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BLAS functions

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1 Matrix operations

1.1 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.

qmcklcontext context in Global state
bool TransA in Number of rows of the input matrix
bool TransB in Number of rows of the input matrix
int64t m in Number of rows of the input matrix
int64t n in Number of columns of the input matrix
int64t 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 \(m \times n\) matrix \(A\)
int64t lda in Leading dimension of array A
double B[][ldb] in Array containing the \(n \times m\) matrix \(B\)
int64t ldb in Leading dimension of array B
double beta in Array containing the \(n \times m\) matrix \(B\)
double C[][ldc] out Array containing the \(n \times m\) matrix \(B\)
int64t ldc in Leading dimension of array B

1.1.1 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

1.1.2 C header

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 );

1.1.3 Source

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_4
     return
  endif

  if (n <= 0_8) then
     info = QMCKL_INVALID_ARG_5
     return
  endif

  if (k <= 0_8) then
     info = QMCKL_INVALID_ARG_6
     return
  endif

  if (LDA /= m) then
     info = QMCKL_INVALID_ARG_9
     return
  endif

  if (LDB /= k) then
     info = QMCKL_INVALID_ARG_10
     return
  endif

  if (LDC /= m) then
     info = QMCKL_INVALID_ARG_13
     return
  endif

  if (alpha == 1.0d0 .and. beta == 0.0d0) then
    C = matmul(A,B)
  else
    C = beta*C + alpha*matmul(A,B)
  endif
end function qmckl_dgemm_N_N_f

1.2 qmckl_adjoint

Matrix adjoint. Given a matrix M, returns a matrix M⁻¹ such that:

\[ M · M^{-1} = I \]

This is a native Fortran implementation hand written (by: A. Scemama) only for small matrices (<=5x5).

TODO: Add description about the external library dependence.

qmcklcontext context in Global state
int64t m in Number of rows of the input matrix
int64t n in Number of columns of the input matrix
int64t lda in Leading dimension of array A
double A[][lda] inout Array containing the \(m \times n\) matrix \(A\)
double detl inout determinant of A

1.2.1 Requirements

  • context is not QMCKL_NULL_CONTEXT
  • m > 0
  • n > 0
  • lda >= m
  • A is allocated with at least \(m \times n \times 8\) bytes

1.2.2 C header

qmckl_exit_code qmckl_adjoint (
      const qmckl_context context,
      const int64_t m,
      const int64_t n,
      const int64_t lda,
      double* A,
      double* det_l );

1.2.3 Source

integer function qmckl_adjoint_f(context, ma, na, LDA, A, det_l) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
 double precision, intent(inout) :: A (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: ma
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 integer :: i,j

 info = QMCKL_SUCCESS

 select case (na)
  case default
!DIR$ forceinline
    print *," TODO: Implement general adjoint"
    stop 0
  case (5)
!DIR$ forceinline
    call adjoint5(a,LDA,na,det_l)
  case (4)
!DIR$ forceinline
    call adjoint4(a,LDA,na,det_l)

  case (3)
!DIR$ forceinline
    call adjoint3(a,LDA,na,det_l)
  case (2)
!DIR$ forceinline
    call adjoint2(a,LDA,na,det_l)
  case (1)
!DIR$ forceinline
    call adjoint1(a,LDA,na,det_l)
  case (0)
    det_l=1.d0
 end select
end function qmckl_adjoint_f

subroutine adjoint1(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l

 call cofactor1(a,LDA,na,det_l)
end

subroutine adjoint2(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(2,2)

 call cofactor2(a,LDA,na,det_l)

 ! Calculate the transpose
 b(1,1) = a(1,1)
 b(1,2) = a(2,1)
 b(2,1) = a(1,2)
 b(2,2) = a(2,2)
 a(1,1) = b(1,1)
 a(1,2) = b(1,2)
 a(2,1) = b(2,1)
 a(2,2) = b(2,2)
end

subroutine adjoint3(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(3,3)

 call cofactor3(a,LDA,na,det_l)

 ! Calculate the transpose
 b(1,1) = a(1,1)
 b(1,2) = a(2,1)
 b(1,3) = a(3,1)
 b(2,1) = a(1,2)
 b(2,2) = a(2,2)
 b(2,3) = a(3,2)
 b(3,1) = a(1,3)
 b(3,2) = a(2,3)
 b(3,3) = a(3,3)
 ! copy
 a(1,1) = b(1,1)
 a(2,1) = b(2,1)
 a(3,1) = b(3,1)
 a(1,2) = b(1,2)
 a(2,2) = b(2,2)
 a(3,2) = b(3,2)
 a(1,3) = b(1,3)
 a(2,3) = b(2,3)
 a(3,3) = b(3,3)
end

subroutine adjoint4(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(4,4)

 call cofactor4(a,LDA,na,det_l)

 ! Calculate the transpose
 b(1,1) = a(1,1)
 b(1,2) = a(2,1)
 b(1,3) = a(3,1)
 b(1,4) = a(4,1)
 b(2,1) = a(1,2)
 b(2,2) = a(2,2)
 b(2,3) = a(3,2)
 b(2,4) = a(4,2)
 b(3,1) = a(1,3)
 b(3,2) = a(2,3)
 b(3,3) = a(3,3)
 b(3,4) = a(4,3)
 b(4,1) = a(1,4)
 b(4,2) = a(2,4)
 b(4,3) = a(3,4)
 b(4,4) = a(4,4)
 ! copy
 a(1,1) = b(1,1)
 a(2,1) = b(2,1)
 a(3,1) = b(3,1)
 a(4,1) = b(4,1)
 a(1,2) = b(1,2)
 a(2,2) = b(2,2)
 a(3,2) = b(3,2)
 a(4,2) = b(4,2)
 a(1,3) = b(1,3)
 a(2,3) = b(2,3)
 a(3,3) = b(3,3)
 a(4,3) = b(4,3)
 a(1,4) = b(1,4)
 a(2,4) = b(2,4)
 a(3,4) = b(3,4)
 a(4,4) = b(4,4)
end

subroutine adjoint5(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(5,5)

 call cofactor5(a,LDA,na,det_l)

 ! Calculate the transpose
 b(1,1) = a(1,1)
 b(1,2) = a(2,1)
 b(1,3) = a(3,1)
 b(1,4) = a(4,1)
 b(1,5) = a(5,1)
 b(2,1) = a(1,2)
 b(2,2) = a(2,2)
 b(2,3) = a(3,2)
 b(2,4) = a(4,2)
 b(2,5) = a(5,2)
 b(3,1) = a(1,3)
 b(3,2) = a(2,3)
 b(3,3) = a(3,3)
 b(3,4) = a(4,3)
 b(3,5) = a(5,3)
 b(4,1) = a(1,4)
 b(4,2) = a(2,4)
 b(4,3) = a(3,4)
 b(4,4) = a(4,4)
 b(4,5) = a(5,4)
 b(5,1) = a(1,5)
 b(5,2) = a(2,5)
 b(5,3) = a(3,5)
 b(5,4) = a(4,5)
 b(5,5) = a(5,5)
 ! copy
 a(1,1) = b(1,1)
 a(2,1) = b(2,1)
 a(3,1) = b(3,1)
 a(4,1) = b(4,1)
 a(5,1) = b(5,1)
 a(1,2) = b(1,2)
 a(2,2) = b(2,2)
 a(3,2) = b(3,2)
 a(4,2) = b(4,2)
 a(5,2) = b(5,2)
 a(1,3) = b(1,3)
 a(2,3) = b(2,3)
 a(3,3) = b(3,3)
 a(4,3) = b(4,3)
 a(5,3) = b(5,3)
 a(1,4) = b(1,4)
 a(2,4) = b(2,4)
 a(3,4) = b(3,4)
 a(4,4) = b(4,4)
 a(5,4) = b(5,4)
 a(1,5) = b(1,5)
 a(2,5) = b(2,5)
 a(3,5) = b(3,5)
 a(4,5) = b(4,5)
 a(5,5) = b(5,5)
end

subroutine cofactor1(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l

 det_l = a(1,1)
 a(1,1) = 1.d0
end

subroutine cofactor2(a,LDA,na,det_l)
 implicit none
 double precision :: a (LDA,na)
 integer*8        :: LDA
 integer*8        :: na
 double precision :: det_l
 double precision :: b(2,2)

 b(1,1) = a(1,1)
 b(2,1) = a(2,1)
 b(1,2) = a(1,2)
 b(2,2) = a(2,2)
 det_l = a(1,1)*a(2,2) - a(1,2)*a(2,1)
 a(1,1) = b(2,2)
 a(2,1) = -b(2,1)
 a(1,2) = -b(1,2)
 a(2,2) = b(1,1)
end

subroutine cofactor3(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(4,3)
 !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
 integer :: i
 det_l = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) &
        -a(1,2)*(a(2,1)*a(3,3)-a(2,3)*a(3,1)) &
        +a(1,3)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
 do i=1,4
  b(i,1) = a(i,1)
  b(i,2) = a(i,2)
  b(i,3) = a(i,3)
 enddo
 a(1,1) =  b(2,2)*b(3,3) - b(2,3)*b(3,2)
 a(2,1) =  b(2,3)*b(3,1) - b(2,1)*b(3,3)
 a(3,1) =  b(2,1)*b(3,2) - b(2,2)*b(3,1)

 a(1,2) =  b(1,3)*b(3,2) - b(1,2)*b(3,3)
 a(2,2) =  b(1,1)*b(3,3) - b(1,3)*b(3,1)
 a(3,2) =  b(1,2)*b(3,1) - b(1,1)*b(3,2)

 a(1,3) =  b(1,2)*b(2,3) - b(1,3)*b(2,2)
 a(2,3) =  b(1,3)*b(2,1) - b(1,1)*b(2,3)
 a(3,3) =  b(1,1)*b(2,2) - b(1,2)*b(2,1)

end

subroutine cofactor4(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(4,4)
 !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
 integer :: i,j
 det_l =  a(1,1)*(a(2,2)*(a(3,3)*a(4,4)-a(3,4)*a(4,3))  &
                 -a(2,3)*(a(3,2)*a(4,4)-a(3,4)*a(4,2))  &
                 +a(2,4)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))) &
         -a(1,2)*(a(2,1)*(a(3,3)*a(4,4)-a(3,4)*a(4,3))  &
                 -a(2,3)*(a(3,1)*a(4,4)-a(3,4)*a(4,1))  &
                 +a(2,4)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))) &
         +a(1,3)*(a(2,1)*(a(3,2)*a(4,4)-a(3,4)*a(4,2))  &
                 -a(2,2)*(a(3,1)*a(4,4)-a(3,4)*a(4,1))  &
                 +a(2,4)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))) &
         -a(1,4)*(a(2,1)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))  &
                 -a(2,2)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))  &
                 +a(2,3)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))
 do i=1,4
  b(1,i) = a(1,i)
  b(2,i) = a(2,i)
  b(3,i) = a(3,i)
  b(4,i) = a(4,i)
 enddo

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

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

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

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

end

subroutine cofactor5(a,LDA,na,det_l)
 implicit none
 double precision, intent(inout) :: a (LDA,na)
 integer*8, intent(in)             :: LDA
 integer*8, intent(in)             :: na
 double precision, intent(inout) :: det_l
 double precision :: b(5,5)
 !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
 integer :: i,j
 det_l = a(1,1)*(a(2,2)*(a(3,3)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*( &
 a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(3,5)*(a(4,3)*a(5,4)-a(4,4)*a(5,3)))- &
 a(2,3)*(a(3,2)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*(a(4,2)*a(5,5)- &
 a(4,5)*a(5,2))+a(3,5)*(a(4,2)*a(5,4)-a(4,4)*a(5,2)))+a(2,4)*(a(3,2)*( &
 a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+ &
 a(3,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,5)*(a(3,2)*(a(4,3)*a(5,4)- &
 a(4,4)*a(5,3))-a(3,3)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))+a(3,4)*(a(4,2)* &
 a(5,3)-a(4,3)*a(5,2))))-a(1,2)*(a(2,1)*(a(3,3)*(a(4,4)*a(5,5)-a(4,5)* &
 a(5,4))-a(3,4)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(3,5)*(a(4,3)*a(5,4)- &
 a(4,4)*a(5,3)))-a(2,3)*(a(3,1)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*( &
 a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,4)-a(4,4)*a(5,1)))+ &
 a(2,4)*(a(3,1)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,1)*a(5,5)- &
 a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))-a(2,5)*(a(3,1)*( &
 a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+ &
 a(3,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))))+a(1,3)*(a(2,1)*(a(3,2)*(a(4,4)* &
 a(5,5)-a(4,5)*a(5,4))-a(3,4)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(3,5)*( &
 a(4,2)*a(5,4)-a(4,4)*a(5,2)))-a(2,2)*(a(3,1)*(a(4,4)*a(5,5)-a(4,5)* &
 a(5,4))-a(3,4)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,4)- &
 a(4,4)*a(5,1)))+a(2,4)*(a(3,1)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))-a(3,2)*( &
 a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,2)-a(4,2)*a(5,1)))- &
 a(2,5)*(a(3,1)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))-a(3,2)*(a(4,1)*a(5,4)- &
 a(4,4)*a(5,1))+a(3,4)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))-a(1,4)*(a(2,1)*( &
 a(3,2)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,2)*a(5,5)-a(4,5)* &
 a(5,2))+a(3,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,2)*(a(3,1)*(a(4,3)* &
 a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*( &
 a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(2,3)*(a(3,1)*(a(4,2)*a(5,5)-a(4,5)* &
 a(5,2))-a(3,2)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,2)- &
 a(4,2)*a(5,1)))-a(2,5)*(a(3,1)*(a(4,2)*a(5,3)-a(4,3)*a(5,2))-a(3,2)*( &
 a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(3,3)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))+ &
 a(1,5)*(a(2,1)*(a(3,2)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,2)* &
 a(5,4)-a(4,4)*a(5,2))+a(3,4)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,2)*( &
 a(3,1)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,1)*a(5,4)-a(4,4)* &
 a(5,1))+a(3,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(2,3)*(a(3,1)*(a(4,2)* &
 a(5,4)-a(4,4)*a(5,2))-a(3,2)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(3,4)*( &
 a(4,1)*a(5,2)-a(4,2)*a(5,1)))-a(2,4)*(a(3,1)*(a(4,2)*a(5,3)-a(4,3)* &
 a(5,2))-a(3,2)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(3,3)*(a(4,1)*a(5,2)- &
 a(4,2)*a(5,1))))

 do i=1,5
  b(1,i) = a(1,i)
  b(2,i) = a(2,i)
  b(3,i) = a(3,i)
  b(4,i) = a(4,i)
  b(5,i) = a(5,i)
 enddo

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

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

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

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

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

end

Author: TREX CoE

Created: 2021-11-25 Thu 14:27

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