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#+TITLE: BLAS functions
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org
* Headers :noexport:
#+begin_src elisp :noexport :results none
(org-babel-lob-ingest "../tools/lib.org")
#+end_src
#+begin_src c :comments link :tangle (eval c_test) :noweb yes
#include "qmckl.h"
#include "assert.h"
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
int main() {
qmckl_context context;
context = qmckl_context_create();
#+end_src
* Matrix operations
** ~qmckl_dgemm~
Matrix multiply: $C_{ij} = \beta C_{ij} + \alpha \sum_{k} A_{ik} \cdot B_{kj}$ using Fortran ~matmul~ function.
TODO: Add description about the external library dependence.
#+NAME: qmckl_dgemm_args
| qmckl_context | context | in | Global state |
| bool | TransA | in | Number of rows of the input matrix |
| bool | TransB | in | Number of rows of the input matrix |
| int64_t | m | in | Number of rows of the input matrix |
| int64_t | n | in | Number of columns of the input matrix |
| int64_t | k | in | Number of columns of the input matrix |
| double | alpha | in | Number of columns of the input matrix |
| double | A[][lda] | in | Array containing the matrix $A$ |
| int64_t | lda | in | Leading dimension of array ~A~ |
| double | B[][ldb] | in | Array containing the matrix $B$ |
| int64_t | ldb | in | Leading dimension of array ~B~ |
| double | beta | in | Array containing the matrix $B$ |
| double | C[][ldc] | out | Array containing the matrix $B$ |
| int64_t | ldc | in | Leading dimension of array ~B~ |
*** Requirements
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~m > 0~
- ~n > 0~
- ~k > 0~
- ~lda >= m~
- ~ldb >= n~
- ~ldc >= n~
- ~A~ is allocated with at least $m \times k \times 8$ bytes
- ~B~ is allocated with at least $k \times n \times 8$ bytes
- ~C~ is allocated with at least $m \times n \times 8$ bytes
*** C header
#+CALL: generate_c_header(table=qmckl_dgemm_args,rettyp="qmckl_exit_code",fname="qmckl_dgemm")
#+RESULTS:
#+BEGIN_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_dgemm (
const qmckl_context context,
const bool TransA,
const bool TransB,
const int64_t m,
const int64_t n,
const int64_t k,
const double alpha,
const double* A,
const int64_t lda,
const double* B,
const int64_t ldb,
const double beta,
double* const C,
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) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
logical*8 , intent(in) :: TransA, TransB
integer*8 , intent(in) :: m, n, k
real*8 , intent(in) :: alpha, beta
integer*8 , intent(in) :: lda
real*8 , intent(in) :: A(lda,*)
integer*8 , intent(in) :: ldb
real*8 , intent(in) :: B(ldb,*)
integer*8 , intent(in) :: ldc
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(m,k))
do i = 1, k
do j = 1, m
AT(j,i) = A(i,j)
end do
end do
LDA_2 = M
else
LDA_2 = LDA
endif
if (TransB) then
allocate(BT(k,n))
do i = 1, n
do j = 1, k
BT(j,i) = B(i,j)
end do
end do
LDB_2 = K
else
LDB_2 = LDB
endif
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_2 /= m) then
info = QMCKL_INVALID_ARG_9
return
endif
if (LDB_2 /= k) then
info = QMCKL_INVALID_ARG_10
return
endif
if (LDC /= m) then
info = QMCKL_INVALID_ARG_13
return
endif
if (TransA) then
info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, AT, LDA_2, B, LDB_2, beta, c, LDC)
else if (TransB) then
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
info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA_2, B, LDB_2, beta, c, LDC)
endif
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_2
return
endif
if (n <= 0_8) then
info = QMCKL_INVALID_ARG_3
return
endif
if (k <= 0_8) then
info = QMCKL_INVALID_ARG_4
return
endif
if (LDA /= m) then
info = QMCKL_INVALID_ARG_7
return
endif
if (LDB /= k) then
info = QMCKL_INVALID_ARG_8
return
endif
if (LDC /= m) then
info = QMCKL_INVALID_ARG_11
return
endif
if (alpha == 1.0d0 .and. beta == 0.0d0) then
C = matmul(A,B)
else
C = beta*C + alpha*matmul(A,B)
endif
end function qmckl_dgemm_N_N_f
#+end_src
*** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_dgemm_args,rettyp="qmckl_exit_code",fname="qmckl_dgemm")
#+RESULTS:
#+BEGIN_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_dgemm &
(context, TransA, TransB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
logical*8 , intent(in) , value :: TransA
logical*8 , intent(in) , value :: TransB
integer (c_int64_t) , intent(in) , value :: m
integer (c_int64_t) , intent(in) , value :: n
integer (c_int64_t) , intent(in) , value :: k
real (c_double ) , intent(in) , value :: alpha
integer (c_int64_t) , intent(in) , value :: lda
real (c_double ) , intent(in) :: A(lda,*)
integer (c_int64_t) , intent(in) , value :: ldb
real (c_double ) , intent(in) :: B(ldb,*)
real (c_double ) , intent(in) , value :: beta
integer (c_int64_t) , intent(in) , value :: ldc
real (c_double ) , intent(out) :: C(ldc,*)
integer(c_int32_t), external :: qmckl_dgemm_f
info = qmckl_dgemm_f &
(context, TransA, TransB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc)
end function qmckl_dgemm
#+END_src
#+CALL: generate_f_interface(table=qmckl_dgemm_args,rettyp="qmckl_exit_code",fname="qmckl_dgemm")
#+RESULTS:
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_dgemm &
(context, TransA, TransB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
logical*8 , intent(in) , value :: TransA
logical*8 , intent(in) , value :: TransB
integer (c_int64_t) , intent(in) , value :: m
integer (c_int64_t) , intent(in) , value :: n
integer (c_int64_t) , intent(in) , value :: k
real (c_double ) , intent(in) , value :: alpha
integer (c_int64_t) , intent(in) , value :: lda
real (c_double ) , intent(in) :: A(lda,*)
integer (c_int64_t) , intent(in) , value :: ldb
real (c_double ) , intent(in) :: B(ldb,*)
real (c_double ) , intent(in) , value :: beta
integer (c_int64_t) , intent(in) , value :: ldc
real (c_double ) , intent(out) :: C(ldc,*)
end function qmckl_dgemm
end interface
#+end_src
*** Test :noexport:
#+begin_src f90 :tangle (eval f_test)
integer(qmckl_exit_code) function test_qmckl_dgemm(context) bind(C)
use qmckl
implicit none
integer(qmckl_context), intent(in), value :: context
double precision, allocatable :: A(:,:), B(:,:), C(:,:), D(:,:)
integer*8 :: m, n, k, LDA, LDB, LDC
integer*8 :: i,j,l
logical*8 :: TransA, TransB
double precision :: x, alpha, beta
TransA = .False.
TransB = .False.
m = 1_8
k = 4_8
n = 6_8
LDA = m
LDB = k
LDC = m
allocate( A(LDA,k), B(LDB,n) , C(LDC,n), D(LDC,n))
A = 0.d0
B = 0.d0
C = 0.d0
D = 0.d0
alpha = 1.0d0
beta = 0.0d0
do j=1,k
do i=1,m
A(i,j) = -10.d0 + dble(i+j)
end do
end do
do j=1,n
do i=1,k
B(i,j) = -10.d0 + dble(i+j)
end do
end do
test_qmckl_dgemm = qmckl_dgemm(context, TransA, TransB, m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC)
if (test_qmckl_dgemm /= QMCKL_SUCCESS) return
test_qmckl_dgemm = QMCKL_FAILURE
x = 0.d0
do j=1,n
do i=1,m
do l=1,k
D(i,j) = D(i,j) + A(i,l)*B(l,j)
end do
x = x + (D(i,j) - C(i,j))**2
end do
end do
if (dabs(x) <= 1.d-12) then
test_qmckl_dgemm = QMCKL_SUCCESS
endif
deallocate(A,B,C,D)
end function test_qmckl_dgemm
#+end_src
#+begin_src c :comments link :tangle (eval c_test)
qmckl_exit_code test_qmckl_dgemm(qmckl_context context);
assert(QMCKL_SUCCESS == test_qmckl_dgemm(context));
#+end_src
** ~qmckl_adjugate~
Given a matrix $\mathbf{A}$, the adjugate matrix
$\text{adj}(\mathbf{A})$ is the transpose of the cofactors matrix
of $\mathbf{A}$.
\[
\text{adj}(\mathbf{A}) = \text{det}(\mathbf{A}) \, \mathbf{A}^{-1}
\]
See also: https://en.wikipedia.org/wiki/Adjugate_matrix
#+NAME: qmckl_adjugate_args
| qmckl_context | context | in | Global state |
| int64_t | n | in | Number of rows and columns of the input matrix |
| int64_t | lda | in | Leading dimension of array ~A~ |
| double | A[][lda] | inout | Array containing the $n \times n$ matrix $A$ |
| double | det_l | inout | determinant of $A$ |
*** Requirements
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~n > 0~
- ~lda >= m~
- ~A~ is allocated with at least $m \times m \times 8$ bytes
*** C header
#+CALL: generate_c_header(table=qmckl_adjugate_args,rettyp="qmckl_exit_code",fname="qmckl_adjugate")
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_adjugate (
const qmckl_context context,
const int64_t n,
const int64_t lda,
double* A,
double det_l );
#+end_src
*** Source
For small matrices (\le 5\times 5), we use specialized routines
for performance motivations. For larger sizes, we rely on the
LAPACK library.
#+begin_src f90 :tangle (eval f)
integer function qmckl_adjugate_f(context, 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) :: na
double precision, intent(inout) :: det_l
integer :: i,j
!TODO CHECK ARGUMENTS
info = QMCKL_SUCCESS
select case (na)
case default
call adjugate_general(context, na, LDA, A, det_l)
case (5)
call adjugate5(a,LDA,na,det_l)
case (4)
call adjugate4(a,LDA,na,det_l)
case (3)
call adjugate3(a,LDA,na,det_l)
case (2)
call adjugate2(a,LDA,na,det_l)
case (1)
call adjugate1(a,LDA,na,det_l)
case (0)
det_l=1.d0
end select
end function qmckl_adjugate_f
#+end_src
#+begin_src f90 :tangle (eval f)
subroutine adjugate1(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 adjugate1
subroutine adjugate2(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 adjugate2
subroutine adjugate3(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 adjugate3
subroutine adjugate4(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 adjugate4
subroutine adjugate5(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 adjugate5
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 cofactor1
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 cofactor2
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)
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)
end do
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 cofactor3
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)
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)
end do
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 cofactor4
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)
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)
end do
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
#+begin_src f90 :tangle (eval f)
subroutine adjugate_general(context, na, LDA, A, det_l)
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) :: na
double precision, intent(inout) :: det_l
double precision :: work(LDA*max(na,64))
integer :: inf
integer :: ipiv(LDA)
integer :: lwork
integer :: i, j
#+end_src
For larger matrices, we first compute the LU factorization $LU=A$
using the ~dgetrf~ routine.
#+begin_src f90 :tangle (eval f)
call dgetrf(na, na, a, LDA, ipiv, inf )
#+end_src
By convention, the determinant of $L$ is equal to one, so the
determinant of $A$ is equal to the determinant of $U$, which is
simply computed as the product of its diagonal elements.
#+begin_src f90 :tangle (eval f)
det_l = 1.d0
j=0
do i=1,na
j = j+min(abs(ipiv(i)-i),1)
det_l = det_l*a(i,i)
enddo
#+end_src
As ~dgetrf~ returns $PLU=A$ where $P$ is a permutation matrix, the
sign of the determinant is computed as $-1^m$ where $m$ is the
number of permutations.
#+begin_src f90 :tangle (eval f)
if (iand(j,1) /= 0) then
det_l = -det_l
endif
#+end_src
Then, the inverse of $A$ is computed using ~dgetri~:
#+begin_src f90 :tangle (eval f)
lwork = SIZE(work)
call dgetri(na, a, LDA, ipiv, work, lwork, inf )
#+end_src
and the adjugate matrix is computed as the product of the
determinant with the inverse:
#+begin_src f90 :tangle (eval f)
a(:,:) = a(:,:)*det_l
end subroutine adjugate_general
#+end_src
*** C interface :noexport:
#+CALL: generate_c_interface(table=qmckl_adjugate_args,rettyp="qmckl_exit_code",fname="qmckl_adjugate")
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_adjugate &
(context, 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 :: 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_adjugate_f
info = qmckl_adjugate_f &
(context, n, lda, A, det_l)
end function qmckl_adjugate
#+end_src
#+CALL: generate_f_interface(table=qmckl_adjugate_args,rettyp="qmckl_exit_code",fname="qmckl_adjugate")
#+RESULTS:
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_adjugate &
(context, 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 :: 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_adjugate
end interface
#+end_src
*** Test :noexport:
#+begin_src f90 :tangle (eval f_test)
integer(qmckl_exit_code) function test_qmckl_adjugate(context) bind(C)
use qmckl
implicit none
integer(qmckl_context), intent(in), value :: context
double precision, allocatable :: A(:,:), B(:,:)
integer*8 :: m, n, k, LDA, LDB
integer*8 :: i,j,l
double precision :: x, det_l, det_l_ref
LDA = 6
LDB = 6
allocate( A(LDA,6), B(LDB,6))
A = 0.1d0
A(1,1) = 1.0d0;
A(2,2) = 2.0d0;
A(3,3) = 3.0d0;
A(4,4) = 4.0d0;
A(5,5) = 5.0d0;
A(6,6) = 6.0d0;
test_qmckl_adjugate = QMCKL_SUCCESS
#+end_src
#+begin_src python :results output :output drawer
import numpy as np
import numpy.linalg as la
N=6
A = np.zeros( (N,N) )
A += 0.1
for i in range(N):
A[i][i] = i+1
def adj(A):
return la.det(A) * la.inv(A)
print ("#+begin_src f90 :tangle (eval f_test)")
for i in range(N):
print ("! N = ", i+1)
print (f" B(:,:) = A(:,:)")
print (f" test_qmckl_adjugate = qmckl_adjugate(context, {i+1}_8, LDB, B, det_l)")
print (f" if (test_qmckl_adjugate /= QMCKL_SUCCESS) return")
print (f" if (dabs((det_l - ({la.det(A[0:i+1,0:i+1])}d0))/det_l) > 1.d-13) then")
print (f" print *, 'N = {i+1}: det = ', det_l, {la.det(A[0:i+1,0:i+1])}d0")
print (f" test_qmckl_adjugate = {i+1}")
print (f" return")
print (f" end if")
print (f"")
print (f" x = 0.d0")
for j in range(i+1):
C = adj(A[0:i+1,0:i+1])
for k in range(i+1):
print (f" x = x + (B({j+1},{k+1}) - ({C[j,k]}) )**2")
print (f" if (dabs(x / det_l) > 1.d-12) then")
print (f" print *, 'N = {i+1}: x = ', x")
print (f" test_qmckl_adjugate = {i+1}")
print (f" return")
print (f" end if")
print (f"")
print ("#+end_src")
# print(adj(A[0:i+1,0:i+1]))
#+end_src
#+RESULTS:
#+begin_src f90 :tangle (eval f_test)
! N = 1
B(:,:) = A(:,:)
test_qmckl_adjugate = qmckl_adjugate(context, 1_8, LDB, B, det_l)
if (test_qmckl_adjugate /= QMCKL_SUCCESS) return
if (dabs((det_l - (1.0d0))/det_l) > 1.d-13) then
print *, 'N = 1: det = ', det_l, 1.0d0
test_qmckl_adjugate = 1
return
end if
x = 0.d0
x = x + (B(1,1) - (1.0) )**2
if (dabs(x / det_l) > 1.d-12) then
print *, 'N = 1: x = ', x
test_qmckl_adjugate = 1
return
end if
! N = 2
B(:,:) = A(:,:)
test_qmckl_adjugate = qmckl_adjugate(context, 2_8, LDB, B, det_l)
if (test_qmckl_adjugate /= QMCKL_SUCCESS) return
if (dabs((det_l - (1.99d0))/det_l) > 1.d-13) then
print *, 'N = 2: det = ', det_l, 1.99d0
test_qmckl_adjugate = 2
return
end if
x = 0.d0
x = x + (B(1,1) - (1.9999999999999998) )**2
x = x + (B(1,2) - (-0.09999999999999999) )**2
x = x + (B(2,1) - (-0.09999999999999999) )**2
x = x + (B(2,2) - (0.9999999999999999) )**2
if (dabs(x / det_l) > 1.d-12) then
print *, 'N = 2: x = ', x
test_qmckl_adjugate = 2
return
end if
! N = 3
B(:,:) = A(:,:)
test_qmckl_adjugate = qmckl_adjugate(context, 3_8, LDB, B, det_l)
if (test_qmckl_adjugate /= QMCKL_SUCCESS) return
if (dabs((det_l - (5.942000000000001d0))/det_l) > 1.d-13) then
print *, 'N = 3: det = ', det_l, 5.942000000000001d0
test_qmckl_adjugate = 3
return
end if
x = 0.d0
x = x + (B(1,1) - (5.990000000000001) )**2
x = x + (B(1,2) - (-0.29000000000000004) )**2
x = x + (B(1,3) - (-0.19000000000000003) )**2
x = x + (B(2,1) - (-0.29000000000000004) )**2
x = x + (B(2,2) - (2.9900000000000007) )**2
x = x + (B(2,3) - (-0.09000000000000001) )**2
x = x + (B(3,1) - (-0.19000000000000003) )**2
x = x + (B(3,2) - (-0.09) )**2
x = x + (B(3,3) - (1.9900000000000002) )**2
if (dabs(x / det_l) > 1.d-12) then
print *, 'N = 3: x = ', x
test_qmckl_adjugate = 3
return
end if
! N = 4
B(:,:) = A(:,:)
test_qmckl_adjugate = qmckl_adjugate(context, 4_8, LDB, B, det_l)
if (test_qmckl_adjugate /= QMCKL_SUCCESS) return
if (dabs((det_l - (23.669700000000006d0))/det_l) > 1.d-13) then
print *, 'N = 4: det = ', det_l, 23.669700000000006d0
test_qmckl_adjugate = 4
return
end if
x = 0.d0
x = x + (B(1,1) - (23.91200000000001) )**2
x = x + (B(1,2) - (-1.1310000000000004) )**2
x = x + (B(1,3) - (-0.7410000000000001) )**2
x = x + (B(1,4) - (-0.5510000000000002) )**2
x = x + (B(2,1) - (-1.1310000000000002) )**2
x = x + (B(2,2) - (11.922000000000002) )**2
x = x + (B(2,3) - (-0.351) )**2
x = x + (B(2,4) - (-0.261) )**2
x = x + (B(3,1) - (-0.7410000000000002) )**2
x = x + (B(3,2) - (-0.351) )**2
x = x + (B(3,3) - (7.932000000000001) )**2
x = x + (B(3,4) - (-0.17100000000000004) )**2
x = x + (B(4,1) - (-0.5510000000000002) )**2
x = x + (B(4,2) - (-0.261) )**2
x = x + (B(4,3) - (-0.17100000000000004) )**2
x = x + (B(4,4) - (5.942000000000001) )**2
if (dabs(x / det_l) > 1.d-12) then
print *, 'N = 4: x = ', x
test_qmckl_adjugate = 4
return
end if
! N = 5
B(:,:) = A(:,:)
test_qmckl_adjugate = qmckl_adjugate(context, 5_8, LDB, B, det_l)
if (test_qmckl_adjugate /= QMCKL_SUCCESS) return
if (dabs((det_l - (117.91554000000008d0))/det_l) > 1.d-13) then
print *, 'N = 5: det = ', det_l, 117.91554000000008d0
test_qmckl_adjugate = 5
return
end if
x = 0.d0
x = x + (B(1,1) - (119.31770000000006) )**2
x = x + (B(1,2) - (-5.541900000000004) )**2
x = x + (B(1,3) - (-3.6309000000000022) )**2
x = x + (B(1,4) - (-2.6999000000000017) )**2
x = x + (B(1,5) - (-2.1489000000000016) )**2
x = x + (B(2,1) - (-5.541900000000004) )**2
x = x + (B(2,2) - (59.435700000000026) )**2
x = x + (B(2,3) - (-1.7199000000000007) )**2
x = x + (B(2,4) - (-1.2789000000000006) )**2
x = x + (B(2,5) - (-1.0179000000000005) )**2
x = x + (B(3,1) - (-3.6309000000000027) )**2
x = x + (B(3,2) - (-1.7199000000000007) )**2
x = x + (B(3,3) - (39.53370000000002) )**2
x = x + (B(3,4) - (-0.8379000000000005) )**2
x = x + (B(3,5) - (-0.6669000000000004) )**2
x = x + (B(4,1) - (-2.699900000000002) )**2
x = x + (B(4,2) - (-1.2789000000000006) )**2
x = x + (B(4,3) - (-0.8379000000000004) )**2
x = x + (B(4,4) - (29.611700000000017) )**2
x = x + (B(4,5) - (-0.4959000000000003) )**2
x = x + (B(5,1) - (-2.1489000000000016) )**2
x = x + (B(5,2) - (-1.0179000000000005) )**2
x = x + (B(5,3) - (-0.6669000000000004) )**2
x = x + (B(5,4) - (-0.4959000000000003) )**2
x = x + (B(5,5) - (23.669700000000013) )**2
if (dabs(x / det_l) > 1.d-12) then
print *, 'N = 5: x = ', x
test_qmckl_adjugate = 5
return
end if
! N = 6
B(:,:) = A(:,:)
test_qmckl_adjugate = qmckl_adjugate(context, 6_8, LDB, B, det_l)
if (test_qmckl_adjugate /= QMCKL_SUCCESS) return
if (dabs((det_l - (705.1783350000001d0))/det_l) > 1.d-13) then
print *, 'N = 6: det = ', det_l, 705.1783350000001d0
test_qmckl_adjugate = 6
return
end if
x = 0.d0
x = x + (B(1,1) - (714.5040400000001) )**2
x = x + (B(1,2) - (-32.697210000000005) )**2
x = x + (B(1,3) - (-21.422310000000003) )**2
x = x + (B(1,4) - (-15.929410000000006) )**2
x = x + (B(1,5) - (-12.678510000000003) )**2
x = x + (B(1,6) - (-10.529610000000003) )**2
x = x + (B(2,1) - (-32.69721) )**2
x = x + (B(2,2) - (355.65834) )**2
x = x + (B(2,3) - (-10.147409999999997) )**2
x = x + (B(2,4) - (-7.54551) )**2
x = x + (B(2,5) - (-6.005610000000001) )**2
x = x + (B(2,6) - (-4.987709999999999) )**2
x = x + (B(3,1) - (-21.422310000000003) )**2
x = x + (B(3,2) - (-10.147409999999999) )**2
x = x + (B(3,3) - (236.51663999999997) )**2
x = x + (B(3,4) - (-4.943610000000001) )**2
x = x + (B(3,5) - (-3.93471) )**2
x = x + (B(3,6) - (-3.267810000000001) )**2
x = x + (B(4,1) - (-15.929410000000003) )**2
x = x + (B(4,2) - (-7.54551) )**2
x = x + (B(4,3) - (-4.9436100000000005) )**2
x = x + (B(4,4) - (177.13894000000002) )**2
x = x + (B(4,5) - (-2.92581) )**2
x = x + (B(4,6) - (-2.42991) )**2
x = x + (B(5,1) - (-12.678510000000001) )**2
x = x + (B(5,2) - (-6.005609999999999) )**2
x = x + (B(5,3) - (-3.9347100000000004) )**2
x = x + (B(5,4) - (-2.92581) )**2
x = x + (B(5,5) - (141.58524) )**2
x = x + (B(5,6) - (-1.93401) )**2
x = x + (B(6,1) - (-10.529610000000003) )**2
x = x + (B(6,2) - (-4.98771) )**2
x = x + (B(6,3) - (-3.2678100000000003) )**2
x = x + (B(6,4) - (-2.42991) )**2
x = x + (B(6,5) - (-1.9340100000000005) )**2
x = x + (B(6,6) - (117.91554000000001) )**2
if (dabs(x / det_l) > 1.d-12) then
print *, 'N = 6: x = ', x
test_qmckl_adjugate = 6
return
end if
#+end_src
#+begin_src f90 :tangle (eval f_test)
deallocate(A,B)
end function test_qmckl_adjugate
#+end_src
#+begin_src c :comments link :tangle (eval c_test)
qmckl_exit_code test_qmckl_adjugate(qmckl_context context);
assert(QMCKL_SUCCESS == test_qmckl_adjugate(context));
#+end_src
* End of files :noexport:
#+begin_src c :comments link :tangle (eval c_test)
assert (qmckl_context_destroy(context) == QMCKL_SUCCESS);
return 0;
}
#+end_src
# -*- mode: org -*-
# vim: syntax=c
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