mirror of
https://github.com/TREX-CoE/qmckl.git
synced 2024-08-18 11:21:44 +02:00
1067 lines
40 KiB
Org Mode
1067 lines
40 KiB
Org Mode
#+TITLE: BLAS functions
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#+SETUPFILE: ../tools/theme.setup
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#+INCLUDE: ../tools/lib.org
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* Headers :noexport:
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#+begin_src elisp :noexport :results none
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(org-babel-lob-ingest "../tools/lib.org")
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#+end_src
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#+begin_src c :comments link :tangle (eval c_test) :noweb yes
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#include "qmckl.h"
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#include "assert.h"
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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int main() {
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qmckl_context context;
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context = qmckl_context_create();
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#+end_src
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* Matrix operations
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** ~qmckl_dgemm~
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Matrix multiply: $C_{ij} = \beta C_{ij} + \alpha \sum_{k} A_{ik} \cdot B_{kj}$ using Fortran ~matmul~ function.
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TODO: Add description about the external library dependence.
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#+NAME: qmckl_dgemm_args
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| qmckl_context | context | in | Global state |
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| bool | TransA | in | Number of rows of the input matrix |
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| bool | TransB | in | Number of rows of the input matrix |
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| int64_t | m | in | Number of rows of the input matrix |
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| int64_t | n | in | Number of columns of the input matrix |
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| int64_t | k | in | Number of columns of the input matrix |
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| double | alpha | in | Number of columns of the input matrix |
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| double | A[][lda] | in | Array containing the $m \times n$ matrix $A$ |
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| int64_t | lda | in | Leading dimension of array ~A~ |
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| double | B[][ldb] | in | Array containing the $n \times m$ matrix $B$ |
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| int64_t | ldb | in | Leading dimension of array ~B~ |
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| double | beta | in | Array containing the $n \times m$ matrix $B$ |
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| double | C[][ldc] | out | Array containing the $n \times m$ matrix $B$ |
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| int64_t | ldc | in | Leading dimension of array ~B~ |
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*** Requirements
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- ~context~ is not ~QMCKL_NULL_CONTEXT~
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- ~m > 0~
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- ~n > 0~
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- ~k > 0~
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- ~lda >= m~
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- ~ldb >= n~
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- ~ldc >= n~
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- ~A~ is allocated with at least $m \times k \times 8$ bytes
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- ~B~ is allocated with at least $k \times n \times 8$ bytes
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- ~C~ is allocated with at least $m \times n \times 8$ bytes
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*** C header
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#+CALL: generate_c_header(table=qmckl_dgemm_args,rettyp="qmckl_exit_code",fname="qmckl_dgemm")
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#+RESULTS:
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#+BEGIN_src c :tangle (eval h_func) :comments org
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qmckl_exit_code qmckl_dgemm (
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const qmckl_context context,
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const bool TransA,
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const bool TransB,
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const int64_t m,
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const int64_t n,
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const int64_t k,
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const double alpha,
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const double* A,
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const int64_t lda,
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const double* B,
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const int64_t ldb,
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const double beta,
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double* const C,
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const int64_t ldc );
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#+END_src
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*** Source
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#+begin_src f90 :tangle (eval f)
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integer function qmckl_dgemm_f(context, TransA, TransB, m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC) &
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result(info)
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use qmckl
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implicit none
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integer(qmckl_context) , intent(in) :: context
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logical*8 , intent(in) :: TransA, TransB
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integer*8 , intent(in) :: m, n, k
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real*8 , intent(in) :: alpha, beta
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integer*8 , intent(in) :: lda
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real*8 , intent(in) :: A(lda,*)
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integer*8 , intent(in) :: ldb
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real*8 , intent(in) :: B(ldb,*)
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integer*8 , intent(in) :: ldc
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real*8 , intent(out) :: C(ldc,*)
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real*8, allocatable :: AT(:,:), BT(:,:), CT(:,:)
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integer*4 :: qmckl_dgemm_N_N_f
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integer*8 :: i,j,l, LDA_2, LDB_2
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info = QMCKL_SUCCESS
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if (TransA) then
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allocate(AT(m,k))
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do i = 1, k
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do j = 1, m
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AT(j,i) = A(i,j)
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end do
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end do
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LDA_2 = M
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else
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LDA_2 = LDA
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endif
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if (TransB) then
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allocate(BT(k,n))
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do i = 1, n
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do j = 1, k
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BT(j,i) = B(i,j)
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end do
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end do
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LDB_2 = K
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else
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LDB_2 = LDB
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endif
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if (context == QMCKL_NULL_CONTEXT) then
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info = QMCKL_INVALID_CONTEXT
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return
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endif
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if (m <= 0_8) then
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info = QMCKL_INVALID_ARG_4
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return
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endif
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if (n <= 0_8) then
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info = QMCKL_INVALID_ARG_5
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return
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endif
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if (k <= 0_8) then
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info = QMCKL_INVALID_ARG_6
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return
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endif
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if (LDA_2 /= m) then
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info = QMCKL_INVALID_ARG_9
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return
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endif
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if (LDB_2 /= k) then
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info = QMCKL_INVALID_ARG_10
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return
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endif
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if (LDC /= m) then
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info = QMCKL_INVALID_ARG_13
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return
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endif
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if (TransA) then
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info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, AT, LDA_2, B, LDB_2, beta, c, LDC)
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else if (TransB) then
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info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA_2, BT, LDB_2, beta, c, LDC)
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else if (TransA .and. TransB) then
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info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, AT, LDA_2, BT, LDB_2, beta, c, LDC)
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else
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info = qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA_2, B, LDB_2, beta, c, LDC)
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endif
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end function qmckl_dgemm_f
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integer function qmckl_dgemm_N_N_f(context, m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC) &
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result(info)
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use qmckl
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implicit none
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integer(qmckl_context) , intent(in) :: context
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integer*8 , intent(in) :: m, n, k
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real*8 , intent(in) :: alpha, beta
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integer*8 , intent(in) :: lda
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real*8 , intent(in) :: A(lda,k)
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integer*8 , intent(in) :: ldb
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real*8 , intent(in) :: B(ldb,n)
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integer*8 , intent(in) :: ldc
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real*8 , intent(out) :: C(ldc,n)
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integer*8 :: i,j,l, LDA_2, LDB_2
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info = QMCKL_SUCCESS
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if (context == QMCKL_NULL_CONTEXT) then
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info = QMCKL_INVALID_CONTEXT
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return
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endif
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if (m <= 0_8) then
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info = QMCKL_INVALID_ARG_4
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return
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endif
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if (n <= 0_8) then
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info = QMCKL_INVALID_ARG_5
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return
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endif
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if (k <= 0_8) then
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info = QMCKL_INVALID_ARG_6
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return
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endif
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if (LDA /= m) then
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info = QMCKL_INVALID_ARG_9
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return
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endif
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if (LDB /= k) then
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info = QMCKL_INVALID_ARG_10
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return
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endif
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if (LDC /= m) then
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info = QMCKL_INVALID_ARG_13
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return
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endif
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if (alpha == 1.0d0 .and. beta == 0.0d0) then
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C = matmul(A,B)
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else
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C = beta*C + alpha*matmul(A,B)
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endif
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end function qmckl_dgemm_N_N_f
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#+end_src
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*** C interface :noexport:
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#+CALL: generate_c_interface(table=qmckl_dgemm_args,rettyp="qmckl_exit_code",fname="qmckl_dgemm")
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#+RESULTS:
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#+BEGIN_src f90 :tangle (eval f) :comments org :exports none
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integer(c_int32_t) function qmckl_dgemm &
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(context, TransA, TransB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc) &
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bind(C) result(info)
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use, intrinsic :: iso_c_binding
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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logical*8 , intent(in) , value :: TransA
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logical*8 , intent(in) , value :: TransB
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integer (c_int64_t) , intent(in) , value :: m
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integer (c_int64_t) , intent(in) , value :: n
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integer (c_int64_t) , intent(in) , value :: k
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real (c_double ) , intent(in) , value :: alpha
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integer (c_int64_t) , intent(in) , value :: lda
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real (c_double ) , intent(in) :: A(lda,*)
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integer (c_int64_t) , intent(in) , value :: ldb
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real (c_double ) , intent(in) :: B(ldb,*)
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real (c_double ) , intent(in) , value :: beta
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integer (c_int64_t) , intent(in) , value :: ldc
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real (c_double ) , intent(out) :: C(ldc,*)
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integer(c_int32_t), external :: qmckl_dgemm_f
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info = qmckl_dgemm_f &
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(context, TransA, TransB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc)
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end function qmckl_dgemm
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#+END_src
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#+CALL: generate_f_interface(table=qmckl_dgemm_args,rettyp="qmckl_exit_code",fname="qmckl_dgemm")
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#+RESULTS:
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#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
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interface
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integer(c_int32_t) function qmckl_dgemm &
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(context, TransA, TransB, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc) &
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bind(C)
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use, intrinsic :: iso_c_binding
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import
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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logical*8 , intent(in) , value :: TransA
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logical*8 , intent(in) , value :: TransB
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integer (c_int64_t) , intent(in) , value :: m
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integer (c_int64_t) , intent(in) , value :: n
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integer (c_int64_t) , intent(in) , value :: k
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real (c_double ) , intent(in) , value :: alpha
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integer (c_int64_t) , intent(in) , value :: lda
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real (c_double ) , intent(in) :: A(lda,*)
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integer (c_int64_t) , intent(in) , value :: ldb
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real (c_double ) , intent(in) :: B(ldb,*)
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real (c_double ) , intent(in) , value :: beta
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integer (c_int64_t) , intent(in) , value :: ldc
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real (c_double ) , intent(out) :: C(ldc,*)
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end function qmckl_dgemm
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end interface
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#+end_src
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*** Test :noexport:
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#+begin_src f90 :tangle (eval f_test)
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integer(qmckl_exit_code) function test_qmckl_dgemm(context) bind(C)
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use qmckl
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implicit none
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integer(qmckl_context), intent(in), value :: context
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double precision, allocatable :: A(:,:), B(:,:), C(:,:), D(:,:)
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integer*8 :: m, n, k, LDA, LDB, LDC
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integer*8 :: i,j,l
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logical*8 :: TransA, TransB
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double precision :: x, alpha, beta
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TransA = .False.
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TransB = .False.
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m = 1_8
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k = 4_8
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n = 6_8
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LDA = m
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LDB = k
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LDC = m
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allocate( A(LDA,k), B(LDB,n) , C(LDC,n), D(LDC,n))
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A = 0.d0
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B = 0.d0
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C = 0.d0
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D = 0.d0
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alpha = 1.0d0
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beta = 0.0d0
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do j=1,k
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do i=1,m
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A(i,j) = -10.d0 + dble(i+j)
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end do
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end do
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do j=1,n
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do i=1,k
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B(i,j) = -10.d0 + dble(i+j)
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end do
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end do
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test_qmckl_dgemm = qmckl_dgemm(context, TransA, TransB, m, n, k, alpha, A, LDA, B, LDB, beta, C, LDC)
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if (test_qmckl_dgemm /= QMCKL_SUCCESS) return
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test_qmckl_dgemm = QMCKL_FAILURE
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x = 0.d0
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do j=1,n
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do i=1,m
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do l=1,k
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D(i,j) = D(i,j) + A(i,l)*B(l,j)
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end do
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x = x + (D(i,j) - C(i,j))**2
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end do
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end do
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if (dabs(x) <= 1.d-15) then
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test_qmckl_dgemm = QMCKL_SUCCESS
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endif
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deallocate(A,B,C,D)
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end function test_qmckl_dgemm
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#+end_src
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#+begin_src c :comments link :tangle (eval c_test)
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qmckl_exit_code test_qmckl_dgemm(qmckl_context context);
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assert(QMCKL_SUCCESS == test_qmckl_dgemm(context));
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#+end_src
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** ~qmckl_adjoint~
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Matrix adjoint. Given a matrix M, returns a matrix M⁻¹ such that:
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\[
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M · M^{-1} = I
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\]
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This is a native Fortran implementation hand written (by: A. Scemama)
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only for small matrices (<=5x5).
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TODO: Add description about the external library dependence.
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#+NAME: qmckl_adjoint_args
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| qmckl_context | context | in | Global state |
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| int64_t | m | in | Number of rows of the input matrix |
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| int64_t | n | in | Number of columns of the input matrix |
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| int64_t | lda | in | Leading dimension of array ~A~ |
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| double | A[][lda] | inout | Array containing the $m \times n$ matrix $A$ |
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| double | det_l | inout | determinant of A |
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*** Requirements
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- ~context~ is not ~QMCKL_NULL_CONTEXT~
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- ~m > 0~
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- ~n > 0~
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- ~lda >= m~
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- ~A~ is allocated with at least $m \times n \times 8$ bytes
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*** C header
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#+CALL: generate_c_header(table=qmckl_adjoint_args,rettyp="qmckl_exit_code",fname="qmckl_adjoint")
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#+RESULTS:
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#+begin_src c :tangle (eval h_func) :comments org
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qmckl_exit_code qmckl_adjoint (
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const qmckl_context context,
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const int64_t m,
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const int64_t n,
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const int64_t lda,
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double* A,
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double det_l );
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#+end_src
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*** Source
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#+begin_src f90 :tangle (eval f)
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integer function qmckl_adjoint_f(context, ma, na, LDA, A, det_l) &
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result(info)
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use qmckl
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implicit none
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integer(qmckl_context) , intent(in) :: context
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double precision, intent(inout) :: A (LDA,na)
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integer*8, intent(in) :: LDA
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integer*8, intent(in) :: ma
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integer*8, intent(in) :: na
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double precision, intent(inout) :: det_l
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integer :: i,j
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info = QMCKL_SUCCESS
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select case (na)
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case default
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!DIR$ forceinline
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print *," TODO: Implement general adjoint"
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stop 0
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case (5)
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!DIR$ forceinline
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call adjoint5(a,LDA,na,det_l)
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case (4)
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!DIR$ forceinline
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call adjoint4(a,LDA,na,det_l)
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case (3)
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!DIR$ forceinline
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call adjoint3(a,LDA,na,det_l)
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case (2)
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!DIR$ forceinline
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call adjoint2(a,LDA,na,det_l)
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case (1)
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!DIR$ forceinline
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call adjoint1(a,LDA,na,det_l)
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case (0)
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det_l=1.d0
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end select
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end function qmckl_adjoint_f
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subroutine adjoint1(a,LDA,na,det_l)
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implicit none
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double precision, intent(inout) :: a (LDA,na)
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integer*8, intent(in) :: LDA
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integer*8, intent(in) :: na
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double precision, intent(inout) :: det_l
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call cofactor1(a,LDA,na,det_l)
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end
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subroutine adjoint2(a,LDA,na,det_l)
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implicit none
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double precision, intent(inout) :: a (LDA,na)
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integer*8, intent(in) :: LDA
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integer*8, intent(in) :: na
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double precision, intent(inout) :: det_l
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double precision :: b(2,2)
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call cofactor2(a,LDA,na,det_l)
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! Calculate the transpose
|
|
b(1,1) = a(1,1)
|
|
b(1,2) = a(2,1)
|
|
b(2,1) = a(1,2)
|
|
b(2,2) = a(2,2)
|
|
a(1,1) = b(1,1)
|
|
a(1,2) = b(1,2)
|
|
a(2,1) = b(2,1)
|
|
a(2,2) = b(2,2)
|
|
end
|
|
|
|
subroutine adjoint3(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(3,3)
|
|
|
|
call cofactor3(a,LDA,na,det_l)
|
|
|
|
! Calculate the transpose
|
|
b(1,1) = a(1,1)
|
|
b(1,2) = a(2,1)
|
|
b(1,3) = a(3,1)
|
|
b(2,1) = a(1,2)
|
|
b(2,2) = a(2,2)
|
|
b(2,3) = a(3,2)
|
|
b(3,1) = a(1,3)
|
|
b(3,2) = a(2,3)
|
|
b(3,3) = a(3,3)
|
|
! copy
|
|
a(1,1) = b(1,1)
|
|
a(2,1) = b(2,1)
|
|
a(3,1) = b(3,1)
|
|
a(1,2) = b(1,2)
|
|
a(2,2) = b(2,2)
|
|
a(3,2) = b(3,2)
|
|
a(1,3) = b(1,3)
|
|
a(2,3) = b(2,3)
|
|
a(3,3) = b(3,3)
|
|
end
|
|
|
|
subroutine adjoint4(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(4,4)
|
|
|
|
call cofactor4(a,LDA,na,det_l)
|
|
|
|
! Calculate the transpose
|
|
b(1,1) = a(1,1)
|
|
b(1,2) = a(2,1)
|
|
b(1,3) = a(3,1)
|
|
b(1,4) = a(4,1)
|
|
b(2,1) = a(1,2)
|
|
b(2,2) = a(2,2)
|
|
b(2,3) = a(3,2)
|
|
b(2,4) = a(4,2)
|
|
b(3,1) = a(1,3)
|
|
b(3,2) = a(2,3)
|
|
b(3,3) = a(3,3)
|
|
b(3,4) = a(4,3)
|
|
b(4,1) = a(1,4)
|
|
b(4,2) = a(2,4)
|
|
b(4,3) = a(3,4)
|
|
b(4,4) = a(4,4)
|
|
! copy
|
|
a(1,1) = b(1,1)
|
|
a(2,1) = b(2,1)
|
|
a(3,1) = b(3,1)
|
|
a(4,1) = b(4,1)
|
|
a(1,2) = b(1,2)
|
|
a(2,2) = b(2,2)
|
|
a(3,2) = b(3,2)
|
|
a(4,2) = b(4,2)
|
|
a(1,3) = b(1,3)
|
|
a(2,3) = b(2,3)
|
|
a(3,3) = b(3,3)
|
|
a(4,3) = b(4,3)
|
|
a(1,4) = b(1,4)
|
|
a(2,4) = b(2,4)
|
|
a(3,4) = b(3,4)
|
|
a(4,4) = b(4,4)
|
|
end
|
|
|
|
subroutine adjoint5(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(5,5)
|
|
|
|
call cofactor5(a,LDA,na,det_l)
|
|
|
|
! Calculate the transpose
|
|
b(1,1) = a(1,1)
|
|
b(1,2) = a(2,1)
|
|
b(1,3) = a(3,1)
|
|
b(1,4) = a(4,1)
|
|
b(1,5) = a(5,1)
|
|
b(2,1) = a(1,2)
|
|
b(2,2) = a(2,2)
|
|
b(2,3) = a(3,2)
|
|
b(2,4) = a(4,2)
|
|
b(2,5) = a(5,2)
|
|
b(3,1) = a(1,3)
|
|
b(3,2) = a(2,3)
|
|
b(3,3) = a(3,3)
|
|
b(3,4) = a(4,3)
|
|
b(3,5) = a(5,3)
|
|
b(4,1) = a(1,4)
|
|
b(4,2) = a(2,4)
|
|
b(4,3) = a(3,4)
|
|
b(4,4) = a(4,4)
|
|
b(4,5) = a(5,4)
|
|
b(5,1) = a(1,5)
|
|
b(5,2) = a(2,5)
|
|
b(5,3) = a(3,5)
|
|
b(5,4) = a(4,5)
|
|
b(5,5) = a(5,5)
|
|
! copy
|
|
a(1,1) = b(1,1)
|
|
a(2,1) = b(2,1)
|
|
a(3,1) = b(3,1)
|
|
a(4,1) = b(4,1)
|
|
a(5,1) = b(5,1)
|
|
a(1,2) = b(1,2)
|
|
a(2,2) = b(2,2)
|
|
a(3,2) = b(3,2)
|
|
a(4,2) = b(4,2)
|
|
a(5,2) = b(5,2)
|
|
a(1,3) = b(1,3)
|
|
a(2,3) = b(2,3)
|
|
a(3,3) = b(3,3)
|
|
a(4,3) = b(4,3)
|
|
a(5,3) = b(5,3)
|
|
a(1,4) = b(1,4)
|
|
a(2,4) = b(2,4)
|
|
a(3,4) = b(3,4)
|
|
a(4,4) = b(4,4)
|
|
a(5,4) = b(5,4)
|
|
a(1,5) = b(1,5)
|
|
a(2,5) = b(2,5)
|
|
a(3,5) = b(3,5)
|
|
a(4,5) = b(4,5)
|
|
a(5,5) = b(5,5)
|
|
end
|
|
|
|
subroutine cofactor1(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
|
|
det_l = a(1,1)
|
|
a(1,1) = 1.d0
|
|
end
|
|
|
|
subroutine cofactor2(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision :: a (LDA,na)
|
|
integer*8 :: LDA
|
|
integer*8 :: na
|
|
double precision :: det_l
|
|
double precision :: b(2,2)
|
|
|
|
b(1,1) = a(1,1)
|
|
b(2,1) = a(2,1)
|
|
b(1,2) = a(1,2)
|
|
b(2,2) = a(2,2)
|
|
det_l = a(1,1)*a(2,2) - a(1,2)*a(2,1)
|
|
a(1,1) = b(2,2)
|
|
a(2,1) = -b(2,1)
|
|
a(1,2) = -b(1,2)
|
|
a(2,2) = b(1,1)
|
|
end
|
|
|
|
subroutine cofactor3(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(4,3)
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
|
|
integer :: i
|
|
det_l = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) &
|
|
-a(1,2)*(a(2,1)*a(3,3)-a(2,3)*a(3,1)) &
|
|
+a(1,3)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
|
|
do i=1,4
|
|
b(i,1) = a(i,1)
|
|
b(i,2) = a(i,2)
|
|
b(i,3) = a(i,3)
|
|
enddo
|
|
a(1,1) = b(2,2)*b(3,3) - b(2,3)*b(3,2)
|
|
a(2,1) = b(2,3)*b(3,1) - b(2,1)*b(3,3)
|
|
a(3,1) = b(2,1)*b(3,2) - b(2,2)*b(3,1)
|
|
|
|
a(1,2) = b(1,3)*b(3,2) - b(1,2)*b(3,3)
|
|
a(2,2) = b(1,1)*b(3,3) - b(1,3)*b(3,1)
|
|
a(3,2) = b(1,2)*b(3,1) - b(1,1)*b(3,2)
|
|
|
|
a(1,3) = b(1,2)*b(2,3) - b(1,3)*b(2,2)
|
|
a(2,3) = b(1,3)*b(2,1) - b(1,1)*b(2,3)
|
|
a(3,3) = b(1,1)*b(2,2) - b(1,2)*b(2,1)
|
|
|
|
end
|
|
|
|
subroutine cofactor4(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(4,4)
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
|
|
integer :: i,j
|
|
det_l = a(1,1)*(a(2,2)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
|
|
-a(2,3)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
|
|
+a(2,4)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))) &
|
|
-a(1,2)*(a(2,1)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
|
|
-a(2,3)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
|
|
+a(2,4)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))) &
|
|
+a(1,3)*(a(2,1)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
|
|
-a(2,2)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
|
|
+a(2,4)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))) &
|
|
-a(1,4)*(a(2,1)*(a(3,2)*a(4,3)-a(3,3)*a(4,2)) &
|
|
-a(2,2)*(a(3,1)*a(4,3)-a(3,3)*a(4,1)) &
|
|
+a(2,3)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))
|
|
do i=1,4
|
|
b(1,i) = a(1,i)
|
|
b(2,i) = a(2,i)
|
|
b(3,i) = a(3,i)
|
|
b(4,i) = a(4,i)
|
|
enddo
|
|
|
|
a(1,1) = b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))
|
|
a(2,1) = -b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))+b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))-b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))
|
|
a(3,1) = b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
|
|
a(4,1) = -b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))+b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))-b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
|
|
|
|
a(1,2) = -b(1,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))+b(1,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(1,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))
|
|
a(2,2) = b(1,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(1,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(1,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))
|
|
a(3,2) = -b(1,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(1,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))-b(1,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
|
|
a(4,2) = b(1,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(1,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(1,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))
|
|
|
|
a(1,3) = b(1,2)*(b(2,3)*b(4,4)-b(2,4)*b(4,3))-b(1,3)*(b(2,2)*b(4,4)-b(2,4)*b(4,2))+b(1,4)*(b(2,2)*b(4,3)-b(2,3)*b(4,2))
|
|
a(2,3) = -b(1,1)*(b(2,3)*b(4,4)-b(2,4)*b(4,3))+b(1,3)*(b(2,1)*b(4,4)-b(2,4)*b(4,1))-b(1,4)*(b(2,1)*b(4,3)-b(2,3)*b(4,1))
|
|
a(3,3) = b(1,1)*(b(2,2)*b(4,4)-b(2,4)*b(4,2))-b(1,2)*(b(2,1)*b(4,4)-b(2,4)*b(4,1))+b(1,4)*(b(2,1)*b(4,2)-b(2,2)*b(4,1))
|
|
a(4,3) = -b(1,1)*(b(2,2)*b(4,3)-b(2,3)*b(4,2))+b(1,2)*(b(2,1)*b(4,3)-b(2,3)*b(4,1))-b(1,3)*(b(2,1)*b(4,2)-b(2,2)*b(4,1))
|
|
|
|
a(1,4) = -b(1,2)*(b(2,3)*b(3,4)-b(2,4)*b(3,3))+b(1,3)*(b(2,2)*b(3,4)-b(2,4)*b(3,2))-b(1,4)*(b(2,2)*b(3,3)-b(2,3)*b(3,2))
|
|
a(2,4) = b(1,1)*(b(2,3)*b(3,4)-b(2,4)*b(3,3))-b(1,3)*(b(2,1)*b(3,4)-b(2,4)*b(3,1))+b(1,4)*(b(2,1)*b(3,3)-b(2,3)*b(3,1))
|
|
a(3,4) = -b(1,1)*(b(2,2)*b(3,4)-b(2,4)*b(3,2))+b(1,2)*(b(2,1)*b(3,4)-b(2,4)*b(3,1))-b(1,4)*(b(2,1)*b(3,2)-b(2,2)*b(3,1))
|
|
a(4,4) = b(1,1)*(b(2,2)*b(3,3)-b(2,3)*b(3,2))-b(1,2)*(b(2,1)*b(3,3)-b(2,3)*b(3,1))+b(1,3)*(b(2,1)*b(3,2)-b(2,2)*b(3,1))
|
|
|
|
end
|
|
|
|
subroutine cofactor5(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer*8, intent(in) :: LDA
|
|
integer*8, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(5,5)
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
|
|
integer :: i,j
|
|
det_l = a(1,1)*(a(2,2)*(a(3,3)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*( &
|
|
a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(3,5)*(a(4,3)*a(5,4)-a(4,4)*a(5,3)))- &
|
|
a(2,3)*(a(3,2)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*(a(4,2)*a(5,5)- &
|
|
a(4,5)*a(5,2))+a(3,5)*(a(4,2)*a(5,4)-a(4,4)*a(5,2)))+a(2,4)*(a(3,2)*( &
|
|
a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+ &
|
|
a(3,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,5)*(a(3,2)*(a(4,3)*a(5,4)- &
|
|
a(4,4)*a(5,3))-a(3,3)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))+a(3,4)*(a(4,2)* &
|
|
a(5,3)-a(4,3)*a(5,2))))-a(1,2)*(a(2,1)*(a(3,3)*(a(4,4)*a(5,5)-a(4,5)* &
|
|
a(5,4))-a(3,4)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))+a(3,5)*(a(4,3)*a(5,4)- &
|
|
a(4,4)*a(5,3)))-a(2,3)*(a(3,1)*(a(4,4)*a(5,5)-a(4,5)*a(5,4))-a(3,4)*( &
|
|
a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,4)-a(4,4)*a(5,1)))+ &
|
|
a(2,4)*(a(3,1)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,1)*a(5,5)- &
|
|
a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))-a(2,5)*(a(3,1)*( &
|
|
a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+ &
|
|
a(3,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))))+a(1,3)*(a(2,1)*(a(3,2)*(a(4,4)* &
|
|
a(5,5)-a(4,5)*a(5,4))-a(3,4)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))+a(3,5)*( &
|
|
a(4,2)*a(5,4)-a(4,4)*a(5,2)))-a(2,2)*(a(3,1)*(a(4,4)*a(5,5)-a(4,5)* &
|
|
a(5,4))-a(3,4)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,4)- &
|
|
a(4,4)*a(5,1)))+a(2,4)*(a(3,1)*(a(4,2)*a(5,5)-a(4,5)*a(5,2))-a(3,2)*( &
|
|
a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,2)-a(4,2)*a(5,1)))- &
|
|
a(2,5)*(a(3,1)*(a(4,2)*a(5,4)-a(4,4)*a(5,2))-a(3,2)*(a(4,1)*a(5,4)- &
|
|
a(4,4)*a(5,1))+a(3,4)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))-a(1,4)*(a(2,1)*( &
|
|
a(3,2)*(a(4,3)*a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,2)*a(5,5)-a(4,5)* &
|
|
a(5,2))+a(3,5)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,2)*(a(3,1)*(a(4,3)* &
|
|
a(5,5)-a(4,5)*a(5,3))-a(3,3)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*( &
|
|
a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(2,3)*(a(3,1)*(a(4,2)*a(5,5)-a(4,5)* &
|
|
a(5,2))-a(3,2)*(a(4,1)*a(5,5)-a(4,5)*a(5,1))+a(3,5)*(a(4,1)*a(5,2)- &
|
|
a(4,2)*a(5,1)))-a(2,5)*(a(3,1)*(a(4,2)*a(5,3)-a(4,3)*a(5,2))-a(3,2)*( &
|
|
a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(3,3)*(a(4,1)*a(5,2)-a(4,2)*a(5,1))))+ &
|
|
a(1,5)*(a(2,1)*(a(3,2)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,2)* &
|
|
a(5,4)-a(4,4)*a(5,2))+a(3,4)*(a(4,2)*a(5,3)-a(4,3)*a(5,2)))-a(2,2)*( &
|
|
a(3,1)*(a(4,3)*a(5,4)-a(4,4)*a(5,3))-a(3,3)*(a(4,1)*a(5,4)-a(4,4)* &
|
|
a(5,1))+a(3,4)*(a(4,1)*a(5,3)-a(4,3)*a(5,1)))+a(2,3)*(a(3,1)*(a(4,2)* &
|
|
a(5,4)-a(4,4)*a(5,2))-a(3,2)*(a(4,1)*a(5,4)-a(4,4)*a(5,1))+a(3,4)*( &
|
|
a(4,1)*a(5,2)-a(4,2)*a(5,1)))-a(2,4)*(a(3,1)*(a(4,2)*a(5,3)-a(4,3)* &
|
|
a(5,2))-a(3,2)*(a(4,1)*a(5,3)-a(4,3)*a(5,1))+a(3,3)*(a(4,1)*a(5,2)- &
|
|
a(4,2)*a(5,1))))
|
|
|
|
do i=1,5
|
|
b(1,i) = a(1,i)
|
|
b(2,i) = a(2,i)
|
|
b(3,i) = a(3,i)
|
|
b(4,i) = a(4,i)
|
|
b(5,i) = a(5,i)
|
|
enddo
|
|
|
|
a(1,1) = &
|
|
(b(2,2)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))-b(2,3)* &
|
|
(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))+b(2,4)* &
|
|
(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(2,5)* &
|
|
(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))))
|
|
a(2,1) = &
|
|
(-b(2,1)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))+b(2,3)* &
|
|
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))-b(2,4)* &
|
|
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(2,5)* &
|
|
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))))
|
|
a(3,1) = &
|
|
(b(2,1)*(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))-b(2,2)* &
|
|
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))+b(2,4)* &
|
|
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(2,5)* &
|
|
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
a(4,1) = &
|
|
(-b(2,1)*(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(2,2)* &
|
|
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(2,3)* &
|
|
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(2,5)* &
|
|
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
a(5,1) = &
|
|
(b(2,1)*(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(2,2)* &
|
|
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(2,3)* &
|
|
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(2,4)* &
|
|
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
|
|
a(1,2) = &
|
|
(-b(1,2)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))+b(1,3)* &
|
|
(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))-b(1,4)* &
|
|
(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(1,5)* &
|
|
(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))))
|
|
a(2,2) = &
|
|
(b(1,1)*(b(3,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(3,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))-b(1,3)* &
|
|
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))+b(1,4)* &
|
|
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(1,5)* &
|
|
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))))
|
|
a(3,2) = &
|
|
(-b(1,1)*(b(3,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))+b(1,2)* &
|
|
(b(3,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(3,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))-b(1,4)* &
|
|
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(1,5)* &
|
|
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
a(4,2) = &
|
|
(b(1,1)*(b(3,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(3,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(1,2)* &
|
|
(b(3,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(3,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(1,3)* &
|
|
(b(3,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(3,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(3,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(1,5)* &
|
|
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
a(5,2) = &
|
|
(-b(1,1)*(b(3,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(3,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(1,2)* &
|
|
(b(3,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(3,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(1,3)* &
|
|
(b(3,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(3,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(3,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(1,4)* &
|
|
(b(3,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(3,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(3,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
|
|
a(1,3) = &
|
|
(b(1,2)*(b(2,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(2,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))-b(1,3)* &
|
|
(b(2,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))+b(1,4)* &
|
|
(b(2,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(1,5)* &
|
|
(b(2,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(2,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))))
|
|
a(2,3) = &
|
|
(-b(1,1)*(b(2,3)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))+b(2,5)*(b(4,3)*b(5,4)-b(4,4)*b(5,3)))+b(1,3)* &
|
|
(b(2,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))-b(1,4)* &
|
|
(b(2,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(1,5)* &
|
|
(b(2,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))))
|
|
a(3,3) = &
|
|
(b(1,1)*(b(2,2)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,4)-b(4,4)*b(5,2)))-b(1,2)* &
|
|
(b(2,1)*(b(4,4)*b(5,5)-b(4,5)*b(5,4))-b(2,4)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,4)-b(4,4)*b(5,1)))+b(1,4)* &
|
|
(b(2,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(2,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(1,5)* &
|
|
(b(2,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(2,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
a(4,3) = &
|
|
(-b(1,1)*(b(2,2)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))+b(2,5)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))+b(1,2)* &
|
|
(b(2,1)*(b(4,3)*b(5,5)-b(4,5)*b(5,3))-b(2,3)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))-b(1,3)* &
|
|
(b(2,1)*(b(4,2)*b(5,5)-b(4,5)*b(5,2))-b(2,2)*(b(4,1)*b(5,5)-b(4,5)*b(5,1))+b(2,5)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))+b(1,5)* &
|
|
(b(2,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(2,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(2,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
a(5,3) = &
|
|
(b(1,1)*(b(2,2)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))+b(2,4)*(b(4,2)*b(5,3)-b(4,3)*b(5,2)))-b(1,2)* &
|
|
(b(2,1)*(b(4,3)*b(5,4)-b(4,4)*b(5,3))-b(2,3)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,3)-b(4,3)*b(5,1)))+b(1,3)* &
|
|
(b(2,1)*(b(4,2)*b(5,4)-b(4,4)*b(5,2))-b(2,2)*(b(4,1)*b(5,4)-b(4,4)*b(5,1))+b(2,4)*(b(4,1)*b(5,2)-b(4,2)*b(5,1)))-b(1,4)* &
|
|
(b(2,1)*(b(4,2)*b(5,3)-b(4,3)*b(5,2))-b(2,2)*(b(4,1)*b(5,3)-b(4,3)*b(5,1))+b(2,3)*(b(4,1)*b(5,2)-b(4,2)*b(5,1))))
|
|
|
|
a(1,4) = &
|
|
(-b(1,2)*(b(2,3)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))+b(2,5)*(b(3,3)*b(5,4)-b(3,4)*b(5,3)))+b(1,3)* &
|
|
(b(2,2)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,4)-b(3,4)*b(5,2)))-b(1,4)* &
|
|
(b(2,2)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,3)-b(3,3)*b(5,2)))+b(1,5)* &
|
|
(b(2,2)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))+b(2,4)*(b(3,2)*b(5,3)-b(3,3)*b(5,2))))
|
|
a(2,4) = &
|
|
(b(1,1)*(b(2,3)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))+b(2,5)*(b(3,3)*b(5,4)-b(3,4)*b(5,3)))-b(1,3)* &
|
|
(b(2,1)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,4)-b(3,4)*b(5,1)))+b(1,4)* &
|
|
(b(2,1)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,3)-b(3,3)*b(5,1)))-b(1,5)* &
|
|
(b(2,1)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,3)-b(3,3)*b(5,1))))
|
|
a(3,4) = &
|
|
(-b(1,1)*(b(2,2)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,4)-b(3,4)*b(5,2)))+b(1,2)* &
|
|
(b(2,1)*(b(3,4)*b(5,5)-b(3,5)*b(5,4))-b(2,4)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,4)-b(3,4)*b(5,1)))-b(1,4)* &
|
|
(b(2,1)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))-b(2,2)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,2)-b(3,2)*b(5,1)))+b(1,5)* &
|
|
(b(2,1)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))-b(2,2)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,2)-b(3,2)*b(5,1))))
|
|
a(4,4) = &
|
|
(b(1,1)*(b(2,2)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))+b(2,5)*(b(3,2)*b(5,3)-b(3,3)*b(5,2)))-b(1,2)* &
|
|
(b(2,1)*(b(3,3)*b(5,5)-b(3,5)*b(5,3))-b(2,3)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,3)-b(3,3)*b(5,1)))+b(1,3)* &
|
|
(b(2,1)*(b(3,2)*b(5,5)-b(3,5)*b(5,2))-b(2,2)*(b(3,1)*b(5,5)-b(3,5)*b(5,1))+b(2,5)*(b(3,1)*b(5,2)-b(3,2)*b(5,1)))-b(1,5)* &
|
|
(b(2,1)*(b(3,2)*b(5,3)-b(3,3)*b(5,2))-b(2,2)*(b(3,1)*b(5,3)-b(3,3)*b(5,1))+b(2,3)*(b(3,1)*b(5,2)-b(3,2)*b(5,1))))
|
|
a(5,4) = &
|
|
(-b(1,1)*(b(2,2)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))+b(2,4)*(b(3,2)*b(5,3)-b(3,3)*b(5,2)))+b(1,2)* &
|
|
(b(2,1)*(b(3,3)*b(5,4)-b(3,4)*b(5,3))-b(2,3)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,3)-b(3,3)*b(5,1)))-b(1,3)* &
|
|
(b(2,1)*(b(3,2)*b(5,4)-b(3,4)*b(5,2))-b(2,2)*(b(3,1)*b(5,4)-b(3,4)*b(5,1))+b(2,4)*(b(3,1)*b(5,2)-b(3,2)*b(5,1)))+b(1,4)* &
|
|
(b(2,1)*(b(3,2)*b(5,3)-b(3,3)*b(5,2))-b(2,2)*(b(3,1)*b(5,3)-b(3,3)*b(5,1))+b(2,3)*(b(3,1)*b(5,2)-b(3,2)*b(5,1))))
|
|
|
|
a(1,5) = &
|
|
(b(1,2)*(b(2,3)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))+b(2,5)*(b(3,3)*b(4,4)-b(3,4)*b(4,3)))-b(1,3)* &
|
|
(b(2,2)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,4)-b(3,4)*b(4,2)))+b(1,4)* &
|
|
(b(2,2)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,3)-b(3,3)*b(4,2)))-b(1,5)* &
|
|
(b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))))
|
|
a(2,5) = &
|
|
(-b(1,1)*(b(2,3)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))+b(2,5)*(b(3,3)*b(4,4)-b(3,4)*b(4,3)))+b(1,3)* &
|
|
(b(2,1)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,4)-b(3,4)*b(4,1)))-b(1,4)* &
|
|
(b(2,1)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,3)-b(3,3)*b(4,1)))+b(1,5)* &
|
|
(b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))))
|
|
a(3,5) = &
|
|
(b(1,1)*(b(2,2)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,4)-b(3,4)*b(4,2)))-b(1,2)* &
|
|
(b(2,1)*(b(3,4)*b(4,5)-b(3,5)*b(4,4))-b(2,4)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,4)-b(3,4)*b(4,1)))+b(1,4)* &
|
|
(b(2,1)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))-b(2,2)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,2)-b(3,2)*b(4,1)))-b(1,5)* &
|
|
(b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))))
|
|
a(4,5) = &
|
|
(-b(1,1)*(b(2,2)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))+b(2,5)*(b(3,2)*b(4,3)-b(3,3)*b(4,2)))+b(1,2)* &
|
|
(b(2,1)*(b(3,3)*b(4,5)-b(3,5)*b(4,3))-b(2,3)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,3)-b(3,3)*b(4,1)))-b(1,3)* &
|
|
(b(2,1)*(b(3,2)*b(4,5)-b(3,5)*b(4,2))-b(2,2)*(b(3,1)*b(4,5)-b(3,5)*b(4,1))+b(2,5)*(b(3,1)*b(4,2)-b(3,2)*b(4,1)))+b(1,5)* &
|
|
(b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))))
|
|
a(5,5) = &
|
|
(b(1,1)*(b(2,2)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))+b(2,4)*(b(3,2)*b(4,3)-b(3,3)*b(4,2)))-b(1,2)* &
|
|
(b(2,1)*(b(3,3)*b(4,4)-b(3,4)*b(4,3))-b(2,3)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,3)-b(3,3)*b(4,1)))+b(1,3)* &
|
|
(b(2,1)*(b(3,2)*b(4,4)-b(3,4)*b(4,2))-b(2,2)*(b(3,1)*b(4,4)-b(3,4)*b(4,1))+b(2,4)*(b(3,1)*b(4,2)-b(3,2)*b(4,1)))-b(1,4)* &
|
|
(b(2,1)*(b(3,2)*b(4,3)-b(3,3)*b(4,2))-b(2,2)*(b(3,1)*b(4,3)-b(3,3)*b(4,1))+b(2,3)*(b(3,1)*b(4,2)-b(3,2)*b(4,1))))
|
|
|
|
end
|
|
#+end_src
|
|
|
|
*** C interface :noexport:
|
|
|
|
#+CALL: generate_c_interface(table=qmckl_adjoint_args,rettyp="qmckl_exit_code",fname="qmckl_adjoint")
|
|
|
|
#+RESULTS:
|
|
#+begin_src f90 :tangle (eval f) :comments org :exports none
|
|
integer(c_int32_t) function qmckl_adjoint &
|
|
(context, m, n, lda, A, det_l) &
|
|
bind(C) result(info)
|
|
|
|
use, intrinsic :: iso_c_binding
|
|
implicit none
|
|
|
|
integer (c_int64_t) , intent(in) , value :: context
|
|
integer (c_int64_t) , intent(in) , value :: m
|
|
integer (c_int64_t) , intent(in) , value :: n
|
|
integer (c_int64_t) , intent(in) , value :: lda
|
|
real (c_double ) , intent(inout) :: A(lda,*)
|
|
real (c_double ) , intent(inout) :: det_l
|
|
|
|
integer(c_int32_t), external :: qmckl_adjoint_f
|
|
info = qmckl_adjoint_f &
|
|
(context, m, n, lda, A, det_l)
|
|
|
|
end function qmckl_adjoint
|
|
#+end_src
|
|
|
|
#+CALL: generate_f_interface(table=qmckl_adjoint_args,rettyp="qmckl_exit_code",fname="qmckl_adjoint")
|
|
|
|
#+RESULTS:
|
|
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
|
|
interface
|
|
integer(c_int32_t) function qmckl_adjoint &
|
|
(context, m, n, lda, A, det_l) &
|
|
bind(C)
|
|
use, intrinsic :: iso_c_binding
|
|
import
|
|
implicit none
|
|
|
|
integer (c_int64_t) , intent(in) , value :: context
|
|
integer (c_int64_t) , intent(in) , value :: m
|
|
integer (c_int64_t) , intent(in) , value :: n
|
|
integer (c_int64_t) , intent(in) , value :: lda
|
|
real (c_double ) , intent(inout) :: A(lda,*)
|
|
real (c_double ) , intent(inout) :: det_l
|
|
|
|
end function qmckl_adjoint
|
|
end interface
|
|
#+end_src
|
|
|
|
*** Test :noexport:
|
|
#+begin_src f90 :tangle (eval f_test)
|
|
integer(qmckl_exit_code) function test_qmckl_adjoint(context) bind(C)
|
|
use qmckl
|
|
implicit none
|
|
integer(qmckl_context), intent(in), value :: context
|
|
|
|
double precision, allocatable :: A(:,:), C(:,:)
|
|
integer*8 :: m, n, k, LDA, LDB, LDC
|
|
integer*8 :: i,j,l
|
|
double precision :: x, det_l, det_l_ref
|
|
|
|
m = 4_8
|
|
k = 4_8
|
|
LDA = m
|
|
LDB = m
|
|
LDC = m
|
|
|
|
allocate( A(LDA,k), C(LDC,k))
|
|
|
|
A = 0.10d0
|
|
C = 0.d0
|
|
A(1,1) = 1.0d0;
|
|
A(2,2) = 2.0d0;
|
|
A(3,3) = 3.0d0;
|
|
A(4,4) = 4.0d0;
|
|
|
|
! Exact inverse (Mathematica)
|
|
C(1,1) = 1.0102367161391992d0
|
|
C(2,2) = 0.5036819224578257d0
|
|
C(3,3) = 0.33511197860555897d0
|
|
C(4,4) = 0.2510382472105688d0
|
|
C(1,2) = -0.047782608144589914d0
|
|
C(1,3) = -0.031305846715420985d0
|
|
C(1,4) = -0.023278706531979707d0
|
|
C(2,3) = -0.014829085286252043d0
|
|
C(2,4) = -0.011026755725674596d0
|
|
C(3,4) = -0.007224426165097149d0
|
|
C(2,1) = -0.047782608144589914d0
|
|
C(3,1) = -0.031305846715420985d0
|
|
C(4,1) = -0.023278706531979707d0
|
|
C(3,2) = -0.014829085286252043d0
|
|
C(4,2) = -0.011026755725674596d0
|
|
C(4,3) = -0.007224426165097149d0
|
|
det_l_ref = 23.6697d0
|
|
|
|
test_qmckl_adjoint = qmckl_adjoint(context, m, k, LDA, A, det_l)
|
|
|
|
if (test_qmckl_adjoint /= QMCKL_SUCCESS) return
|
|
|
|
test_qmckl_adjoint = QMCKL_FAILURE
|
|
|
|
x = 0.d0
|
|
do j=1,m
|
|
do i=1,k
|
|
x = x + (A(i,j) - (C(i,j) * det_l_ref))**2
|
|
end do
|
|
end do
|
|
|
|
if (dabs(x) <= 1.d-15 .and. (dabs(det_l_ref - det_l)) <= 1.d-15) then
|
|
test_qmckl_adjoint = QMCKL_SUCCESS
|
|
endif
|
|
|
|
deallocate(A,C)
|
|
end function test_qmckl_adjoint
|
|
#+end_src
|
|
|
|
#+begin_src c :comments link :tangle (eval c_test)
|
|
qmckl_exit_code test_qmckl_adjoint(qmckl_context context);
|
|
assert(QMCKL_SUCCESS == test_qmckl_adjoint(context));
|
|
#+end_src
|
|
|
|
* End of files :noexport:
|
|
|
|
#+begin_src c :comments link :tangle (eval c_test)
|
|
assert (qmckl_context_destroy(context) == QMCKL_SUCCESS);
|
|
return 0;
|
|
}
|
|
|
|
#+end_src
|
|
|
|
|
|
# -*- mode: org -*-
|
|
# vim: syntax=c
|