qmckl/org/qmckl_blas.org

#+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 multiplication:

   \[
   C_{ij} = \beta C_{ij} + \alpha \sum_{k} A_{ik} \cdot B_{kj}
   \] 

#  TODO: Add description about the external library dependence.

   #+NAME: qmckl_dgemm_args
   | Variable  | Type            | In/Out | Description                           |
   |-----------+-----------------+--------+---------------------------------------|
   | ~context~ | ~qmckl_context~ | in     | Global state                          |
   | ~TransA~  | ~bool~          | in     | Number of rows of the input matrix    |
   | ~TransB~  | ~bool~          | in     | Number of rows of the input matrix    |
   | ~m~       | ~int64_t~       | in     | Number of rows of the input matrix    |
   | ~n~       | ~int64_t~       | in     | Number of columns of the input matrix |
   | ~k~       | ~int64_t~       | in     | Number of columns of the input matrix |
   | ~alpha~   | ~double~        | in     | Number of columns of the input matrix |
   | ~A~       | ~double[][lda]~ | in     | Array containing the matrix $A$       |
   | ~lda~     | ~int64_t~       | in     | Leading dimension of array ~A~        |
   | ~B~       | ~double[][ldb]~ | in     | Array containing the matrix $B$       |
   | ~ldb~     | ~int64_t~       | in     | Leading dimension of array ~B~        |
   | ~beta~    | ~double~        | in     | Array containing the matrix $B$       |
   | ~C~       | ~double[][ldc]~ | out    | Array containing the matrix $B$       |
   | ~ldc~     | ~int64_t~       | 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
      
    #+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

    #+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
  double precision      , intent(in)  :: alpha, beta
  integer*8             , intent(in)  :: lda
  double precision      , intent(in)  :: A(lda,*)
  integer*8             , intent(in)  :: ldb
  double precision      , intent(in)  :: B(ldb,*)
  integer*8             , intent(in)  :: ldc
  double precision      , intent(out) :: C(ldc,*)

  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_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

  call dgemm(transA, transB, int(m,4), int(n,4), int(k,4), &
       alpha, A, int(LDA,4), B, int(LDB,4), beta, C, int(LDC,4))

end function qmckl_dgemm_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
      real    (c_double ) , intent(in)          :: A(lda,*)
      integer (c_int64_t) , intent(in)  , value :: lda
      real    (c_double ) , intent(in)          :: B(ldb,*)
      integer (c_int64_t) , intent(in)  , value :: ldb
      real    (c_double ) , intent(in)  , value :: beta
      real    (c_double ) , intent(out)         :: C(ldc,*)
      integer (c_int64_t) , intent(in)  , value :: 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
        real    (c_double ) , intent(in)          :: A(lda,*)
        integer (c_int64_t) , intent(in)  , value :: lda
        real    (c_double ) , intent(in)          :: B(ldb,*)
        integer (c_int64_t) , intent(in)  , value :: ldb
        real    (c_double ) , intent(in)  , value :: beta
        real    (c_double ) , intent(out)         :: C(ldc,*)
        integer (c_int64_t) , intent(in)  , value :: 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 $\mathbf{A}$.

   \[
   \mathbf{B} = \text{adj}(\mathbf{A}) = \text{det}(\mathbf{A}) \, \mathbf{A}^{-1}
   \]

   See also: https://en.wikipedia.org/wiki/Adjugate_matrix

   #+NAME: qmckl_adjugate_args
   | Variable  | Type            | In/Out | Description                                    |
   |-----------+-----------------+--------+------------------------------------------------|
   | ~context~ | ~qmckl_context~ | in     | Global state                                   |
   | ~n~       | ~int64_t~       | in     | Number of rows and columns of the input matrix |
   | ~A~       | ~double[][lda]~ | in     | Array containing the $n \times n$ matrix $A$   |
   | ~lda~     | ~int64_t~       | in     | Leading dimension of array ~A~                 |
   | ~B~       | ~double[][ldb]~ | out    | Adjugate of $A$                                |
   | ~ldb~     | ~int64_t~       | in     | Leading dimension of array ~B~                 |
   | ~det_l~   | ~double~        | 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
    - ~ldb >= m~
    - ~B~ is allocated with at least $m \times m \times 8$ bytes
      
    #+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 double* A,
          const int64_t lda,
          double* const B,
          const int64_t ldb,
          double* det_l ); 
    #+end_src
    
   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, A, LDA, B, ldb, det_l) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  double precision, intent(in)          :: A (LDA,*)
  integer*8, intent(in)                 :: LDA
  double precision, intent(out)         :: B (LDB,*)
  integer*8, intent(in)                 :: LDB
  integer*8, intent(in)                 :: na
  double precision, intent(inout)       :: det_l

  integer    :: i,j
  
  info = QMCKL_SUCCESS
  
  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif
  
  if (na <= 0_8) then
     info = QMCKL_INVALID_ARG_2
     return
  endif

  if (LDA <= 0_8) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  if (LDA < na) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  select case (na)
  case (5)
     call adjugate5(A,LDA,B,LDB,na,det_l)
  case (4)
     call adjugate4(A,LDA,B,LDB,na,det_l)
  case (3)
     call adjugate3(A,LDA,B,LDB,na,det_l)
  case (2)
     call adjugate2(A,LDA,B,LDB,na,det_l)
  case (1)
    det_l = a(1,1)
    b(1,1) = 1.d0
  case default
     call adjugate_general(context, na, A, LDA, B, LDB, det_l)
  end select
   
end function qmckl_adjugate_f
    #+end_src

    #+begin_src f90 :tangle (eval f) :exports none
subroutine adjugate2(A,LDA,B,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  integer*8, intent(in)           :: na
  double precision, intent(inout) :: det_l

  double precision :: C(2,2)
  
  call cofactor2(A,LDA,C,2,na,det_l)
  
  B(1,1) = C(1,1)
  B(2,1) = C(1,2)
  B(1,2) = C(2,1)
  B(2,2) = C(2,2)

end subroutine adjugate2

subroutine adjugate3(a,LDA,B,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  integer*8, intent(in)           :: na
  double precision, intent(inout) :: det_l

  double precision :: C(4,3)
  
  call cofactor3(A,LDA,C,4,na,det_l)
  
  B(1,1) = C(1,1)
  B(1,2) = C(2,1)
  B(1,3) = C(3,1)
  B(2,1) = C(1,2)
  B(2,2) = C(2,2)
  B(2,3) = C(3,2)
  B(3,1) = C(1,3)
  B(3,2) = C(2,3)
  B(3,3) = C(3,3)

end subroutine adjugate3

subroutine adjugate4(a,LDA,B,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  integer*8, intent(in)           :: na
  double precision, intent(inout) :: det_l

  double precision :: C(4,4)
  
  call cofactor4(A,LDA,B,4,na,det_l)
  
  B(1,1) = C(1,1)
  B(1,2) = C(2,1)
  B(1,3) = C(3,1)
  B(1,4) = C(4,1)
  B(2,1) = C(1,2)
  B(2,2) = C(2,2)
  B(2,3) = C(3,2)
  B(2,4) = C(4,2)
  B(3,1) = C(1,3)
  B(3,2) = C(2,3)
  B(3,3) = C(3,3)
  B(3,4) = C(4,3)
  B(4,1) = C(1,4)
  B(4,2) = C(2,4)
  B(4,3) = C(3,4)
  B(4,4) = C(4,4)

end subroutine adjugate4

subroutine adjugate5(A,LDA,B,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  integer*8, intent(in)           :: na
  double precision, intent(inout) :: det_l

  double precision  :: C(8,5)
  
  call cofactor5(A,LDA,C,8,na,det_l)
  
  B(1,1) = C(1,1)
  B(1,2) = C(2,1)
  B(1,3) = C(3,1)
  B(1,4) = C(4,1)
  B(1,5) = C(5,1)
  B(2,1) = C(1,2)
  B(2,2) = C(2,2)
  B(2,3) = C(3,2)
  B(2,4) = C(4,2)
  B(2,5) = C(5,2)
  B(3,1) = C(1,3)
  B(3,2) = C(2,3)
  B(3,3) = C(3,3)
  B(3,4) = C(4,3)
  B(3,5) = C(5,3)
  B(4,1) = C(1,4)
  B(4,2) = C(2,4)
  B(4,3) = C(3,4)
  B(4,4) = C(4,4)
  B(4,5) = C(5,4)
  B(5,1) = C(1,5)
  B(5,2) = C(2,5)
  B(5,3) = C(3,5)
  B(5,4) = C(4,5)
  B(5,5) = C(5,5)

end subroutine adjugate5

subroutine cofactor2(a,LDA,b,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  integer*8        :: na
  double precision :: det_l
  
  det_l  =  a(1,1)*a(2,2) - a(1,2)*a(2,1)
  b(1,1) =  a(2,2)
  b(2,1) = -a(2,1)
  b(1,2) = -a(1,2)
  b(2,2) =  a(1,1)
end subroutine cofactor2

subroutine cofactor3(a,LDA,b,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  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))

  b(1,1) =  a(2,2)*a(3,3) - a(2,3)*a(3,2)
  b(2,1) =  a(2,3)*a(3,1) - a(2,1)*a(3,3)
  b(3,1) =  a(2,1)*a(3,2) - a(2,2)*a(3,1)
  
  b(1,2) =  a(1,3)*a(3,2) - a(1,2)*a(3,3)
  b(2,2) =  a(1,1)*a(3,3) - a(1,3)*a(3,1)
  b(3,2) =  a(1,2)*a(3,1) - a(1,1)*a(3,2)
  
  b(1,3) =  a(1,2)*a(2,3) - a(1,3)*a(2,2)
  b(2,3) =  a(1,3)*a(2,1) - a(1,1)*a(2,3)
  b(3,3) =  a(1,1)*a(2,2) - a(1,2)*a(2,1)
  
end subroutine cofactor3

subroutine cofactor4(a,LDA,b,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  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)))

  b(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))
  b(2,1) = -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))
  b(3,1) =  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))
  b(4,1) = -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))
  
  b(1,2) = -a(1,2)*(a(3,3)*a(4,4)-a(3,4)*a(4,3))+a(1,3)*(a(3,2)*a(4,4)-a(3,4)*a(4,2))-a(1,4)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))
  b(2,2) =  a(1,1)*(a(3,3)*a(4,4)-a(3,4)*a(4,3))-a(1,3)*(a(3,1)*a(4,4)-a(3,4)*a(4,1))+a(1,4)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))
  b(3,2) = -a(1,1)*(a(3,2)*a(4,4)-a(3,4)*a(4,2))+a(1,2)*(a(3,1)*a(4,4)-a(3,4)*a(4,1))-a(1,4)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))
  b(4,2) =  a(1,1)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))-a(1,2)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))+a(1,3)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))
  
  b(1,3) =  a(1,2)*(a(2,3)*a(4,4)-a(2,4)*a(4,3))-a(1,3)*(a(2,2)*a(4,4)-a(2,4)*a(4,2))+a(1,4)*(a(2,2)*a(4,3)-a(2,3)*a(4,2))
  b(2,3) = -a(1,1)*(a(2,3)*a(4,4)-a(2,4)*a(4,3))+a(1,3)*(a(2,1)*a(4,4)-a(2,4)*a(4,1))-a(1,4)*(a(2,1)*a(4,3)-a(2,3)*a(4,1))
  b(3,3) =  a(1,1)*(a(2,2)*a(4,4)-a(2,4)*a(4,2))-a(1,2)*(a(2,1)*a(4,4)-a(2,4)*a(4,1))+a(1,4)*(a(2,1)*a(4,2)-a(2,2)*a(4,1))
  b(4,3) = -a(1,1)*(a(2,2)*a(4,3)-a(2,3)*a(4,2))+a(1,2)*(a(2,1)*a(4,3)-a(2,3)*a(4,1))-a(1,3)*(a(2,1)*a(4,2)-a(2,2)*a(4,1))
  
  b(1,4) = -a(1,2)*(a(2,3)*a(3,4)-a(2,4)*a(3,3))+a(1,3)*(a(2,2)*a(3,4)-a(2,4)*a(3,2))-a(1,4)*(a(2,2)*a(3,3)-a(2,3)*a(3,2))
  b(2,4) =  a(1,1)*(a(2,3)*a(3,4)-a(2,4)*a(3,3))-a(1,3)*(a(2,1)*a(3,4)-a(2,4)*a(3,1))+a(1,4)*(a(2,1)*a(3,3)-a(2,3)*a(3,1))
  b(3,4) = -a(1,1)*(a(2,2)*a(3,4)-a(2,4)*a(3,2))+a(1,2)*(a(2,1)*a(3,4)-a(2,4)*a(3,1))-a(1,4)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
  b(4,4) =  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))
  
end subroutine cofactor4

subroutine cofactor5(A,LDA,B,LDB,na,det_l)
  implicit none
  double precision, intent(in)    :: A (LDA,na)
  double precision, intent(out)   :: B (LDA,na)
  integer*8, intent(in)           :: LDA, LDB
  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))))

 b(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))))
 b(2,1) = &
 (-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))))
 b(3,1) = &
 (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))))
 b(4,1) = &
 (-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))))
 b(5,1) = &
 (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))))

 b(1,2) = &
 (-a(1,2)*(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(1,3)* &
 (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(1,4)* &
 (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(1,5)* &
 (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))))
 b(2,2) = &
 (a(1,1)*(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(1,3)* &
 (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(1,4)* &
 (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(1,5)* &
 (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))))
 b(3,2) = &
 (-a(1,1)*(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(1,2)* &
 (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(1,4)* &
 (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(1,5)* &
 (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))))
 b(4,2) = &
 (a(1,1)*(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(1,2)* &
 (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(1,3)* &
 (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(1,5)* &
 (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))))
 b(5,2) = &
 (-a(1,1)*(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(1,2)* &
 (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(1,3)* &
 (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(1,4)* &
 (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))))

 b(1,3) = &
 (a(1,2)*(a(2,3)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(2,4)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(2,5)*(a(4,3)*a(5,4)-a(4,4)*a(5,3)))-a(1,3)* &
 (a(2,2)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(2,4)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(2,5)*(a(4,2)*a(5,4)-a(4,4)*a(5,2)))+a(1,4)* &
 (a(2,2)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(2,3)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(2,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(1,5)* &
 (a(2,2)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(2,3)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))+a(2,4)*(a(4,2)*a(5,3)-a(4,3)*a(5,2))))
 b(2,3) = &
 (-a(1,1)*(a(2,3)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(2,4)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(2,5)*(a(4,3)*a(5,4)-a(4,4)*a(5,3)))+a(1,3)* &
 (a(2,1)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(2,4)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(2,5)*(a(4,1)*a(5,4)-a(4,4)*a(5,1)))-a(1,4)* &
 (a(2,1)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(2,3)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(2,5)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(1,5)* &
 (a(2,1)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(2,3)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(2,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))))
 b(3,3) = &
 (a(1,1)*(a(2,2)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(2,4)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(2,5)*(a(4,2)*a(5,4)-a(4,4)*a(5,2)))-a(1,2)* &
 (a(2,1)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(2,4)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(2,5)*(a(4,1)*a(5,4)-a(4,4)*a(5,1)))+a(1,4)* &
 (a(2,1)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))-a(2,2)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(2,5)*(a(4,1)*a(5,2)-a(4,2)*a(5,1)))-a(1,5)* &
 (a(2,1)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))-a(2,2)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(2,4)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))
 b(4,3) = &
 (-a(1,1)*(a(2,2)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(2,3)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(2,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))+a(1,2)* &
 (a(2,1)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(2,3)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(2,5)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))-a(1,3)* &
 (a(2,1)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))-a(2,2)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(2,5)*(a(4,1)*a(5,2)-a(4,2)*a(5,1)))+a(1,5)* &
 (a(2,1)*(a(4,2)*a(5,3)-a(4,3)*a(5,2))-a(2,2)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(2,3)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))
 b(5,3) = &
 (a(1,1)*(a(2,2)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(2,3)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))+a(2,4)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(1,2)* &
 (a(2,1)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(2,3)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(2,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(1,3)* &
 (a(2,1)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))-a(2,2)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(2,4)*(a(4,1)*a(5,2)-a(4,2)*a(5,1)))-a(1,4)* &
 (a(2,1)*(a(4,2)*a(5,3)-a(4,3)*a(5,2))-a(2,2)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(2,3)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))

 b(1,4) = &
 (-a(1,2)*(a(2,3)*(a(3,4)*a(5,5)-a(3,5)*a(5,4))-a(2,4)*(a(3,3)*a(5,5)-a(3,5)*a(5,3))+a(2,5)*(a(3,3)*a(5,4)-a(3,4)*a(5,3)))+a(1,3)* &
 (a(2,2)*(a(3,4)*a(5,5)-a(3,5)*a(5,4))-a(2,4)*(a(3,2)*a(5,5)-a(3,5)*a(5,2))+a(2,5)*(a(3,2)*a(5,4)-a(3,4)*a(5,2)))-a(1,4)* &
 (a(2,2)*(a(3,3)*a(5,5)-a(3,5)*a(5,3))-a(2,3)*(a(3,2)*a(5,5)-a(3,5)*a(5,2))+a(2,5)*(a(3,2)*a(5,3)-a(3,3)*a(5,2)))+a(1,5)* &
 (a(2,2)*(a(3,3)*a(5,4)-a(3,4)*a(5,3))-a(2,3)*(a(3,2)*a(5,4)-a(3,4)*a(5,2))+a(2,4)*(a(3,2)*a(5,3)-a(3,3)*a(5,2))))
 b(2,4) = &
 (a(1,1)*(a(2,3)*(a(3,4)*a(5,5)-a(3,5)*a(5,4))-a(2,4)*(a(3,3)*a(5,5)-a(3,5)*a(5,3))+a(2,5)*(a(3,3)*a(5,4)-a(3,4)*a(5,3)))-a(1,3)* &
 (a(2,1)*(a(3,4)*a(5,5)-a(3,5)*a(5,4))-a(2,4)*(a(3,1)*a(5,5)-a(3,5)*a(5,1))+a(2,5)*(a(3,1)*a(5,4)-a(3,4)*a(5,1)))+a(1,4)* &
 (a(2,1)*(a(3,3)*a(5,5)-a(3,5)*a(5,3))-a(2,3)*(a(3,1)*a(5,5)-a(3,5)*a(5,1))+a(2,5)*(a(3,1)*a(5,3)-a(3,3)*a(5,1)))-a(1,5)* &
 (a(2,1)*(a(3,3)*a(5,4)-a(3,4)*a(5,3))-a(2,3)*(a(3,1)*a(5,4)-a(3,4)*a(5,1))+a(2,4)*(a(3,1)*a(5,3)-a(3,3)*a(5,1))))
 b(3,4) = &
 (-a(1,1)*(a(2,2)*(a(3,4)*a(5,5)-a(3,5)*a(5,4))-a(2,4)*(a(3,2)*a(5,5)-a(3,5)*a(5,2))+a(2,5)*(a(3,2)*a(5,4)-a(3,4)*a(5,2)))+a(1,2)* &
 (a(2,1)*(a(3,4)*a(5,5)-a(3,5)*a(5,4))-a(2,4)*(a(3,1)*a(5,5)-a(3,5)*a(5,1))+a(2,5)*(a(3,1)*a(5,4)-a(3,4)*a(5,1)))-a(1,4)* &
 (a(2,1)*(a(3,2)*a(5,5)-a(3,5)*a(5,2))-a(2,2)*(a(3,1)*a(5,5)-a(3,5)*a(5,1))+a(2,5)*(a(3,1)*a(5,2)-a(3,2)*a(5,1)))+a(1,5)* &
 (a(2,1)*(a(3,2)*a(5,4)-a(3,4)*a(5,2))-a(2,2)*(a(3,1)*a(5,4)-a(3,4)*a(5,1))+a(2,4)*(a(3,1)*a(5,2)-a(3,2)*a(5,1))))
 b(4,4) = &
 (a(1,1)*(a(2,2)*(a(3,3)*a(5,5)-a(3,5)*a(5,3))-a(2,3)*(a(3,2)*a(5,5)-a(3,5)*a(5,2))+a(2,5)*(a(3,2)*a(5,3)-a(3,3)*a(5,2)))-a(1,2)* &
 (a(2,1)*(a(3,3)*a(5,5)-a(3,5)*a(5,3))-a(2,3)*(a(3,1)*a(5,5)-a(3,5)*a(5,1))+a(2,5)*(a(3,1)*a(5,3)-a(3,3)*a(5,1)))+a(1,3)* &
 (a(2,1)*(a(3,2)*a(5,5)-a(3,5)*a(5,2))-a(2,2)*(a(3,1)*a(5,5)-a(3,5)*a(5,1))+a(2,5)*(a(3,1)*a(5,2)-a(3,2)*a(5,1)))-a(1,5)* &
 (a(2,1)*(a(3,2)*a(5,3)-a(3,3)*a(5,2))-a(2,2)*(a(3,1)*a(5,3)-a(3,3)*a(5,1))+a(2,3)*(a(3,1)*a(5,2)-a(3,2)*a(5,1))))
 b(5,4) = &
 (-a(1,1)*(a(2,2)*(a(3,3)*a(5,4)-a(3,4)*a(5,3))-a(2,3)*(a(3,2)*a(5,4)-a(3,4)*a(5,2))+a(2,4)*(a(3,2)*a(5,3)-a(3,3)*a(5,2)))+a(1,2)* &
 (a(2,1)*(a(3,3)*a(5,4)-a(3,4)*a(5,3))-a(2,3)*(a(3,1)*a(5,4)-a(3,4)*a(5,1))+a(2,4)*(a(3,1)*a(5,3)-a(3,3)*a(5,1)))-a(1,3)* &
 (a(2,1)*(a(3,2)*a(5,4)-a(3,4)*a(5,2))-a(2,2)*(a(3,1)*a(5,4)-a(3,4)*a(5,1))+a(2,4)*(a(3,1)*a(5,2)-a(3,2)*a(5,1)))+a(1,4)* &
 (a(2,1)*(a(3,2)*a(5,3)-a(3,3)*a(5,2))-a(2,2)*(a(3,1)*a(5,3)-a(3,3)*a(5,1))+a(2,3)*(a(3,1)*a(5,2)-a(3,2)*a(5,1))))

 b(1,5) = &
 (a(1,2)*(a(2,3)*(a(3,4)*a(4,5)-a(3,5)*a(4,4))-a(2,4)*(a(3,3)*a(4,5)-a(3,5)*a(4,3))+a(2,5)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)))-a(1,3)* &
 (a(2,2)*(a(3,4)*a(4,5)-a(3,5)*a(4,4))-a(2,4)*(a(3,2)*a(4,5)-a(3,5)*a(4,2))+a(2,5)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)))+a(1,4)* &
 (a(2,2)*(a(3,3)*a(4,5)-a(3,5)*a(4,3))-a(2,3)*(a(3,2)*a(4,5)-a(3,5)*a(4,2))+a(2,5)*(a(3,2)*a(4,3)-a(3,3)*a(4,2)))-a(1,5)* &
 (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))))
 b(2,5) = &
 (-a(1,1)*(a(2,3)*(a(3,4)*a(4,5)-a(3,5)*a(4,4))-a(2,4)*(a(3,3)*a(4,5)-a(3,5)*a(4,3))+a(2,5)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)))+a(1,3)* &
 (a(2,1)*(a(3,4)*a(4,5)-a(3,5)*a(4,4))-a(2,4)*(a(3,1)*a(4,5)-a(3,5)*a(4,1))+a(2,5)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)))-a(1,4)* &
 (a(2,1)*(a(3,3)*a(4,5)-a(3,5)*a(4,3))-a(2,3)*(a(3,1)*a(4,5)-a(3,5)*a(4,1))+a(2,5)*(a(3,1)*a(4,3)-a(3,3)*a(4,1)))+a(1,5)* &
 (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))))
 b(3,5) = &
 (a(1,1)*(a(2,2)*(a(3,4)*a(4,5)-a(3,5)*a(4,4))-a(2,4)*(a(3,2)*a(4,5)-a(3,5)*a(4,2))+a(2,5)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)))-a(1,2)* &
 (a(2,1)*(a(3,4)*a(4,5)-a(3,5)*a(4,4))-a(2,4)*(a(3,1)*a(4,5)-a(3,5)*a(4,1))+a(2,5)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)))+a(1,4)* &
 (a(2,1)*(a(3,2)*a(4,5)-a(3,5)*a(4,2))-a(2,2)*(a(3,1)*a(4,5)-a(3,5)*a(4,1))+a(2,5)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))-a(1,5)* &
 (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))))
 b(4,5) = &
 (-a(1,1)*(a(2,2)*(a(3,3)*a(4,5)-a(3,5)*a(4,3))-a(2,3)*(a(3,2)*a(4,5)-a(3,5)*a(4,2))+a(2,5)*(a(3,2)*a(4,3)-a(3,3)*a(4,2)))+a(1,2)* &
 (a(2,1)*(a(3,3)*a(4,5)-a(3,5)*a(4,3))-a(2,3)*(a(3,1)*a(4,5)-a(3,5)*a(4,1))+a(2,5)*(a(3,1)*a(4,3)-a(3,3)*a(4,1)))-a(1,3)* &
 (a(2,1)*(a(3,2)*a(4,5)-a(3,5)*a(4,2))-a(2,2)*(a(3,1)*a(4,5)-a(3,5)*a(4,1))+a(2,5)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))+a(1,5)* &
 (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))))
 b(5,5) = &
 (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))))

end
    #+end_src

    #+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, A, lda, B, ldb, 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
      real    (c_double ) , intent(in)          :: A(lda,*)
      integer (c_int64_t) , intent(in)  , value :: lda
      real    (c_double ) , intent(out)         :: B(ldb,*)
      integer (c_int64_t) , intent(in)  , value :: ldb
      real    (c_double ) , intent(inout)        :: det_l

      integer(c_int32_t), external :: qmckl_adjugate_f
      info = qmckl_adjugate_f &
             (context, n, A, lda, B, ldb, 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, A, lda, B, ldb, 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
        real    (c_double ) , intent(in)          :: A(lda,*)
        integer (c_int64_t) , intent(in)  , value :: lda
        real    (c_double ) , intent(out)         :: B(ldb,*)
        integer (c_int64_t) , intent(in)  , value :: ldb
        real    (c_double ) , intent(inout)        :: det_l

      end function qmckl_adjugate
    end interface
    #+end_src
    

    #+begin_src f90 :tangle (eval f)
subroutine adjugate_general(context, na, A, LDA, det_l)
  use qmckl
  implicit none
  integer(qmckl_context) intent(in)  :: context
  double precision, intent(in)       :: A (LDA,na)
  integer*8, intent(in)              :: LDA
  double precision, intent(out)      :: B (LDB,na)
  integer*8, intent(in)              :: LDB
  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

    We first copy the array ~A~ into array ~B~.

    #+begin_src f90 :tangle (eval f)
  B(1:na,1:na) = A(1:na,1:na)
    #+end_src

    Then, we compute the LU factorization $LU=A$
    using the ~dgetrf~ routine.

    #+begin_src f90 :tangle (eval f)
  call dgetrf(na, na, B, LDB, 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*B(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, B, LDB, 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)
  B(:,:) = B(:,:)*det_l

end subroutine adjugate_general
    #+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"  test_qmckl_adjugate = qmckl_adjugate(context, {i+1}_8, A, LDA, B, LDB, 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_example
    ,#+begin_src f90 :tangle (eval f_test)
    ! N =  1
      test_qmckl_adjugate = qmckl_adjugate(context, 1_8, A, LDA, B, LDB, 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
      test_qmckl_adjugate = qmckl_adjugate(context, 2_8, A, LDA, B, LDB, 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
      test_qmckl_adjugate = qmckl_adjugate(context, 3_8, A, LDA, B, LDB, 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
      test_qmckl_adjugate = qmckl_adjugate(context, 4_8, A, LDA, B, LDB, 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
      test_qmckl_adjugate = qmckl_adjugate(context, 5_8, A, LDA, B, LDB, 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
      test_qmckl_adjugate = qmckl_adjugate(context, 6_8, A, LDA, B, LDB, 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
    #+end_example

    #+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