575 lines
14 KiB
Fortran
575 lines
14 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,n)
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double precision,intent(out) :: Vt(LDVt,n)
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double precision,intent(out) :: D(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', n, n, A_tmp, LDA, &
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D, U, LDU, Vt, LDVt, work, lwork, info)
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lwork = work(1)
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deallocate(work)
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allocate(work(lwork))
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call dgesvd('A','A', n, 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_half(:,:)
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!DEC$ 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_half(lda,n))
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call svd(overlap,lda,U,ldc,D,Vt,lda,n,n)
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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/dsqrt(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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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(S_half,U,D,Vt,n,C,m) &
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!$OMP PRIVATE(i,j)
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!$OMP DO
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do j=1,n
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do i=1,n
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S_half(i,j) = U(i,j)*D(j)
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enddo
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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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!$OMP END DO
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!$OMP END PARALLEL
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call dgemm('N','N',n,m,n,1.d0,U,size(U,1),S_half,size(S_half,1),0.d0,C,size(C,1))
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deallocate (U, Vt, D, S_half)
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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_half(:,:)
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!DEC$ ATTRIBUTES ALIGN : 64 :: U, Vt, D
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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_half(lda,n),D(n))
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call svd(overlap,lda,U,ldc,D,Vt,lda,m,n)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(S_half,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_half(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_half(i,j) = S_half(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_half,size(S_half,1),0.d0,C,size(C,1))
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deallocate(U,Vt,S_half,D)
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end
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subroutine get_pseudo_inverse(A,m,n,C,LDA)
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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
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double precision, intent(in) :: A(LDA,n)
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double precision, intent(out) :: C(n,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 = 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 (abs(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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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) += 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,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 = 2*n*n + 6*n+ 1
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liwork = 5*n + 3
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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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! print*,'Diagonalization by jacobi'
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! print*,'n = ',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'
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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_s2(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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! print*,'Diagonalization by jacobi'
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! print*,'n = ',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'
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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_partial_diag(eigvalues,eigvectors,H,nmax,n,n_st)
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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,n_st
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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 :: work(:)
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integer ,allocatable :: iwork(:), isuppz(:)
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double precision,allocatable :: A(:,:)
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integer :: lwork, info, i,j,l,k,m, liwork
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allocate(A(nmax,n))
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|
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A=H
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lwork = 2*n*n + 6*n+ 1
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liwork = 5*n + 3
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allocate (work(lwork),iwork(liwork),isuppz(2*N_st))
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|
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lwork = -1
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liwork = -1
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call DSYEVR( 'V', 'I', 'U', n, A, nmax, 0.d0, 0.d0, 1, n_st, 1.d-10, m, eigvalues, eigvectors, nmax, isuppz, work, lwork, &
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|
iwork, liwork, info )
|
|
if (info < 0) then
|
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print *, irp_here, ': DSYEVR: the ',-info,'-th argument had an illegal value'
|
|
stop 2
|
|
endif
|
|
lwork = int( work( 1 ) )
|
|
liwork = iwork(1)
|
|
deallocate (work,iwork)
|
|
|
|
allocate (work(lwork),iwork(liwork))
|
|
call DSYEVR( 'V', 'I', 'U', n, A, nmax, 0.d0, 0.d0, 1, n_st, 1.d-10, m, eigvalues, eigvectors, nmax, isuppz, work, lwork, &
|
|
iwork, liwork, info )
|
|
deallocate(work,iwork)
|
|
|
|
if (info < 0) then
|
|
print *, irp_here, ': DSYEVR: the ',-info,'-th argument had an illegal value'
|
|
stop 2
|
|
else if( info > 0 ) then
|
|
write(*,*)'DSYEVR Failed'
|
|
stop 1
|
|
end if
|
|
|
|
deallocate(A)
|
|
end
|
|
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|
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subroutine set_zero_extra_diag(i1,i2,matrix,lda,m)
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|
implicit none
|
|
integer, intent(in) :: i1,i2,lda,m
|
|
double precision, intent(inout) :: matrix(lda,m)
|
|
integer :: i,j
|
|
do j=i1,i2
|
|
do i = 1,i1-1
|
|
matrix(i,j) = 0.d0
|
|
matrix(j,i) = 0.d0
|
|
enddo
|
|
enddo
|
|
|
|
do i = i2,i1
|
|
do j=i2+1,m
|
|
matrix(i,j) = 0.d0
|
|
matrix(j,i) = 0.d0
|
|
enddo
|
|
enddo
|
|
|
|
|
|
end
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|
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