mirror of
https://github.com/pfloos/quack
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added non-sym diag with biorthog condition
This commit is contained in:
AbdAmmar
parent
08bf6632df
commit
eb6e0bcc02
134
src/LR/ppLR.f90
134
src/LR/ppLR.f90
@ -1,93 +1,123 @@
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subroutine ppLR(TDA,nOO,nVV,Bpp,Cpp,Dpp,Om1,X1,Y1,Om2,X2,Y2,EcRPA)
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! Solve the pp-RPA linear eigenvalue problem
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! ---
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subroutine ppLR(TDA, nOO, nVV, Bpp, Cpp, Dpp, Om1, X1, Y1, Om2, X2, Y2, EcRPA)
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!
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! Solve the pp-RPA linear eigenvalue problem
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!
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! right eigen-problem: H R = R w
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! left eigen-problem: H.T L = L w
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!
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! where L.T R = 1
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!
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!
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! (+C +B)
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! H = ( ) where C = C.T and D = D.T
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! (-B.T -D)
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!
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! (w1 0) (X1 X2) (+X1 +X2)
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! w = ( ), R = ( ) and L = ( )
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! (0 w2) (Y1 Y2) (-Y1 -Y2)
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!
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!
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! the normalisation condition reduces to
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!
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! X1.T X2 - Y1.T Y2 = 0
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! X1.T X1 - Y1.T Y1 = 1
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! X2.T X2 - Y2.T Y2 = 1
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!
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implicit none
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include 'parameters.h'
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! Input variables
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logical, intent(in) :: TDA
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integer, intent(in) :: nOO, nVV
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double precision, intent(in) :: Bpp(nVV,nOO), Cpp(nVV,nVV), Dpp(nOO,nOO)
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double precision, intent(out) :: Om1(nVV), X1(nVV,nVV), Y1(nOO,nVV)
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double precision, intent(out) :: Om2(nOO), X2(nVV,nOO), Y2(nOO,nOO)
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double precision, intent(out) :: EcRPA
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logical,intent(in) :: TDA
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integer,intent(in) :: nOO
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integer,intent(in) :: nVV
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double precision,intent(in) :: Bpp(nVV,nOO)
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double precision,intent(in) :: Cpp(nVV,nVV)
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double precision,intent(in) :: Dpp(nOO,nOO)
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logical :: imp_bio, verbose
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integer :: i, j, N
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double precision :: EcRPA1, EcRPA2
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double precision :: thr_d, thr_nd, thr_deg
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double precision,allocatable :: M(:,:), Z(:,:), Om(:)
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! Local variables
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double precision, external :: trace_matrix
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double precision :: trace_matrix
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double precision :: EcRPA1
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double precision :: EcRPA2
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double precision,allocatable :: M(:,:)
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double precision,allocatable :: Z(:,:)
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double precision,allocatable :: Om(:)
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! Output variables
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double precision,intent(out) :: Om1(nVV)
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double precision,intent(out) :: X1(nVV,nVV)
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double precision,intent(out) :: Y1(nOO,nVV)
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double precision,intent(out) :: Om2(nOO)
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double precision,intent(out) :: X2(nVV,nOO)
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double precision,intent(out) :: Y2(nOO,nOO)
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double precision,intent(out) :: EcRPA
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N = nOO + nVV
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! Memory allocation
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allocate(M(nOO+nVV,nOO+nVV),Z(nOO+nVV,nOO+nVV),Om(nOO+nVV))
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!-------------------------------------------------!
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! Solve the p-p eigenproblem !
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!-------------------------------------------------!
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! !
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! | C B | | X1 X2 | | w1 0 | | X1 X2 | !
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! | | | | = | | | | !
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! | -Bt -D | | Y1 Y2 | | 0 w2 | | Y1 Y2 | !
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! !
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!-------------------------------------------------!
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allocate(M(N,N), Z(N,N), Om(N))
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if(TDA) then
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X1(:,:) = +Cpp(:,:)
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Y1(:,:) = 0d0
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if(nVV > 0) call diagonalize_matrix(nVV,X1,Om1)
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if(nVV > 0) call diagonalize_matrix(nVV, X1, Om1)
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X2(:,:) = 0d0
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Y2(:,:) = -Dpp(:,:)
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if(nOO > 0) call diagonalize_matrix(nOO,Y2,Om2)
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if(nOO > 0) call diagonalize_matrix(nOO, Y2, Om2)
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else
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! Diagonal blocks
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M( 1:nVV , 1:nVV) = + Cpp(1:nVV,1:nVV)
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M(nVV+1:nVV+nOO,nVV+1:nVV+nOO) = - Dpp(1:nOO,1:nOO)
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! Off-diagonal blocks
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M( 1:nVV ,nVV+1:nOO+nVV) = - Bpp(1:nVV,1:nOO)
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M(nVV+1:nOO+nVV, 1:nVV) = + transpose(Bpp(1:nVV,1:nOO))
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! call matout(nOO,nOO,Dpp)
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!! Diagonalize the p-p matrix
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!if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV, M, Om, Z)
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!! Split the various quantities in p-p and h-h parts
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!call sort_ppRPA(nOO, nVV, Om, Z, Om1, X1, Y1, Om2, X2, Y2)
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! Diagonalize the p-p matrix
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if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV,M,Om,Z)
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thr_d = 1d-6 ! to determine if diagonal elements of L.T x R are close enouph to 1
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thr_nd = 1d-6 ! to determine if non-diagonal elements of L.T x R are close enouph to 1
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thr_deg = 1d-8 ! to determine if two eigenvectors are degenerate or not
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imp_bio = .True. ! impose bi-orthogonality
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verbose = .False.
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call diagonalize_nonsym_matrix(N, M, Z, Om, thr_d, thr_nd, thr_deg, imp_bio, verbose)
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! Split the various quantities in p-p and h-h parts
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do i = 1, nOO
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Om2(i) = Om(i)
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do j = 1, nVV
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X2(j,i) = Z(j,i)
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enddo
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do j = 1, nOO
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Y2(j,i) = Z(nVV+j,i)
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enddo
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enddo
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call sort_ppRPA(nOO,nVV,Om,Z,Om1,X1,Y1,Om2,X2,Y2)
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do i = 1, nVV
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Om1(i) = Om(nOO+i)
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do j = 1, nVV
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X1(j,i) = M(j,nOO+i)
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enddo
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do j = 1, nOO
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Y1(j,i) = M(nVV+j,nOO+i)
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enddo
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enddo
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end if
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! Compute the RPA correlation energy
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! Compute the RPA correlation energy
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EcRPA = 0.5d0 * (sum(Om1) - sum(Om2) - trace_matrix(nVV, Cpp) - trace_matrix(nOO, Dpp))
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EcRPA1 = +sum(Om1) - trace_matrix(nVV, Cpp)
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EcRPA2 = -sum(Om2) - trace_matrix(nOO, Dpp)
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EcRPA = 0.5d0*( sum(Om1) - sum(Om2) - trace_matrix(nVV,Cpp) - trace_matrix(nOO,Dpp) )
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EcRPA1 = +sum(Om1) - trace_matrix(nVV,Cpp)
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EcRPA2 = -sum(Om2) - trace_matrix(nOO,Dpp)
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if(abs(EcRPA - EcRPA1) > 1d-6 .or. abs(EcRPA - EcRPA2) > 1d-6) &
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if(abs(EcRPA - EcRPA1) > 1d-6 .or. abs(EcRPA - EcRPA2) > 1d-6) then
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print*,'!!! Issue in pp-RPA linear reponse calculation RPA1 != RPA2 !!!'
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endif
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deallocate(M, Z, Om)
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end subroutine
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@ -89,8 +89,8 @@ FIX_ORDER_OF_LIBS=-Wl,--start-group
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if sys.platform in ["linux", "linux2"]:
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# compiler = compile_gfortran_linux
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# compiler = compile_ifort_linux
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compiler = compile_olympe
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compiler = compile_ifort_linux
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# compiler = compile_olympe
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elif sys.platform == "darwin":
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compiler = compile_gfortran_mac
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else:
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571
src/utils/non_sym_diag.f90
Normal file
571
src/utils/non_sym_diag.f90
Normal file
@ -0,0 +1,571 @@
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! ---
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subroutine diagonalize_nonsym_matrix(N, A, L, e_re, thr_d, thr_nd, thr_deg, imp_bio, verbose)
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! Diagonalize a non-symmetric matrix
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!
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! Output
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! right-eigenvectors are saved in A
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! left-eigenvectors are saved in L
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! eigenvalues are saved in e = e_re + i e_im
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implicit none
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integer, intent(in) :: N
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logical, intent(in) :: imp_bio, verbose
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double precision, intent(in) :: thr_d, thr_nd, thr_deg
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double precision, intent(inout) :: A(N,N)
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double precision, intent(out) :: e_re(N), L(N,N)
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integer :: i, j, ii
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integer :: lwork, info
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double precision :: accu_d, accu_nd
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integer, allocatable :: iorder(:), deg_num(:)
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double precision, allocatable :: Atmp(:,:), Ltmp(:,:), work(:), e_im(:)
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double precision, allocatable :: S(:,:)
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if(verbose) then
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print*, ' Starting a non-Hermitian diagonalization ...'
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print*, ' Good Luck ;)'
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print*, ' imp_bio = ', imp_bio
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endif
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! ---
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! diagonalize
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allocate(Atmp(N,N), e_im(N))
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Atmp(1:N,1:N) = A(1:N,1:N)
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allocate(work(1))
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lwork = -1
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call dgeev('V', 'V', N, Atmp, N, e_re, e_im, L, N, A, N, work, lwork, info)
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if(info .gt. 0) then
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print*,'dgeev failed !!', info
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stop
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endif
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lwork = max(int(work(1)), 1)
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deallocate(work)
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allocate(work(lwork))
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call dgeev('V', 'V', N, Atmp, N, e_re, e_im, L, N, A, N, work, lwork, info)
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if(info .ne. 0) then
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print*,'dgeev failed !!', info
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stop
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endif
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deallocate(Atmp, WORK)
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! ---
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! check if eigenvalues are real
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i = 1
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ii = 0
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do while(i .le. N)
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if(dabs(e_im(i)) .gt. 1.d-12) then
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ii = ii + 1
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if(verbose) then
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print*, ' Warning: complex eigenvalue !'
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print*, i, e_re(i), e_im(i)
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if(dabs(e_im(i)/e_re(i)) .lt. 1.d-6) then
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print*, ' small enouph to be igored'
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else
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print*, ' IMAGINARY PART IS SIGNIFANT !!!'
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endif
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endif
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endif
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i = i + 1
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enddo
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if(verbose) then
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if(ii .eq. 0) print*, ' congratulations :) eigenvalues are real-valued !!'
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endif
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! ---
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! track & sort the real eigenvalues
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allocate(Atmp(N,N), Ltmp(N,N), iorder(N))
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do i = 1, N
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iorder(i) = i
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enddo
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call quick_sort(e_re, iorder, N)
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Atmp(:,:) = A(:,:)
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Ltmp(:,:) = L(:,:)
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do i = 1, N
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do j = 1, N
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A(j,i) = Atmp(j,iorder(i))
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L(j,i) = Ltmp(j,iorder(i))
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enddo
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enddo
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deallocate(Atmp, Ltmp, iorder)
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! ---
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! check bi-orthog
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allocate(S(N,N))
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call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .false., verbose)
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if((accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(N))/dble(N) .lt. thr_d)) then
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if(verbose) then
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print *, ' lapack vectors are normalized and bi-orthogonalized'
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endif
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elseif((accu_nd .lt. thr_nd) .and. (dabs(accu_d - dble(N)) .gt. thr_d)) then
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if(verbose) then
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print *, ' lapack vectors are not normalized but bi-orthogonalized'
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endif
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call check_biorthog_binormalize(N, N, L, A, thr_d, thr_nd, .true.)
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call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .true., verbose)
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else
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if(verbose) then
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print *, ' lapack vectors are not normalized neither bi-orthogonalized'
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endif
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allocate(deg_num(N))
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call reorder_degen_eigvec(N, thr_deg, deg_num, e_re, L, A)
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call impose_biorthog_degen_eigvec(N, deg_num, e_re, L, A)
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deallocate(deg_num)
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call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .false., verbose)
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if((accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(N))/dble(N) .lt. thr_d)) then
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if(verbose) then
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print *, ' lapack vectors are now normalized and bi-orthogonalized'
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endif
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elseif((accu_nd .lt. thr_nd) .and. (dabs(accu_d - dble(N)) .gt. thr_d)) then
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if(verbose) then
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print *, ' lapack vectors are now not normalized but bi-orthogonalized'
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endif
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call check_biorthog_binormalize(N, N, L, A, thr_d, thr_nd, .true.)
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call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .true., verbose)
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else
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if(verbose) then
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print*, ' bi-orthogonalization failed !'
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endif
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if(imp_bio) then
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print*, ' bi-orthogonalization failed !'
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deallocate(S)
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stop
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endif
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endif
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endif
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deallocate(S)
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return
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end
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! ---
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subroutine check_biorthog(n, m, Vl, Vr, accu_d, accu_nd, S, thr_d, thr_nd, stop_ifnot, verbose)
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implicit none
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integer, intent(in) :: n, m
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logical, intent(in) :: stop_ifnot, verbose
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double precision, intent(in) :: Vl(n,m), Vr(n,m)
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double precision, intent(in) :: thr_d, thr_nd
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double precision, intent(out) :: accu_d, accu_nd, S(m,m)
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integer :: i, j
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double precision, allocatable :: SS(:,:)
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if(verbose) then
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print *, ' check bi-orthogonality'
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endif
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! ---
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call dgemm( 'T', 'N', m, m, n, 1.d0 &
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, Vl, size(Vl, 1), Vr, size(Vr, 1) &
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, 0.d0, S, size(S, 1) )
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accu_d = 0.d0
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accu_nd = 0.d0
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do i = 1, m
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do j = 1, m
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if(i==j) then
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accu_d = accu_d + dabs(S(i,i))
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else
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accu_nd = accu_nd + S(j,i) * S(j,i)
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endif
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enddo
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enddo
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accu_nd = dsqrt(accu_nd) / dble(m)
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if(verbose) then
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if((accu_nd .gt. thr_nd) .or. dabs(accu_d-dble(m))/dble(m) .gt. thr_d) then
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print *, ' non bi-orthogonal vectors !'
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print *, ' accu_nd = ', accu_nd
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print *, ' accu_d = ', dabs(accu_d-dble(m))/dble(m)
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else
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print *, ' vectors are bi-orthogonals'
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endif
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endif
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! ---
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if(stop_ifnot .and. ((accu_nd .gt. thr_nd) .or. dabs(accu_d-dble(m))/dble(m) .gt. thr_d)) then
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print *, ' non bi-orthogonal vectors !'
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print *, ' accu_nd = ', accu_nd
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print *, ' accu_d = ', dabs(accu_d-dble(m))/dble(m)
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stop
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endif
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end
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! ---
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subroutine check_biorthog_binormalize(n, m, Vl, Vr, thr_d, thr_nd, stop_ifnot)
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implicit none
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integer, intent(in) :: n, m
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logical, intent(in) :: stop_ifnot
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double precision, intent(in) :: thr_d, thr_nd
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double precision, intent(inout) :: Vl(n,m), Vr(n,m)
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integer :: i, j
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double precision :: accu_d, accu_nd, s_tmp
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double precision, allocatable :: S(:,:)
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! ---
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allocate(S(m,m))
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call dgemm( 'T', 'N', m, m, n, 1.d0 &
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, Vl, size(Vl, 1), Vr, size(Vr, 1) &
|
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, 0.d0, S, size(S, 1) )
|
||||
|
||||
do i = 1, m
|
||||
if(S(i,i) .lt. 0.d0) then
|
||||
do j = 1, n
|
||||
Vl(j,i) = -1.d0 * Vl(j,i)
|
||||
enddo
|
||||
S(i,i) = -S(i,i)
|
||||
endif
|
||||
enddo
|
||||
|
||||
accu_d = 0.d0
|
||||
accu_nd = 0.d0
|
||||
do i = 1, m
|
||||
do j = 1, m
|
||||
if(i==j) then
|
||||
accu_d = accu_d + S(i,i)
|
||||
else
|
||||
accu_nd = accu_nd + S(j,i) * S(j,i)
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
accu_nd = dsqrt(accu_nd) / dble(m)
|
||||
|
||||
! ---
|
||||
|
||||
if( (accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(m))/dble(m) .gt. thr_d) ) then
|
||||
|
||||
do i = 1, m
|
||||
if(S(i,i) <= 0.d0) then
|
||||
print *, ' overap negative'
|
||||
print *, i, S(i,i)
|
||||
exit
|
||||
endif
|
||||
if(dabs(S(i,i) - 1.d0) .gt. thr_d) then
|
||||
s_tmp = 1.d0 / dsqrt(S(i,i))
|
||||
do j = 1, n
|
||||
Vl(j,i) = Vl(j,i) * s_tmp
|
||||
Vr(j,i) = Vr(j,i) * s_tmp
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
|
||||
endif
|
||||
|
||||
! ---
|
||||
|
||||
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||
, Vl, size(Vl, 1), Vr, size(Vr, 1) &
|
||||
, 0.d0, S, size(S, 1) )
|
||||
|
||||
accu_d = 0.d0
|
||||
accu_nd = 0.d0
|
||||
do i = 1, m
|
||||
do j = 1, m
|
||||
if(i==j) then
|
||||
accu_d = accu_d + S(i,i)
|
||||
else
|
||||
accu_nd = accu_nd + S(j,i) * S(j,i)
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
accu_nd = dsqrt(accu_nd) / dble(m)
|
||||
|
||||
deallocate(S)
|
||||
|
||||
! ---
|
||||
|
||||
if( stop_ifnot .and. ((accu_nd .gt. thr_nd) .or. (dabs(accu_d-dble(m))/dble(m) .gt. thr_d)) ) then
|
||||
print *, accu_nd, thr_nd
|
||||
print *, dabs(accu_d-dble(m))/dble(m), thr_d
|
||||
print *, ' biorthog_binormalize failed !'
|
||||
stop
|
||||
endif
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine reorder_degen_eigvec(n, thr_deg, deg_num, e0, L0, R0)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: thr_deg
|
||||
double precision, intent(inout) :: e0(n), L0(n,n), R0(n,n)
|
||||
integer, intent(out) :: deg_num(n)
|
||||
|
||||
logical :: complex_root
|
||||
integer :: i, j, k, m, ii, j_tmp
|
||||
double precision :: ei, ej, de
|
||||
double precision :: accu_d, accu_nd
|
||||
double precision :: e0_tmp, L0_tmp(n), R0_tmp(n)
|
||||
double precision, allocatable :: L(:,:), R(:,:), S(:,:), S_inv_half(:,:)
|
||||
|
||||
do i = 1, n
|
||||
deg_num(i) = 1
|
||||
enddo
|
||||
|
||||
do i = 1, n-1
|
||||
ei = e0(i)
|
||||
|
||||
! already considered in degen vectors
|
||||
if(deg_num(i) .eq. 0) cycle
|
||||
|
||||
ii = 0
|
||||
do j = i+1, n
|
||||
ej = e0(j)
|
||||
de = dabs(ei - ej)
|
||||
|
||||
if(de .lt. thr_deg) then
|
||||
ii = ii + 1
|
||||
|
||||
j_tmp = i + ii
|
||||
|
||||
deg_num(j_tmp) = 0
|
||||
|
||||
e0_tmp = e0(j_tmp)
|
||||
e0(j_tmp) = e0(j)
|
||||
e0(j) = e0_tmp
|
||||
|
||||
L0_tmp(1:n) = L0(1:n,j_tmp)
|
||||
L0(1:n,j_tmp) = L0(1:n,j)
|
||||
L0(1:n,j) = L0_tmp(1:n)
|
||||
|
||||
R0_tmp(1:n) = R0(1:n,j_tmp)
|
||||
R0(1:n,j_tmp) = R0(1:n,j)
|
||||
R0(1:n,j) = R0_tmp(1:n)
|
||||
endif
|
||||
enddo
|
||||
|
||||
deg_num(i) = ii + 1
|
||||
enddo
|
||||
|
||||
ii = 0
|
||||
do i = 1, n
|
||||
if(deg_num(i) .gt. 1) then
|
||||
ii = ii + 1
|
||||
endif
|
||||
enddo
|
||||
|
||||
if(ii .eq. 0) then
|
||||
print*, ' WARNING: bi-orthogonality is lost but there is no degeneracies'
|
||||
print*, ' rotations may change energy'
|
||||
stop
|
||||
endif
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine impose_biorthog_degen_eigvec(n, deg_num, e0, L0, R0)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n, deg_num(n)
|
||||
double precision, intent(in) :: e0(n)
|
||||
double precision, intent(inout) :: L0(n,n), R0(n,n)
|
||||
|
||||
logical :: complex_root
|
||||
integer :: i, j, k, m
|
||||
double precision :: ei, ej, de
|
||||
double precision :: accu_d, accu_nd
|
||||
double precision, allocatable :: L(:,:), R(:,:), S(:,:), S_inv_half(:,:)
|
||||
|
||||
!do i = 1, n
|
||||
! if(deg_num(i) .gt. 1) then
|
||||
! print *, ' degen on', i, deg_num(i), e0(i)
|
||||
! endif
|
||||
!enddo
|
||||
|
||||
! ---
|
||||
|
||||
do i = 1, n
|
||||
m = deg_num(i)
|
||||
|
||||
if(m .gt. 1) then
|
||||
|
||||
allocate(L(n,m), R(n,m), S(m,m))
|
||||
|
||||
do j = 1, m
|
||||
L(1:n,j) = L0(1:n,i+j-1)
|
||||
R(1:n,j) = R0(1:n,i+j-1)
|
||||
enddo
|
||||
|
||||
! ---
|
||||
|
||||
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||
, L, size(L, 1), R, size(R, 1) &
|
||||
, 0.d0, S, size(S, 1) )
|
||||
|
||||
accu_nd = 0.d0
|
||||
do j = 1, m
|
||||
do k = 1, m
|
||||
if(j==k) cycle
|
||||
accu_nd = accu_nd + dabs(S(j,k))
|
||||
enddo
|
||||
enddo
|
||||
|
||||
if(accu_nd .lt. 1d-12) then
|
||||
deallocate(S, L, R)
|
||||
cycle
|
||||
endif
|
||||
|
||||
call impose_biorthog_svd(n, m, L, R)
|
||||
|
||||
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||
, L, size(L, 1), R, size(R, 1) &
|
||||
, 0.d0, S, size(S, 1) )
|
||||
accu_nd = 0.d0
|
||||
do j = 1, m
|
||||
do k = 1, m
|
||||
if(j==k) cycle
|
||||
accu_nd = accu_nd + dabs(S(j,k))
|
||||
enddo
|
||||
enddo
|
||||
if(accu_nd .gt. 1d-12) then
|
||||
print*, ' accu_nd =', accu_nd
|
||||
print*, ' your strategy for degenerates orbitals failed !'
|
||||
print*, m, 'deg on', i
|
||||
stop
|
||||
endif
|
||||
|
||||
deallocate(S)
|
||||
|
||||
! ---
|
||||
|
||||
do j = 1, m
|
||||
L0(1:n,i+j-1) = L(1:n,j)
|
||||
R0(1:n,i+j-1) = R(1:n,j)
|
||||
enddo
|
||||
|
||||
deallocate(L, R)
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine impose_biorthog_svd(n, m, L, R)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n, m
|
||||
double precision, intent(inout) :: L(n,m), R(n,m)
|
||||
|
||||
integer :: i, j, num_linear_dependencies
|
||||
double precision :: threshold
|
||||
double precision, allocatable :: S(:,:), tmp(:,:)
|
||||
double precision, allocatable :: U(:,:), V(:,:), Vt(:,:), D(:)
|
||||
|
||||
allocate(S(m,m))
|
||||
|
||||
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||
, L, size(L, 1), R, size(R, 1) &
|
||||
, 0.d0, S, size(S, 1) )
|
||||
|
||||
! ---
|
||||
|
||||
allocate(U(m,m), Vt(m,m), D(m))
|
||||
|
||||
call svd(S, m, U, m, D, Vt, m, m, m)
|
||||
|
||||
deallocate(S)
|
||||
|
||||
threshold = 1.d-6
|
||||
num_linear_dependencies = 0
|
||||
do i = 1, m
|
||||
if(abs(D(i)) <= threshold) then
|
||||
D(i) = 0.d0
|
||||
num_linear_dependencies = num_linear_dependencies + 1
|
||||
else
|
||||
D(i) = 1.d0 / dsqrt(D(i))
|
||||
endif
|
||||
enddo
|
||||
if(num_linear_dependencies > 0) then
|
||||
write(*,*) ' linear dependencies = ', num_linear_dependencies
|
||||
write(*,*) ' m = ', m
|
||||
stop
|
||||
endif
|
||||
|
||||
allocate(V(m,m))
|
||||
do i = 1, m
|
||||
do j = 1, m
|
||||
V(j,i) = Vt(i,j)
|
||||
enddo
|
||||
enddo
|
||||
deallocate(Vt)
|
||||
|
||||
! ---
|
||||
|
||||
! R <-- R x V x D^{-0.5}
|
||||
! L <-- L x U x D^{-0.5}
|
||||
|
||||
do i = 1, m
|
||||
do j = 1, m
|
||||
V(j,i) = V(j,i) * D(i)
|
||||
U(j,i) = U(j,i) * D(i)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
allocate(tmp(n,m))
|
||||
tmp(:,:) = R(:,:)
|
||||
call dgemm( 'N', 'N', n, m, m, 1.d0 &
|
||||
, tmp, size(tmp, 1), V, size(V, 1) &
|
||||
, 0.d0, R, size(R, 1))
|
||||
|
||||
tmp(:,:) = L(:,:)
|
||||
call dgemm( 'N', 'N', n, m, m, 1.d0 &
|
||||
, tmp, size(tmp, 1), U, size(U, 1) &
|
||||
, 0.d0, L, size(L, 1))
|
||||
|
||||
deallocate(tmp, U, V, D)
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
Loading…
Reference in New Issue
Block a user