mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-12-22 11:33:29 +01:00
added exponential of anti-hermitian matrices using the Helgaker's book formulation, and of general matrices using the Taylor expansion. Replaced in casscf_cipsi Umat variable
This commit is contained in:
eginer
parent
22c99a0484
commit
fa877df399
@ -226,27 +226,28 @@ BEGIN_PROVIDER [real*8, Umat, (mo_num,mo_num) ]
|
|||||||
end do
|
end do
|
||||||
|
|
||||||
! Form the exponential
|
! Form the exponential
|
||||||
|
call exp_matrix_taylor(Tmat,mo_num,Umat,converged)
|
||||||
|
|
||||||
Tpotmat(:,:)=0.D0
|
! Tpotmat(:,:)=0.D0
|
||||||
Umat(:,:) =0.D0
|
! Umat(:,:) =0.D0
|
||||||
do i=1,mo_num
|
! do i=1,mo_num
|
||||||
Tpotmat(i,i)=1.D0
|
! Tpotmat(i,i)=1.D0
|
||||||
Umat(i,i) =1.d0
|
! Umat(i,i) =1.d0
|
||||||
end do
|
! end do
|
||||||
iter=0
|
! iter=0
|
||||||
converged=.false.
|
! converged=.false.
|
||||||
do while (.not.converged)
|
! do while (.not.converged)
|
||||||
iter+=1
|
! iter+=1
|
||||||
f = 1.d0 / dble(iter)
|
! f = 1.d0 / dble(iter)
|
||||||
Tpotmat2(:,:) = Tpotmat(:,:) * f
|
! Tpotmat2(:,:) = Tpotmat(:,:) * f
|
||||||
call dgemm('N','N', mo_num,mo_num,mo_num,1.d0, &
|
! call dgemm('N','N', mo_num,mo_num,mo_num,1.d0, &
|
||||||
Tpotmat2, size(Tpotmat2,1), &
|
! Tpotmat2, size(Tpotmat2,1), &
|
||||||
Tmat, size(Tmat,1), 0.d0, &
|
! Tmat, size(Tmat,1), 0.d0, &
|
||||||
Tpotmat, size(Tpotmat,1))
|
! Tpotmat, size(Tpotmat,1))
|
||||||
Umat(:,:) = Umat(:,:) + Tpotmat(:,:)
|
! Umat(:,:) = Umat(:,:) + Tpotmat(:,:)
|
||||||
|
!
|
||||||
converged = ( sum(abs(Tpotmat(:,:))) < 1.d-6).or.(iter>30)
|
! converged = ( sum(abs(Tpotmat(:,:))) < 1.d-6).or.(iter>30)
|
||||||
end do
|
! end do
|
||||||
END_PROVIDER
|
END_PROVIDER
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
@ -1897,3 +1897,140 @@ end do
|
|||||||
|
|
||||||
end subroutine pivoted_cholesky
|
end subroutine pivoted_cholesky
|
||||||
|
|
||||||
|
subroutine exp_matrix(X,n,exp_X)
|
||||||
|
implicit none
|
||||||
|
double precision, intent(in) :: X(n,n)
|
||||||
|
integer, intent(in):: n
|
||||||
|
double precision, intent(out):: exp_X(n,n)
|
||||||
|
BEGIN_DOC
|
||||||
|
! exponential of the matrix X: X has to be ANTI HERMITIAN !!
|
||||||
|
!
|
||||||
|
! taken from Hellgaker, jorgensen, Olsen book
|
||||||
|
!
|
||||||
|
! section evaluation of matrix exponential (Eqs. 3.1.29 to 3.1.31)
|
||||||
|
END_DOC
|
||||||
|
integer :: i
|
||||||
|
double precision, allocatable :: r2_mat(:,:),eigvalues(:),eigvectors(:,:)
|
||||||
|
double precision, allocatable :: matrix_tmp1(:,:),eigvalues_mat(:,:),matrix_tmp2(:,:)
|
||||||
|
include 'constants.include.F'
|
||||||
|
allocate(r2_mat(n,n),eigvalues(n),eigvectors(n,n))
|
||||||
|
allocate(eigvalues_mat(n,n),matrix_tmp1(n,n),matrix_tmp2(n,n))
|
||||||
|
|
||||||
|
! r2_mat = X^2 in the 3.1.30
|
||||||
|
call get_A_squared(X,n,r2_mat)
|
||||||
|
call lapack_diagd(eigvalues,eigvectors,r2_mat,n,n)
|
||||||
|
eigvalues=-eigvalues
|
||||||
|
|
||||||
|
if(.False.)then
|
||||||
|
!!! For debugging and following the book intermediate
|
||||||
|
! rebuilding the matrix : X^2 = -W t^2 W^T as in 3.1.30
|
||||||
|
! matrix_tmp1 = W t^2
|
||||||
|
print*,'eigvalues = '
|
||||||
|
do i = 1, n
|
||||||
|
print*,i,eigvalues(i)
|
||||||
|
write(*,'(100(F16.10,X))')eigvectors(:,i)
|
||||||
|
enddo
|
||||||
|
eigvalues_mat=0.d0
|
||||||
|
do i = 1,n
|
||||||
|
! t = dsqrt(t^2) where t^2 are eigenvalues of X^2
|
||||||
|
eigvalues(i) = dsqrt(eigvalues(i))
|
||||||
|
eigvalues_mat(i,i) = eigvalues(i)*eigvalues(i)
|
||||||
|
enddo
|
||||||
|
call dgemm('N','N',n,n,n,1.d0,eigvectors,size(eigvectors,1), &
|
||||||
|
eigvalues_mat,size(eigvalues_mat,1),0.d0,matrix_tmp1,size(matrix_tmp1,1))
|
||||||
|
call dgemm('N','T',n,n,n,-1.d0,matrix_tmp1,size(matrix_tmp1,1), &
|
||||||
|
eigvectors,size(eigvectors,1),0.d0,matrix_tmp2,size(matrix_tmp2,1))
|
||||||
|
print*,'r2_mat new = '
|
||||||
|
do i = 1, n
|
||||||
|
write(*,'(100(F16.10,X))')matrix_tmp2(:,i)
|
||||||
|
enddo
|
||||||
|
endif
|
||||||
|
|
||||||
|
! building the exponential
|
||||||
|
! exp(X) = W cos(t) W^T + W t^-1 sin(t) W^T X as in Eq. 3.1.31
|
||||||
|
! matrix_tmp1 = W cos(t)
|
||||||
|
do i = 1,n
|
||||||
|
eigvalues_mat(i,i) = dcos(eigvalues(i))
|
||||||
|
enddo
|
||||||
|
! matrix_tmp2 = W cos(t)
|
||||||
|
call dgemm('N','N',n,n,n,1.d0,eigvectors,size(eigvectors,1), &
|
||||||
|
eigvalues_mat,size(eigvalues_mat,1),0.d0,matrix_tmp1,size(matrix_tmp1,1))
|
||||||
|
! matrix_tmp2 = W cos(t) W^T
|
||||||
|
call dgemm('N','T',n,n,n,-1.d0,matrix_tmp1,size(matrix_tmp1,1), &
|
||||||
|
eigvectors,size(eigvectors,1),0.d0,matrix_tmp2,size(matrix_tmp2,1))
|
||||||
|
exp_X = matrix_tmp2
|
||||||
|
! matrix_tmp2 = W t^-1 sin(t) W^T X
|
||||||
|
do i = 1,n
|
||||||
|
if(dabs(eigvalues(i)).gt.1.d-4)then
|
||||||
|
eigvalues_mat(i,i) = dsin(eigvalues(i))/eigvalues(i)
|
||||||
|
else ! Taylor development of sin(x)/x near x=0 = 1 - x^2/6
|
||||||
|
eigvalues_mat(i,i) = 1.d0 - eigvalues(i)*eigvalues(i)*c_1_3*0.5d0
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
! matrix_tmp1 = W t^-1 sin(t)
|
||||||
|
call dgemm('N','N',n,n,n,1.d0,eigvectors,size(eigvectors,1), &
|
||||||
|
eigvalues_mat,size(eigvalues_mat,1),0.d0,matrix_tmp1,size(matrix_tmp1,1))
|
||||||
|
! matrix_tmp2 = W t^-1 sin(t) W^T
|
||||||
|
call dgemm('N','T',n,n,n,-1.d0,matrix_tmp1,size(matrix_tmp1,1), &
|
||||||
|
eigvectors,size(eigvectors,1),0.d0,matrix_tmp2,size(matrix_tmp2,1))
|
||||||
|
! exp_X += matrix_tmp2 X
|
||||||
|
call dgemm('N','N',n,n,n,1.d0,matrix_tmp2,size(matrix_tmp2,1), &
|
||||||
|
X,size(X,1),1.d0,exp_X,size(exp_X,1))
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
subroutine exp_matrix_taylor(X,n,exp_X,converged)
|
||||||
|
implicit none
|
||||||
|
BEGIN_DOC
|
||||||
|
! exponential of a general real matrix X using the Taylor expansion of exp(X)
|
||||||
|
!
|
||||||
|
! returns the logical converged which checks the convergence
|
||||||
|
END_DOC
|
||||||
|
double precision, intent(in) :: X(n,n)
|
||||||
|
integer, intent(in):: n
|
||||||
|
double precision, intent(out):: exp_X(n,n)
|
||||||
|
logical :: converged
|
||||||
|
double precision :: f
|
||||||
|
integer :: i,iter
|
||||||
|
double precision, allocatable :: Tpotmat(:,:),Tpotmat2(:,:)
|
||||||
|
allocate(Tpotmat(n,n),Tpotmat2(n,n))
|
||||||
|
BEGIN_DOC
|
||||||
|
! exponential of X using Taylor expansion
|
||||||
|
END_DOC
|
||||||
|
Tpotmat(:,:)=0.D0
|
||||||
|
exp_X(:,:) =0.D0
|
||||||
|
do i=1,n
|
||||||
|
Tpotmat(i,i)=1.D0
|
||||||
|
exp_X(i,i) =1.d0
|
||||||
|
end do
|
||||||
|
iter=0
|
||||||
|
converged=.false.
|
||||||
|
do while (.not.converged)
|
||||||
|
iter+=1
|
||||||
|
f = 1.d0 / dble(iter)
|
||||||
|
Tpotmat2(:,:) = Tpotmat(:,:) * f
|
||||||
|
call dgemm('N','N', n,n,n,1.d0, &
|
||||||
|
Tpotmat2, size(Tpotmat2,1), &
|
||||||
|
X, size(X,1), 0.d0, &
|
||||||
|
Tpotmat, size(Tpotmat,1))
|
||||||
|
exp_X(:,:) = exp_X(:,:) + Tpotmat(:,:)
|
||||||
|
|
||||||
|
converged = ( sum(abs(Tpotmat(:,:))) < 1.d-6).or.(iter>30)
|
||||||
|
end do
|
||||||
|
if(.not.converged)then
|
||||||
|
print*,'Warning !! exp_matrix_taylor did not converge !'
|
||||||
|
endif
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
subroutine get_A_squared(A,n,A2)
|
||||||
|
implicit none
|
||||||
|
BEGIN_DOC
|
||||||
|
! A2 = A A where A is n x n matrix. Use the dgemm routine
|
||||||
|
END_DOC
|
||||||
|
double precision, intent(in) :: A(n,n)
|
||||||
|
integer, intent(in) :: n
|
||||||
|
double precision, intent(out):: A2(n,n)
|
||||||
|
call dgemm('N','N',n,n,n,1.d0,A,size(A,1),A,size(A,1),0.d0,A2,size(A2,1))
|
||||||
|
end
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user