEVD Failed'
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stop 1
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end if
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eigvectors = 0.d0
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eigvalues = 0.d0
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do j = 1, n
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eigvalues(j) = eigenvalues(j)
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do i = 1, n
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eigvectors(i,j) = A(i,j)
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enddo
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enddo
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deallocate(A,eigenvalues)
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end
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subroutine lapack_diag(eigvalues,eigvectors,H,nmax,n)
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implicit none
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BEGIN_DOC
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! Diagonalize matrix H
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!
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! H is untouched between input and ouptut
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!
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! eigevalues(i) = ith lowest eigenvalue of the H matrix
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!
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! eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
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!
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END_DOC
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integer, intent(in) :: n,nmax
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double precision, intent(out) :: eigvectors(nmax,n)
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double precision, intent(out) :: eigvalues(n)
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double precision, intent(in) :: H(nmax,n)
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double precision,allocatable :: eigenvalues(:)
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double precision,allocatable :: work(:)
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double precision,allocatable :: A(:,:)
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integer :: lwork, info, i,j,l,k, liwork
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allocate(A(nmax,n),eigenvalues(n))
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A=H
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lwork = 2*n*n + 6*n+ 1
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allocate (work(lwork))
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lwork = -1
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call DSYEV( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
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info )
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if (info < 0) then
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print *, irp_here, ': DSYEV: the ',-info,'-th argument had an illegal value'
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stop 2
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endif
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lwork = int( work( 1 ) )
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deallocate (work)
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allocate (work(lwork))
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call DSYEV( 'V', 'U', n, A, nmax, eigenvalues, work, lwork, &
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info )
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deallocate(work)
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if (info < 0) then
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print *, irp_here, ': DSYEV: the ',-info,'-th argument had an illegal value'
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stop 2
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else if( info > 0 ) then
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write(*,*)'DSYEV Failed : ', info
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do i=1,n
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do j=1,n
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print *, H(i,j)
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enddo
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enddo
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stop 1
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end if
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eigvectors = 0.d0
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eigvalues = 0.d0
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do j = 1, n
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eigvalues(j) = eigenvalues(j)
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do i = 1, n
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eigvectors(i,j) = A(i,j)
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enddo
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enddo
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deallocate(A,eigenvalues)
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end
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