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Merge branch 'master' into add_lds

This commit is contained in:
Anthony Scemama 2021-11-17 14:07:47 +01:00 committed by GitHub
commit 7d4292374f
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9 changed files with 5183 additions and 152 deletions

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@ -79,7 +79,6 @@ int main() {
const int64_t ldc );
#+END_src
*** Source
#+begin_src f90 :tangle (eval f)
integer function qmckl_dgemm_f(context, TransA, TransB, m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC) &
@ -91,21 +90,22 @@ integer function qmckl_dgemm_f(context, TransA, TransB, m, n, k, alpha, A, LDA,
integer*8 , intent(in) :: m, n, k
real*8 , intent(in) :: alpha, beta
integer*8 , intent(in) :: lda
real*8 , intent(in) :: A(m,k)
real*8 , intent(in) :: A(lda,*)
integer*8 , intent(in) :: ldb
real*8 , intent(in) :: B(k,n)
real*8 , intent(in) :: B(ldb,*)
integer*8 , intent(in) :: ldc
real*8 , intent(out) :: C(m,n)
real*8 , intent(out) :: C(ldc,*)
real*8, allocatable :: AT(:,:), BT(:,:), CT(:,:)
integer*4 :: qmckl_dgemm_N_N_f
integer*8 :: i,j,l, LDA_2, LDB_2
info = QMCKL_SUCCESS
if (TransA) then
allocate(AT(k,m))
do i = 1, m
do j = 1, k
allocate(AT(m,k))
do i = 1, k
do j = 1, m
AT(j,i) = A(i,j)
end do
end do
@ -115,9 +115,9 @@ integer function qmckl_dgemm_f(context, TransA, TransB, m, n, k, alpha, A, LDA,
endif
if (TransB) then
allocate(BT(n,k))
do i = 1, k
do j = 1, n
allocate(BT(k,n))
do i = 1, n
do j = 1, k
BT(j,i) = B(i,j)
end do
end do
@ -162,25 +162,75 @@ integer function qmckl_dgemm_f(context, TransA, TransB, m, n, k, alpha, A, LDA,
endif
if (TransA) then
if (alpha == 1.d0 .and. beta == 0.d0) then
C = matmul(AT,B)
else
C = beta*C + alpha*matmul(AT,B)
endif
info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, AT, LDA_2, B, LDB_2, beta, c, LDC)
else if (TransB) then
if (alpha == 1.d0 .and. beta == 0.d0) then
C = matmul(A,BT)
info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA_2, BT, LDB_2, beta, c, LDC)
else if (TransA .and. TransB) then
info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, AT, LDA_2, BT, LDB_2, beta, c, LDC)
else
C = beta*C + alpha*matmul(A,BT)
info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA_2, B, LDB_2, beta, c, LDC)
endif
else
if (alpha == 1.d0 .and. beta == 0.d0) then
end function qmckl_dgemm_f
integer function qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC) &
result(info)
use qmckl
implicit none
integer(qmckl_context) , intent(in) :: context
integer*8 , intent(in) :: m, n, k
real*8 , intent(in) :: alpha, beta
integer*8 , intent(in) :: lda
real*8 , intent(in) :: A(lda,k)
integer*8 , intent(in) :: ldb
real*8 , intent(in) :: B(ldb,n)
integer*8 , intent(in) :: ldc
real*8 , intent(out) :: C(ldc,n)
integer*8 :: i,j,l, LDA_2, LDB_2
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (m <= 0_8) then
info = QMCKL_INVALID_ARG_4
return
endif
if (n <= 0_8) then
info = QMCKL_INVALID_ARG_5
return
endif
if (k <= 0_8) then
info = QMCKL_INVALID_ARG_6
return
endif
if (LDA /= m) then
info = QMCKL_INVALID_ARG_9
return
endif
if (LDB /= k) then
info = QMCKL_INVALID_ARG_10
return
endif
if (LDC /= m) then
info = QMCKL_INVALID_ARG_13
return
endif
if (alpha == 1.0d0 .and. beta == 0.0d0) then
C = matmul(A,B)
else
C = beta*C + alpha*matmul(A,B)
endif
endif
end function qmckl_dgemm_f
end function qmckl_dgemm_N_N_f
#+end_src
*** C interface :noexport:
@ -321,6 +371,687 @@ qmckl_exit_code test_qmckl_dgemm(qmckl_context context);
assert(QMCKL_SUCCESS == test_qmckl_dgemm(context));
#+end_src
** ~qmckl_adjoint~
Matrix adjoint. Given a matrix M, returns a matrix M⁻¹ such that:
\[
M · M^{-1} = I
\]
This is a native Fortran implementation hand written (by: A. Scemama)
only for small matrices (<=5x5).
TODO: Add description about the external library dependence.
#+NAME: qmckl_adjoint_args
| qmckl_context | context | in | Global state |
| int64_t | m | in | Number of rows of the input matrix |
| int64_t | n | in | Number of columns of the input matrix |
| int64_t | lda | in | Leading dimension of array ~A~ |
| double | A[][lda] | inout | Array containing the $m \times n$ matrix $A$ |
| double | det_l | inout | determinant of A |
*** Requirements
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~m > 0~
- ~n > 0~
- ~lda >= m~
- ~A~ is allocated with at least $m \times n \times 8$ bytes
*** C header
#+CALL: generate_c_header(table=qmckl_adjoint_args,rettyp="qmckl_exit_code",fname="qmckl_adjoint")
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_adjoint (
const qmckl_context context,
const int64_t m,
const int64_t n,
const int64_t lda,
double* A,
double det_l );
#+end_src
*** Source
#+begin_src f90 :tangle (eval f)
integer function qmckl_adjoint_f(context, ma, na, LDA, A, det_l) &
result(info)
use qmckl
implicit none
integer(qmckl_context) , intent(in) :: context
double precision, intent(inout) :: A (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: ma
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
integer :: i,j
info = QMCKL_SUCCESS
select case (na)
case default
!DIR$ forceinline
print *," TODO: Implement general adjoint"
stop 0
case (5)
!DIR$ forceinline
call adjoint5(a,LDA,na,det_l)
case (4)
!DIR$ forceinline
call adjoint4(a,LDA,na,det_l)
case (3)
!DIR$ forceinline
call adjoint3(a,LDA,na,det_l)
case (2)
!DIR$ forceinline
call adjoint2(a,LDA,na,det_l)
case (1)
!DIR$ forceinline
call adjoint1(a,LDA,na,det_l)
case (0)
det_l=1.d0
end select
end function qmckl_adjoint_f
subroutine adjoint1(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
call cofactor1(a,LDA,na,det_l)
end
subroutine adjoint2(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(2,2)
call cofactor2(a,LDA,na,det_l)
! Calculate the transpose
b(1,1) = a(1,1)
b(1,2) = a(2,1)
b(2,1) = a(1,2)
b(2,2) = a(2,2)
a(1,1) = b(1,1)
a(1,2) = b(1,2)
a(2,1) = b(2,1)
a(2,2) = b(2,2)
end
subroutine adjoint3(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(3,3)
call cofactor3(a,LDA,na,det_l)
! Calculate the transpose
b(1,1) = a(1,1)
b(1,2) = a(2,1)
b(1,3) = a(3,1)
b(2,1) = a(1,2)
b(2,2) = a(2,2)
b(2,3) = a(3,2)
b(3,1) = a(1,3)
b(3,2) = a(2,3)
b(3,3) = a(3,3)
! copy
a(1,1) = b(1,1)
a(2,1) = b(2,1)
a(3,1) = b(3,1)
a(1,2) = b(1,2)
a(2,2) = b(2,2)
a(3,2) = b(3,2)
a(1,3) = b(1,3)
a(2,3) = b(2,3)
a(3,3) = b(3,3)
end
subroutine adjoint4(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(4,4)
call cofactor4(a,LDA,na,det_l)
! Calculate the transpose
b(1,1) = a(1,1)
b(1,2) = a(2,1)
b(1,3) = a(3,1)
b(1,4) = a(4,1)
b(2,1) = a(1,2)
b(2,2) = a(2,2)
b(2,3) = a(3,2)
b(2,4) = a(4,2)
b(3,1) = a(1,3)
b(3,2) = a(2,3)
b(3,3) = a(3,3)
b(3,4) = a(4,3)
b(4,1) = a(1,4)
b(4,2) = a(2,4)
b(4,3) = a(3,4)
b(4,4) = a(4,4)
! copy
a(1,1) = b(1,1)
a(2,1) = b(2,1)
a(3,1) = b(3,1)
a(4,1) = b(4,1)
a(1,2) = b(1,2)
a(2,2) = b(2,2)
a(3,2) = b(3,2)
a(4,2) = b(4,2)
a(1,3) = b(1,3)
a(2,3) = b(2,3)
a(3,3) = b(3,3)
a(4,3) = b(4,3)
a(1,4) = b(1,4)
a(2,4) = b(2,4)
a(3,4) = b(3,4)
a(4,4) = b(4,4)
end
subroutine adjoint5(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(5,5)
call cofactor5(a,LDA,na,det_l)
! Calculate the transpose
b(1,1) = a(1,1)
b(1,2) = a(2,1)
b(1,3) = a(3,1)
b(1,4) = a(4,1)
b(1,5) = a(5,1)
b(2,1) = a(1,2)
b(2,2) = a(2,2)
b(2,3) = a(3,2)
b(2,4) = a(4,2)
b(2,5) = a(5,2)
b(3,1) = a(1,3)
b(3,2) = a(2,3)
b(3,3) = a(3,3)
b(3,4) = a(4,3)
b(3,5) = a(5,3)
b(4,1) = a(1,4)
b(4,2) = a(2,4)
b(4,3) = a(3,4)
b(4,4) = a(4,4)
b(4,5) = a(5,4)
b(5,1) = a(1,5)
b(5,2) = a(2,5)
b(5,3) = a(3,5)
b(5,4) = a(4,5)
b(5,5) = a(5,5)
! copy
a(1,1) = b(1,1)
a(2,1) = b(2,1)
a(3,1) = b(3,1)
a(4,1) = b(4,1)
a(5,1) = b(5,1)
a(1,2) = b(1,2)
a(2,2) = b(2,2)
a(3,2) = b(3,2)
a(4,2) = b(4,2)
a(5,2) = b(5,2)
a(1,3) = b(1,3)
a(2,3) = b(2,3)
a(3,3) = b(3,3)
a(4,3) = b(4,3)
a(5,3) = b(5,3)
a(1,4) = b(1,4)
a(2,4) = b(2,4)
a(3,4) = b(3,4)
a(4,4) = b(4,4)
a(5,4) = b(5,4)
a(1,5) = b(1,5)
a(2,5) = b(2,5)
a(3,5) = b(3,5)
a(4,5) = b(4,5)
a(5,5) = b(5,5)
end
subroutine cofactor1(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
det_l = a(1,1)
a(1,1) = 1.d0
end
subroutine cofactor2(a,LDA,na,det_l)
implicit none
double precision :: a (LDA,na)
integer*8 :: LDA
integer*8 :: na
double precision :: det_l
double precision :: b(2,2)
b(1,1) = a(1,1)
b(2,1) = a(2,1)
b(1,2) = a(1,2)
b(2,2) = a(2,2)
det_l = a(1,1)*a(2,2) - a(1,2)*a(2,1)
a(1,1) = b(2,2)
a(2,1) = -b(2,1)
a(1,2) = -b(1,2)
a(2,2) = b(1,1)
end
subroutine cofactor3(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(4,3)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
integer :: i
det_l = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) &
-a(1,2)*(a(2,1)*a(3,3)-a(2,3)*a(3,1)) &
+a(1,3)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
do i=1,4
b(i,1) = a(i,1)
b(i,2) = a(i,2)
b(i,3) = a(i,3)
enddo
a(1,1) = b(2,2)*b(3,3) - b(2,3)*b(3,2)
a(2,1) = b(2,3)*b(3,1) - b(2,1)*b(3,3)
a(3,1) = b(2,1)*b(3,2) - b(2,2)*b(3,1)
a(1,2) = b(1,3)*b(3,2) - b(1,2)*b(3,3)
a(2,2) = b(1,1)*b(3,3) - b(1,3)*b(3,1)
a(3,2) = b(1,2)*b(3,1) - b(1,1)*b(3,2)
a(1,3) = b(1,2)*b(2,3) - b(1,3)*b(2,2)
a(2,3) = b(1,3)*b(2,1) - b(1,1)*b(2,3)
a(3,3) = b(1,1)*b(2,2) - b(1,2)*b(2,1)
end
subroutine cofactor4(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(4,4)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
integer :: i,j
det_l = a(1,1)*(a(2,2)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
-a(2,3)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
+a(2,4)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))) &
-a(1,2)*(a(2,1)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
-a(2,3)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
+a(2,4)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))) &
+a(1,3)*(a(2,1)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
-a(2,2)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
+a(2,4)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))) &
-a(1,4)*(a(2,1)*(a(3,2)*a(4,3)-a(3,3)*a(4,2)) &
-a(2,2)*(a(3,1)*a(4,3)-a(3,3)*a(4,1)) &
+a(2,3)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))
do i=1,4
b(1,i) = a(1,i)
b(2,i) = a(2,i)
b(3,i) = a(3,i)
b(4,i) = a(4,i)
enddo
a(1,1) = b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))
a(2,1) = -b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))+b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))-b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))
a(3,1) = b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(4,1) = -b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))+b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))-b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(1,2) = -b(1,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))+b(1,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(1,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))
a(2,2) = b(1,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(1,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(1,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))
a(3,2) = -b(1,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(1,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))-b(1,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(4,2) = b(1,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(1,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(1,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
a(1,3) = b(1,2)*(b(2,3)*b(4,4)-b(2,4)*b(4,3))-b(1,3)*(b(2,2)*b(4,4)-b(2,4)*b(4,2))+b(1,4)*(b(2,2)*b(4,3)-b(2,3)*b(4,2))
a(2,3) = -b(1,1)*(b(2,3)*b(4,4)-b(2,4)*b(4,3))+b(1,3)*(b(2,1)*b(4,4)-b(2,4)*b(4,1))-b(1,4)*(b(2,1)*b(4,3)-b(2,3)*b(4,1))
a(3,3) = b(1,1)*(b(2,2)*b(4,4)-b(2,4)*b(4,2))-b(1,2)*(b(2,1)*b(4,4)-b(2,4)*b(4,1))+b(1,4)*(b(2,1)*b(4,2)-b(2,2)*b(4,1))
a(4,3) = -b(1,1)*(b(2,2)*b(4,3)-b(2,3)*b(4,2))+b(1,2)*(b(2,1)*b(4,3)-b(2,3)*b(4,1))-b(1,3)*(b(2,1)*b(4,2)-b(2,2)*b(4,1))
a(1,4) = -b(1,2)*(b(2,3)*b(3,4)-b(2,4)*b(3,3))+b(1,3)*(b(2,2)*b(3,4)-b(2,4)*b(3,2))-b(1,4)*(b(2,2)*b(3,3)-b(2,3)*b(3,2))
a(2,4) = b(1,1)*(b(2,3)*b(3,4)-b(2,4)*b(3,3))-b(1,3)*(b(2,1)*b(3,4)-b(2,4)*b(3,1))+b(1,4)*(b(2,1)*b(3,3)-b(2,3)*b(3,1))
a(3,4) = -b(1,1)*(b(2,2)*b(3,4)-b(2,4)*b(3,2))+b(1,2)*(b(2,1)*b(3,4)-b(2,4)*b(3,1))-b(1,4)*(b(2,1)*b(3,2)-b(2,2)*b(3,1))
a(4,4) = b(1,1)*(b(2,2)*b(3,3)-b(2,3)*b(3,2))-b(1,2)*(b(2,1)*b(3,3)-b(2,3)*b(3,1))+b(1,3)*(b(2,1)*b(3,2)-b(2,2)*b(3,1))
end
subroutine cofactor5(a,LDA,na,det_l)
implicit none
double precision, intent(inout) :: a (LDA,na)
integer*8, intent(in) :: LDA
integer*8, intent(in) :: na
double precision, intent(inout) :: det_l
double precision :: b(5,5)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
integer :: i,j
det_l = a(1,1)*(a(2,2)*(a(3,3)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*( &
a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(3,5)*(a(4,3)*a(5,4)-a(4,4)*a(5,3)))- &
a(2,3)*(a(3,2)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*(a(4,2)*a(5,5)- &
a(4,5)*a(5,2))+a(3,5)*(a(4,2)*a(5,4)-a(4,4)*a(5,2)))+a(2,4)*(a(3,2)*( &
a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+ &
a(3,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,5)*(a(3,2)*(a(4,3)*a(5,4)- &
a(4,4)*a(5,3))-a(3,3)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))+a(3,4)*(a(4,2)* &
a(5,3)-a(4,3)*a(5,2))))-a(1,2)*(a(2,1)*(a(3,3)*(a(4,4)*a(5,5)-a(4,5)* &
a(5,4))-a(3,4)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(3,5)*(a(4,3)*a(5,4)- &
a(4,4)*a(5,3)))-a(2,3)*(a(3,1)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*( &
a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,4)-a(4,4)*a(5,1)))+ &
a(2,4)*(a(3,1)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,1)*a(5,5)- &
a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))-a(2,5)*(a(3,1)*( &
a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+ &
a(3,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))))+a(1,3)*(a(2,1)*(a(3,2)*(a(4,4)* &
a(5,5)-a(4,5)*a(5,4))-a(3,4)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(3,5)*( &
a(4,2)*a(5,4)-a(4,4)*a(5,2)))-a(2,2)*(a(3,1)*(a(4,4)*a(5,5)-a(4,5)* &
a(5,4))-a(3,4)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,4)- &
a(4,4)*a(5,1)))+a(2,4)*(a(3,1)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))-a(3,2)*( &
a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,2)-a(4,2)*a(5,1)))- &
a(2,5)*(a(3,1)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))-a(3,2)*(a(4,1)*a(5,4)- &
a(4,4)*a(5,1))+a(3,4)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))-a(1,4)*(a(2,1)*( &
a(3,2)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,2)*a(5,5)-a(4,5)* &
a(5,2))+a(3,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,2)*(a(3,1)*(a(4,3)* &
a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*( &
a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(2,3)*(a(3,1)*(a(4,2)*a(5,5)-a(4,5)* &
a(5,2))-a(3,2)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,2)- &
a(4,2)*a(5,1)))-a(2,5)*(a(3,1)*(a(4,2)*a(5,3)-a(4,3)*a(5,2))-a(3,2)*( &
a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(3,3)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))+ &
a(1,5)*(a(2,1)*(a(3,2)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,2)* &
a(5,4)-a(4,4)*a(5,2))+a(3,4)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,2)*( &
a(3,1)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,1)*a(5,4)-a(4,4)* &
a(5,1))+a(3,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(2,3)*(a(3,1)*(a(4,2)* &
a(5,4)-a(4,4)*a(5,2))-a(3,2)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(3,4)*( &
a(4,1)*a(5,2)-a(4,2)*a(5,1)))-a(2,4)*(a(3,1)*(a(4,2)*a(5,3)-a(4,3)* &
a(5,2))-a(3,2)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(3,3)*(a(4,1)*a(5,2)- &
a(4,2)*a(5,1))))
do i=1,5
b(1,i) = a(1,i)
b(2,i) = a(2,i)
b(3,i) = a(3,i)
b(4,i) = a(4,i)
b(5,i) = a(5,i)
enddo
a(1,1) = &
(b(2,2)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))-b(2,3)* &
(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))+b(2,4)* &
(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(2,5)* &
(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))))
a(2,1) = &
(-b(2,1)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))+b(2,3)* &
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))-b(2,4)* &
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(2,5)* &
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))))
a(3,1) = &
(b(2,1)*(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))-b(2,2)* &
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))+b(2,4)* &
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(2,5)* &
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(4,1) = &
(-b(2,1)*(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(2,2)* &
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(2,3)* &
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(2,5)* &
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(5,1) = &
(b(2,1)*(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(2,2)* &
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(2,3)* &
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(2,4)* &
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(1,2) = &
(-b(1,2)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))+b(1,3)* &
(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))-b(1,4)* &
(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(1,5)* &
(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))))
a(2,2) = &
(b(1,1)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))-b(1,3)* &
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))+b(1,4)* &
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(1,5)* &
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))))
a(3,2) = &
(-b(1,1)*(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))+b(1,2)* &
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))-b(1,4)* &
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(1,5)* &
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(4,2) = &
(b(1,1)*(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(1,2)* &
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(1,3)* &
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(1,5)* &
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(5,2) = &
(-b(1,1)*(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(1,2)* &
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(1,3)* &
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(1,4)* &
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(1,3) = &
(b(1,2)*(b(2,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(2,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))-b(1,3)* &
(b(2,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))+b(1,4)* &
(b(2,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(1,5)* &
(b(2,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(2,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))))
a(2,3) = &
(-b(1,1)*(b(2,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(2,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))+b(1,3)* &
(b(2,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))-b(1,4)* &
(b(2,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(1,5)* &
(b(2,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))))
a(3,3) = &
(b(1,1)*(b(2,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))-b(1,2)* &
(b(2,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))+b(1,4)* &
(b(2,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(2,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(1,5)* &
(b(2,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(2,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(4,3) = &
(-b(1,1)*(b(2,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(1,2)* &
(b(2,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(1,3)* &
(b(2,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(2,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(1,5)* &
(b(2,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(2,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(2,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(5,3) = &
(b(1,1)*(b(2,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(2,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(1,2)* &
(b(2,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(1,3)* &
(b(2,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(2,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(1,4)* &
(b(2,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(2,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(2,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
a(1,4) = &
(-b(1,2)*(b(2,3)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))+b(2,5)*(b(3,3)*b(5,4)-b(3,4)*b(5,3)))+b(1,3)* &
(b(2,2)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,4)-b(3,4)*b(5,2)))-b(1,4)* &
(b(2,2)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,3)-b(3,3)*b(5,2)))+b(1,5)* &
(b(2,2)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))+b(2,4)*(b(3,2)*b(5,3)-b(3,3)*b(5,2))))
a(2,4) = &
(b(1,1)*(b(2,3)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))+b(2,5)*(b(3,3)*b(5,4)-b(3,4)*b(5,3)))-b(1,3)* &
(b(2,1)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,4)-b(3,4)*b(5,1)))+b(1,4)* &
(b(2,1)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,3)-b(3,3)*b(5,1)))-b(1,5)* &
(b(2,1)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,3)-b(3,3)*b(5,1))))
a(3,4) = &
(-b(1,1)*(b(2,2)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,4)-b(3,4)*b(5,2)))+b(1,2)* &
(b(2,1)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,4)-b(3,4)*b(5,1)))-b(1,4)* &
(b(2,1)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))-b(2,2)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,2)-b(3,2)*b(5,1)))+b(1,5)* &
(b(2,1)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))-b(2,2)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,2)-b(3,2)*b(5,1))))
a(4,4) = &
(b(1,1)*(b(2,2)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,3)-b(3,3)*b(5,2)))-b(1,2)* &
(b(2,1)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,3)-b(3,3)*b(5,1)))+b(1,3)* &
(b(2,1)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))-b(2,2)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,2)-b(3,2)*b(5,1)))-b(1,5)* &
(b(2,1)*(b(3,2)*b(5,3)-b(3,3)*b(5,2))-b(2,2)*(b(3,1)*b(5,3)-b(3,3)*b(5,1))+b(2,3)*(b(3,1)*b(5,2)-b(3,2)*b(5,1))))
a(5,4) = &
(-b(1,1)*(b(2,2)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))+b(2,4)*(b(3,2)*b(5,3)-b(3,3)*b(5,2)))+b(1,2)* &
(b(2,1)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,3)-b(3,3)*b(5,1)))-b(1,3)* &
(b(2,1)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))-b(2,2)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,2)-b(3,2)*b(5,1)))+b(1,4)* &
(b(2,1)*(b(3,2)*b(5,3)-b(3,3)*b(5,2))-b(2,2)*(b(3,1)*b(5,3)-b(3,3)*b(5,1))+b(2,3)*(b(3,1)*b(5,2)-b(3,2)*b(5,1))))
a(1,5) = &
(b(1,2)*(b(2,3)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))+b(2,5)*(b(3,3)*b(4,4)-b(3,4)*b(4,3)))-b(1,3)* &
(b(2,2)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,4)-b(3,4)*b(4,2)))+b(1,4)* &
(b(2,2)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,3)-b(3,3)*b(4,2)))-b(1,5)* &
(b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))))
a(2,5) = &
(-b(1,1)*(b(2,3)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))+b(2,5)*(b(3,3)*b(4,4)-b(3,4)*b(4,3)))+b(1,3)* &
(b(2,1)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,4)-b(3,4)*b(4,1)))-b(1,4)* &
(b(2,1)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,3)-b(3,3)*b(4,1)))+b(1,5)* &
(b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))))
a(3,5) = &
(b(1,1)*(b(2,2)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,4)-b(3,4)*b(4,2)))-b(1,2)* &
(b(2,1)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,4)-b(3,4)*b(4,1)))+b(1,4)* &
(b(2,1)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))-b(2,2)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,2)-b(3,2)*b(4,1)))-b(1,5)* &
(b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))))
a(4,5) = &
(-b(1,1)*(b(2,2)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,3)-b(3,3)*b(4,2)))+b(1,2)* &
(b(2,1)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,3)-b(3,3)*b(4,1)))-b(1,3)* &
(b(2,1)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))-b(2,2)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,2)-b(3,2)*b(4,1)))+b(1,5)* &
(b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))))
a(5,5) = &
(b(1,1)*(b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2)))-b(1,2)* &
(b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1)))+b(1,3)* &
(b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1)))-b(1,4)* &
(b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))))
end
#+end_src
*** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_adjoint_args,rettyp="qmckl_exit_code",fname="qmckl_adjoint")
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_adjoint &
(context, m, n, lda, A, det_l) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: m
integer (c_int64_t) , intent(in) , value :: n
integer (c_int64_t) , intent(in) , value :: lda
real (c_double ) , intent(inout) :: A(lda,*)
real (c_double ) , intent(inout) :: det_l
integer(c_int32_t), external :: qmckl_adjoint_f
info = qmckl_adjoint_f &
(context, m, n, lda, A, det_l)
end function qmckl_adjoint
#+end_src
#+CALL: generate_f_interface(table=qmckl_adjoint_args,rettyp="qmckl_exit_code",fname="qmckl_adjoint")
#+RESULTS:
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_adjoint &
(context, m, n, lda, A, det_l) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: m
integer (c_int64_t) , intent(in) , value :: n
integer (c_int64_t) , intent(in) , value :: lda
real (c_double ) , intent(inout) :: A(lda,*)
real (c_double ) , intent(inout) :: det_l
end function qmckl_adjoint
end interface
#+end_src
*** Test :noexport:
#+begin_src f90 :tangle (eval f_test)
integer(qmckl_exit_code) function test_qmckl_adjoint(context) bind(C)
use qmckl
implicit none
integer(qmckl_context), intent(in), value :: context
double precision, allocatable :: A(:,:), C(:,:)
integer*8 :: m, n, k, LDA, LDB, LDC
integer*8 :: i,j,l
double precision :: x, det_l, det_l_ref
m = 4_8
k = 4_8
LDA = m
LDB = m
LDC = m
allocate( A(LDA,k), C(LDC,k))
A = 0.10d0
C = 0.d0
A(1,1) = 1.0d0;
A(2,2) = 2.0d0;
A(3,3) = 3.0d0;
A(4,4) = 4.0d0;
! Exact inverse (Mathematica)
C(1,1) = 1.0102367161391992d0
C(2,2) = 0.5036819224578257d0
C(3,3) = 0.33511197860555897d0
C(4,4) = 0.2510382472105688d0
C(1,2) = -0.047782608144589914d0
C(1,3) = -0.031305846715420985d0
C(1,4) = -0.023278706531979707d0
C(2,3) = -0.014829085286252043d0
C(2,4) = -0.011026755725674596d0
C(3,4) = -0.007224426165097149d0
C(2,1) = -0.047782608144589914d0
C(3,1) = -0.031305846715420985d0
C(4,1) = -0.023278706531979707d0
C(3,2) = -0.014829085286252043d0
C(4,2) = -0.011026755725674596d0
C(4,3) = -0.007224426165097149d0
det_l_ref = 23.6697d0
test_qmckl_adjoint = qmckl_adjoint(context, m, k, LDA, A, det_l)
if (test_qmckl_adjoint /= QMCKL_SUCCESS) return
test_qmckl_adjoint = QMCKL_FAILURE
x = 0.d0
do j=1,m
do i=1,k
x = x + (A(i,j) - (C(i,j) * det_l_ref))**2
end do
end do
if (dabs(x) <= 1.d-15 .and. (dabs(det_l_ref - det_l)) <= 1.d-15) then
test_qmckl_adjoint = QMCKL_SUCCESS
endif
deallocate(A,C)
end function test_qmckl_adjoint
#+end_src
#+begin_src c :comments link :tangle (eval c_test)
qmckl_exit_code test_qmckl_adjoint(qmckl_context context);
assert(QMCKL_SUCCESS == test_qmckl_adjoint(context));
#+end_src
* End of files :noexport:
#+begin_src c :comments link :tangle (eval c_test)

View File

@ -33,10 +33,14 @@ int main() {
#include "qmckl_ao_private_type.h"
#include "qmckl_mo_private_type.h"
#include "qmckl_jastrow_private_type.h"
#include "qmckl_determinant_private_type.h"
#include "qmckl_local_energy_private_type.h"
#include "qmckl_nucleus_private_func.h"
#include "qmckl_electron_private_func.h"
#include "qmckl_ao_private_func.h"
#include "qmckl_mo_private_func.h"
#include "qmckl_determinant_private_func.h"
#include "qmckl_local_energy_private_func.h"
#+end_src
#+begin_src c :tangle (eval c)
@ -123,10 +127,10 @@ typedef struct qmckl_context_struct {
qmckl_ao_basis_struct ao_basis;
qmckl_mo_basis_struct mo_basis;
qmckl_jastrow_struct jastrow;
qmckl_determinant_struct det;
qmckl_local_energy_struct local_energy;
/* To be implemented:
qmckl_mo_struct mo;
qmckl_determinant_struct det;
,*/
} qmckl_context_struct;
@ -240,6 +244,12 @@ qmckl_context qmckl_context_create() {
rc = qmckl_init_ao_basis(context);
assert (rc == QMCKL_SUCCESS);
rc = qmckl_init_mo_basis(context);
assert (rc == QMCKL_SUCCESS);
rc = qmckl_init_determinant(context);
assert (rc == QMCKL_SUCCESS);
}
/* Allocate qmckl_memory_struct */

2073
org/qmckl_determinant.org Normal file

File diff suppressed because it is too large Load Diff

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@ -68,6 +68,7 @@ int main() {
The following data stored in the context:
|---------------------------+----------------------------+-------------------------------------------|
| ~uninitialized~ | ~int32_t~ | Keeps bit set for uninitialized data |
| ~num~ | ~int64_t~ | Total number of electrons |
| ~up_num~ | ~int64_t~ | Number of up-spin electrons |
@ -79,6 +80,10 @@ int main() {
| ~coord_new~ | ~double[walk_num][3][num]~ | New set of electron coordinates |
| ~coord_old~ | ~double[walk_num][3][num]~ | Old set of electron coordinates |
| ~coord_new_date~ | ~uint64_t~ | Last modification date of the coordinates |
Computed data:
|-------------------------------------+--------------------------------------+----------------------------------------------------------------------|
| ~ee_distance~ | ~double[walk_num][num][num]~ | Electron-electron distances |
| ~ee_distance_date~ | ~uint64_t~ | Last modification date of the electron-electron distances |
| ~en_distance~ | ~double[walk_num][nucl_num][num]~ | Electron-nucleus distances |
@ -87,6 +92,10 @@ int main() {
| ~ee_distance_rescaled_date~ | ~uint64_t~ | Last modification date of the electron-electron distances |
| ~ee_distance_rescaled_deriv_e~ | ~double[walk_num][4][num][num]~ | Electron-electron rescaled distances derivatives |
| ~ee_distance_rescaled_deriv_e_date~ | ~uint64_t~ | Last modification date of the electron-electron distance derivatives |
| ~ee_pot~ | ~double[walk_num]~ | Electron-electron rescaled distances derivatives |
| ~ee_pot_date~ | ~uint64_t~ | Last modification date of the electron-electron distance derivatives |
| ~en_pot~ | double[walk_num] | Electron-nucleus potential energy |
| ~en_pot_date~ | int64_t | Date when the electron-nucleus potential energy was computed |
| ~en_distance_rescaled~ | ~double[walk_num][nucl_num][num]~ | Electron-nucleus distances |
| ~en_distance_rescaled_date~ | ~uint64_t~ | Last modification date of the electron-electron distances |
| ~en_distance_rescaled_deriv_e~ | ~double[walk_num][4][nucl_num][num]~ | Electron-electron rescaled distances derivatives |
@ -105,6 +114,8 @@ typedef struct qmckl_electron_struct {
int64_t coord_new_date;
int64_t ee_distance_date;
int64_t en_distance_date;
int64_t ee_pot_date;
int64_t en_pot_date;
int64_t ee_distance_rescaled_date;
int64_t ee_distance_rescaled_deriv_e_date;
int64_t en_distance_rescaled_date;
@ -113,6 +124,8 @@ typedef struct qmckl_electron_struct {
double* coord_old;
double* ee_distance;
double* en_distance;
double* ee_pot;
double* en_pot;
double* ee_distance_rescaled;
double* ee_distance_rescaled_deriv_e;
double* en_distance_rescaled;
@ -1570,6 +1583,205 @@ rc = qmckl_get_electron_ee_distance_rescaled_deriv_e(context, ee_distance_rescal
#+end_src
** Electron-electron potential
~ee_pot~ calculates the ~ee~ potential energy.
\[
\mathcal{V}_{ee} = \sum_{i=1}^{N_e}\sum_{j>i}^{N_e}\frac{1}{r_{ij}}
\]
where \(\mathcal{V}_{ee}\) is the ~ee~ potential and \[r_{ij}\] the ~ee~
distance.
*** Get
#+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code qmckl_get_electron_ee_potential(qmckl_context context, double* const ee_pot);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_get_electron_ee_potential(qmckl_context context, double* const ee_pot)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_exit_code rc;
rc = qmckl_provide_ee_potential(context);
if (rc != QMCKL_SUCCESS) return rc;
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
size_t sze = ctx->electron.walk_num * sizeof(double);
memcpy(ee_pot, ctx->electron.ee_pot, sze);
return QMCKL_SUCCESS;
}
#+end_src
*** Provide :noexport:
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_provide_ee_potential(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_provide_ee_potential(qmckl_context context)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
if (!ctx->electron.provided) return QMCKL_NOT_PROVIDED;
qmckl_exit_code rc = qmckl_provide_ee_distance(context);
if (rc != QMCKL_SUCCESS) return rc;
/* Compute if necessary */
if (ctx->electron.coord_new_date > ctx->electron.ee_pot_date) {
/* Allocate array */
if (ctx->electron.ee_pot == NULL) {
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = ctx->electron.walk_num * sizeof(double);
double* ee_pot = (double*) qmckl_malloc(context, mem_info);
if (ee_pot == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_ee_potential",
NULL);
}
ctx->electron.ee_pot = ee_pot;
}
qmckl_exit_code rc =
qmckl_compute_ee_potential(context,
ctx->electron.num,
ctx->electron.walk_num,
ctx->electron.ee_distance,
ctx->electron.ee_pot);
if (rc != QMCKL_SUCCESS) {
return rc;
}
ctx->electron.ee_pot_date = ctx->date;
}
return QMCKL_SUCCESS;
}
#+end_src
*** Compute
:PROPERTIES:
:Name: qmckl_compute_ee_potential
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
#+NAME: qmckl_ee_potential_args
| qmckl_context | context | in | Global state |
| int64_t | elec_num | in | Number of electrons |
| int64_t | walk_num | in | Number of walkers |
| double | ee_distance[walk_num][elec_num][elec_num] | in | Electron-electron rescaled distances |
| double | ee_pot[walk_num] | out | Electron-electron potential |
#+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_ee_potential_f(context, elec_num, walk_num, &
ee_distance, ee_pot) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: ee_distance(elec_num,elec_num,walk_num)
double precision , intent(out) :: ee_pot(walk_num)
integer*8 :: nw, i, j
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
ee_pot = 0.0d0
do nw=1,walk_num
do j=2,elec_num
do i=1,j-1
if (dabs(ee_distance(i,j,nw)) > 1e-5) then
ee_pot(nw) = ee_pot(nw) + 1.0d0/(ee_distance(i,j,nw))
endif
end do
end do
end do
end function qmckl_compute_ee_potential_f
#+end_src
#+CALL: generate_c_header(table=qmckl_ee_potential_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_compute_ee_potential (
const qmckl_context context,
const int64_t elec_num,
const int64_t walk_num,
const double* ee_distance,
double* const ee_pot );
#+end_src
#+CALL: generate_c_interface(table=qmckl_ee_potential_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_compute_ee_potential &
(context, elec_num, walk_num, ee_distance, ee_pot) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: elec_num
integer (c_int64_t) , intent(in) , value :: walk_num
real (c_double ) , intent(in) :: ee_distance(elec_num,elec_num,walk_num)
real (c_double ) , intent(out) :: ee_pot(walk_num)
integer(c_int32_t), external :: qmckl_compute_ee_potential_f
info = qmckl_compute_ee_potential_f &
(context, elec_num, walk_num, ee_distance, ee_pot)
end function qmckl_compute_ee_potential
#+end_src
*** Test
#+begin_src c :tangle (eval c_test)
double ee_pot[walk_num];
rc = qmckl_get_electron_ee_potential(context, &(ee_pot[0]));
assert (rc == QMCKL_SUCCESS);
#+end_src
** Electron-nucleus distances
*** Get
@ -2407,6 +2619,216 @@ assert (rc == QMCKL_SUCCESS);
#+end_src
** Electron-nucleus potential
~en_potential~ stores the ~en~ potential energy
\[
\mathcal{V}_{en} = -\sum_{i=1}^{N_e}\sum_{A=1}^{N_n}\frac{Z_A}{r_{iA}}
\]
where \(\mathcal{V}_{en}\) is the ~en~ potential, \[r_{iA}\] the ~en~
distance and \[Z_A\] is the nuclear charge.
*** Get
#+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code qmckl_get_electron_en_potential(qmckl_context context, double* const en_pot);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_get_electron_en_potential(qmckl_context context, double* const en_pot)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_exit_code rc;
rc = qmckl_provide_en_potential(context);
if (rc != QMCKL_SUCCESS) return rc;
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
size_t sze = ctx->electron.walk_num * sizeof(double);
memcpy(en_pot, ctx->electron.en_pot, sze);
return QMCKL_SUCCESS;
}
#+end_src
*** Provide :noexport:
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_provide_en_potential(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_provide_en_potential(qmckl_context context)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
if (!ctx->electron.provided) return QMCKL_NOT_PROVIDED;
if (!ctx->nucleus.provided) return QMCKL_NOT_PROVIDED;
qmckl_exit_code rc = qmckl_provide_en_distance(context);
if (rc != QMCKL_SUCCESS) return rc;
/* Compute if necessary */
if (ctx->electron.coord_new_date > ctx->electron.en_pot_date) {
/* Allocate array */
if (ctx->electron.en_pot == NULL) {
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = ctx->electron.walk_num * sizeof(double);
double* en_pot = (double*) qmckl_malloc(context, mem_info);
if (en_pot == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_en_potential",
NULL);
}
ctx->electron.en_pot = en_pot;
}
qmckl_exit_code rc =
qmckl_compute_en_potential(context,
ctx->electron.num,
ctx->nucleus.num,
ctx->electron.walk_num,
ctx->nucleus.charge,
ctx->electron.en_distance,
ctx->electron.en_pot);
if (rc != QMCKL_SUCCESS) {
return rc;
}
ctx->electron.en_pot_date = ctx->date;
}
return QMCKL_SUCCESS;
}
#+end_src
*** Compute
:PROPERTIES:
:Name: qmckl_compute_en_potential
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
#+NAME: qmckl_en_potential_args
| qmckl_context | context | in | Global state |
| int64_t | elec_num | in | Number of electrons |
| int64_t | nucl_num | in | Number of nucleii |
| int64_t | walk_num | in | Number of walkers |
| double | charge[nucl_num] | in | charge of nucleus |
| double | en_distance[walk_num][nucl_num][elec_num] | in | Electron-electron rescaled distances |
| double | en_pot[walk_num] | out | Electron-electron potential |
#+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_en_potential_f(context, elec_num, nucl_num, walk_num, &
charge, en_distance, en_pot) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: elec_num
integer*8 , intent(in) :: nucl_num
integer*8 , intent(in) :: walk_num
double precision , intent(in) :: charge(nucl_num)
double precision , intent(in) :: en_distance(elec_num,nucl_num,walk_num)
double precision , intent(out) :: en_pot(walk_num)
integer*8 :: nw, i, j
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (elec_num <= 0) then
info = QMCKL_INVALID_ARG_2
return
endif
if (walk_num <= 0) then
info = QMCKL_INVALID_ARG_3
return
endif
en_pot = 0.0d0
do nw=1,walk_num
do j=1,nucl_num
do i=1,elec_num
if (dabs(en_distance(i,j,nw)) > 1e-5) then
en_pot(nw) = en_pot(nw) - charge(j)/(en_distance(i,j,nw))
endif
end do
end do
end do
end function qmckl_compute_en_potential_f
#+end_src
#+CALL: generate_c_header(table=qmckl_en_potential_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_compute_en_potential (
const qmckl_context context,
const int64_t elec_num,
const int64_t nucl_num,
const int64_t walk_num,
const double* charge,
const double* en_distance,
double* const en_pot );
#+end_src
#+CALL: generate_c_interface(table=qmckl_en_potential_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_compute_en_potential &
(context, elec_num, nucl_num, walk_num, charge, en_distance, en_pot) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: elec_num
integer (c_int64_t) , intent(in) , value :: nucl_num
integer (c_int64_t) , intent(in) , value :: walk_num
real (c_double ) , intent(in) :: charge(nucl_num)
real (c_double ) , intent(in) :: en_distance(elec_num,nucl_num,walk_num)
real (c_double ) , intent(out) :: en_pot(walk_num)
integer(c_int32_t), external :: qmckl_compute_en_potential_f
info = qmckl_compute_en_potential_f &
(context, elec_num, nucl_num, walk_num, charge, en_distance, en_pot)
end function qmckl_compute_en_potential
#+end_src
*** Test
#+begin_src c :tangle (eval c_test)
double en_pot[walk_num];
rc = qmckl_get_electron_en_potential(context, &(en_pot[0]));
assert (rc == QMCKL_SUCCESS);
#+end_src
* End of files :noexport:
#+begin_src c :tangle (eval h_private_type)

1705
org/qmckl_local_energy.org Normal file

File diff suppressed because it is too large Load Diff

View File

@ -83,6 +83,7 @@ int main() {
The following arrays are stored in the context:
|---------------+--------------------+----------------------|
| ~mo_num~ | | Number of MOs |
| ~coefficient~ | ~[mo_num][ao_num]~ | Orbital coefficients |
@ -117,6 +118,26 @@ typedef struct qmckl_mo_basis_struct {
Some values are initialized by default, and are not concerned by
this mechanism.
#+begin_src c :comments org :tangle (eval h_private_func)
qmckl_exit_code qmckl_init_mo_basis(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c)
qmckl_exit_code qmckl_init_mo_basis(qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return false;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
ctx->mo_basis.uninitialized = (1 << 2) - 1;
return QMCKL_SUCCESS;
}
#+end_src
** Access functions
#+begin_src c :comments org :tangle (eval h_func) :exports none
@ -258,10 +279,9 @@ qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
ctx->mo_basis.uninitialized &= ~mask;
ctx->mo_basis.provided = (ctx->mo_basis.uninitialized == 0);
if (ctx->mo_basis.provided) {
qmckl_exit_code rc_ = qmckl_finalize_basis(context);
qmckl_exit_code rc_ = qmckl_finalize_mo_basis(context);
if (rc_ != QMCKL_SUCCESS) return rc_;
}
return QMCKL_SUCCESS;
#+end_src
@ -318,6 +338,34 @@ qmckl_exit_code qmckl_set_mo_basis_coefficient(qmckl_context context, const dou
When the basis set is completely entered, other data structures are
computed to accelerate the calculations.
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_mo_basis(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_mo_basis(qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_INVALID_CONTEXT,
"qmckl_finalize_mo_basis",
NULL);
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
qmckl_exit_code rc;
rc = qmckl_provide_mo_vgl(context);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_finalize_mo_basis",
NULL);
}
return rc;
}
#+end_src
* Computation
** Computation of MOs
@ -377,6 +425,7 @@ qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context);
qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context)
{
qmckl_exit_code rc;
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
@ -391,6 +440,14 @@ qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context)
NULL);
}
rc = qmckl_provide_ao_vgl(context);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_ao_basis",
NULL);
}
if(!(ctx->electron.provided)) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
@ -424,7 +481,6 @@ qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context)
ctx->mo_basis.mo_vgl = mo_vgl;
}
qmckl_exit_code rc;
rc = qmckl_compute_mo_basis_vgl(context,
ctx->ao_basis.ao_num,
ctx->mo_basis.mo_num,
@ -450,7 +506,7 @@ qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context)
:FRetType: qmckl_exit_code
:END:
#+NAME: qmckl_mo_basis_gaussian_vgl_args
#+NAME: qmckl_mo_basis_vgl_args
| ~qmckl_context~ | ~context~ | in | Global state |
| ~int64_t~ | ~ao_num~ | in | Number of AOs |
| ~int64_t~ | ~mo_num~ | in | Number of MOs |
@ -459,6 +515,7 @@ qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context)
| ~double~ | ~ao_vgl[5][elec_num][ao_num]~ | in | Value, gradients and Laplacian of the AOs |
| ~double~ | ~mo_vgl[5][elec_num][mo_num]~ | out | Value, gradients and Laplacian of the MOs |
#+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_mo_basis_vgl_f(context, &
ao_num, mo_num, elec_num, &
@ -473,85 +530,70 @@ integer function qmckl_compute_mo_basis_vgl_f(context, &
double precision , intent(in) :: coef_normalized(ao_num,mo_num)
double precision , intent(out) :: mo_vgl(mo_num,elec_num,5)
logical*8 :: TransA, TransB
double precision,dimension(:,:),allocatable :: mo_vgl_big
double precision,dimension(:,:),allocatable :: ao_vgl_big
!double precision,dimension(:,:),allocatable :: coef_trans
!double precision,dimension(:),allocatable :: coef_all
double precision :: alpha, beta
integer :: info_qmckl_dgemm_value
integer :: info_qmckl_dgemm_Gx
integer :: info_qmckl_dgemm_Gy
integer :: info_qmckl_dgemm_Gz
integer :: info_qmckl_dgemm_lap
integer*8 :: M, N, K, LDA, LDB, LDC, i,j
integer*8 :: M, N, K, LDA, LDB, LDC, i,j, idx
integer*8 :: inucl, iprim, iwalk, ielec, ishell
double precision :: x, y, z, two_a, ar2, r2, v, cutoff
TransA = .False.
allocate(mo_vgl_big(mo_num,elec_num*5))
allocate(ao_vgl_big(ao_num,elec_num*5))
!allocate(coef_all(mo_num*ao_num))
!allocate(coef_trans(mo_num,ao_num))
TransA = .True.
TransB = .False.
alpha = 1.0d0
beta = 0.0d0
info = QMCKL_SUCCESS
info_qmckl_dgemm_value = QMCKL_SUCCESS
info_qmckl_dgemm_Gx = QMCKL_SUCCESS
info_qmckl_dgemm_Gy = QMCKL_SUCCESS
info_qmckl_dgemm_Gz = QMCKL_SUCCESS
info_qmckl_dgemm_lap = QMCKL_SUCCESS
! Don't compute exponentials when the result will be almost zero.
! TODO : Use numerical precision here
cutoff = -dlog(1.d-15)
M = 1_8
N = mo_num * 1_8
M = mo_num
N = elec_num*5
K = ao_num * 1_8
LDA = M
LDB = K
LDC = M
LDA = size(coef_normalized,1)
idx = 0
!do j = 1,ao_num
!do i = 1,mo_num
! idx = idx + 1
! coef_all(idx) = coef_normalized(i,j)
!end do
!end do
!idx = 0
!do j = 1,mo_num
!do i = 1,ao_num
! idx = idx + 1
! coef_trans(j,i) = coef_all(idx)
!end do
!end do
do ielec = 1, elec_num
! Value
info_qmckl_dgemm_value = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, 1), LDA, &
coef_normalized(1:ao_num,1:mo_num),size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,1),LDC)
! Grad_x
info_qmckl_dgemm_Gx = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, 2), LDA, &
coef_normalized(1:ao_num,1:mo_num),size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,2),LDC)
! Grad_y
info_qmckl_dgemm_Gy = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, 3), LDA, &
coef_normalized(1:ao_num,1:mo_num),size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,3),LDC)
! Grad_z
info_qmckl_dgemm_Gz = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, 4), LDA, &
coef_normalized(1:ao_num,1:mo_num),size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,4),LDC)
! Lapl_z
info_qmckl_dgemm_lap = qmckl_dgemm(context, TransA, TransB, M, N, K, alpha, &
ao_vgl(:, ielec, 5), LDA, &
coef_normalized(1:ao_num,1:mo_num),size(coef_normalized,1) * 1_8, &
beta, &
mo_vgl(:,ielec,5),LDC)
end do
ao_vgl_big = reshape(ao_vgl(:, :, :),(/ao_num, elec_num*5_8/))
LDB = size(ao_vgl_big,1)
LDC = size(mo_vgl_big,1)
if(info_qmckl_dgemm_value .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_Gx .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_Gy .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_Gz .eq. QMCKL_SUCCESS .and. &
info_qmckl_dgemm_lap .eq. QMCKL_SUCCESS ) then
info = QMCKL_SUCCESS
else
info = QMCKL_FAILURE
end if
info = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, &
coef_normalized,size(coef_normalized,1)*1_8, &
ao_vgl_big, size(ao_vgl_big,1)*1_8, &
beta, &
mo_vgl_big,LDC)
mo_vgl = reshape(mo_vgl_big,(/mo_num,elec_num,5_8/))
deallocate(mo_vgl_big)
deallocate(ao_vgl_big)
end function qmckl_compute_mo_basis_vgl_f
#+end_src
#+CALL: generate_c_header(table=qmckl_mo_basis_gaussian_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_vgl"))
#+CALL: generate_c_header(table=qmckl_mo_basis_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_vgl"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
@ -566,7 +608,7 @@ end function qmckl_compute_mo_basis_vgl_f
#+end_src
#+CALL: generate_c_interface(table=qmckl_mo_basis_gaussian_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_vgl"))
#+CALL: generate_c_interface(table=qmckl_mo_basis_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_vgl"))
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
@ -785,10 +827,10 @@ rc = qmckl_get_mo_basis_vgl(context, &(mo_vgl[0][0][0]));
assert (rc == QMCKL_SUCCESS);
// Test overlap of MO
//double point_x[100];
//double point_y[100];
//double point_z[100];
//int32_t npoints=100;
//double point_x[10];
//double point_y[10];
//double point_z[10];
//int32_t npoints=10;
//// obtain points
//double dr = 20./(npoints-1);
//double dr3 = dr*dr*dr;
@ -802,10 +844,11 @@ assert (rc == QMCKL_SUCCESS);
//double ovlmo1 = 0.0;
//// Calculate overlap
//for (int i=0;i<npoints;++i) {
// printf(".");
// fflush(stdout);
// for (int j=0;j<npoints;++j) {
// printf(" .. ");
// for (int k=0;k<npoints;++k) {
// printf(" . ");
// // Set point
// elec_coord[0] = point_x[i];
// elec_coord[1] = point_y[j];

View File

@ -67,18 +67,24 @@ int main() {
The following data stored in the context:
|------------------------+----------------+-------------------------------------------|
| ~uninitialized~ | int32_t | Keeps bit set for uninitialized data |
| ~num~ | int64_t | Total number of nuclei |
| ~provided~ | bool | If true, ~nucleus~ is valid |
| ~charge~ | double[num] | Nuclear charges |
| ~coord~ | double[3][num] | Nuclear coordinates, in transposed format |
| ~coord_date~ | int64_t | Nuclear coordinates, date if modified |
| ~rescale_factor_kappa~ | double | The distance scaling factor |
Computed data:
|-----------------------------+------------------+------------------------------------------------------------|
| ~nn_distance~ | double[num][num] | Nucleus-nucleus distances |
| ~nn_distance_date~ | int64_t | Date when Nucleus-nucleus distances were computed |
| ~nn_distance_rescaled~ | double[num][num] | Nucleus-nucleus rescaled distances |
| ~nn_distance_rescaled_date~ | int64_t | Date when Nucleus-nucleus rescaled distances were computed |
| ~repulsion~ | double | Nuclear repulsion energy |
| ~repulsion_date~ | int64_t | Date when the nuclear repulsion energy was computed |
| ~rescale_factor_kappa~ | double | The distance scaling factor |
** Data structure
@ -88,6 +94,7 @@ typedef struct qmckl_nucleus_struct {
int64_t repulsion_date;
int64_t nn_distance_date;
int64_t nn_distance_rescaled_date;
int64_t coord_date;
double* coord;
double* charge;
double* nn_distance;
@ -130,8 +137,6 @@ qmckl_exit_code qmckl_init_nucleus(qmckl_context context) {
}
#+end_src
** Access functions
#+begin_src c :comments org :tangle (eval h_func) :exports none
@ -790,7 +795,6 @@ assert(fabs(distance[1]-2.070304721365169) < 1.e-12);
#+end_src
** Nucleus-nucleus rescaled distances
*** Get
@ -1083,7 +1087,9 @@ integer function qmckl_compute_nucleus_repulsion_f(context, nucl_num, charge, nn
energy = 0.d0
do j=2, nucl_num
do i=1, j-1
if (dabs(nn_distance(i,j)) > 1e-5) then
energy = energy + charge(i) * charge(j) / nn_distance(i,j)
endif
end do
end do

View File

@ -704,6 +704,42 @@ qmckl_trexio_read_ao_X(qmckl_context context, trexio_t* const file)
}
#+end_src
*** AO Normalization
#+begin_src c :tangle (eval c)
{
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = ao_num * sizeof(double);
double* ao_normalization = (double*) qmckl_malloc(context, mem_info);
if (ao_normalization == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_trexio_read_ao_normalization_X",
NULL);
}
assert (ao_normalization != NULL);
rcio = trexio_read_ao_normalization_64(file, ao_normalization);
if (rcio != TREXIO_SUCCESS) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"trexio_read_ao_normalization",
trexio_string_of_error(rcio));
}
rc = qmckl_set_ao_basis_ao_factor(context, ao_normalization);
qmckl_free(context, ao_normalization);
ao_normalization = NULL;
if (rc != QMCKL_SUCCESS)
return rc;
}
#+end_src
#+begin_src c :tangle (eval c)
@ -711,7 +747,6 @@ qmckl_trexio_read_ao_X(qmckl_context context, trexio_t* const file)
}
#endif
#+end_src
** Molecular orbitals
In this section we read the MO coefficients.
@ -880,6 +915,7 @@ qmckl_trexio_read(const qmckl_context context, const char* file_name)
#+begin_src c :tangle (eval c_test)
#ifdef HAVE_TREXIO
#define walk_num 2
qmckl_exit_code rc;
char fname[256];
@ -892,6 +928,8 @@ char message[256];
strncpy(fname, QMCKL_TEST_DIR,255);
strncat(fname, "/chbrclf", 255);
printf("Test file: %s\n", fname);
rc = qmckl_set_electron_walk_num(context, walk_num);
rc = qmckl_trexio_read(context, fname);
if (rc != QMCKL_SUCCESS) {

View File

@ -1,17 +1,20 @@
qmckl.org
qmckl_error.org
qmckl_ao.org
qmckl_blas.org
qmckl_context.org
qmckl_determinant.org
qmckl_distance.org
qmckl_electron.org
qmckl_error.org
qmckl_jastrow.org
qmckl_local_energy.org
qmckl_memory.org
qmckl_mo.org
qmckl_numprec.org
qmckl_distance.org
qmckl_nucleus.org
qmckl_electron.org
qmckl_ao.org
qmckl_mo.org
qmckl_jastrow.org
qmckl_sherman_morrison_woodbury.org
qmckl_utils.org
qmckl_blas.org
qmckl_trexio.org
qmckl_verificarlo.org
qmckl_tests.org