mirror of
https://gitlab.com/scemama/qmcchem.git
synced 2024-06-02 11:25:18 +02:00
477 lines
24 KiB
Fortran
477 lines
24 KiB
Fortran
! This file contains the fast inversion routines of QMC=Chem for
|
|
! small matrices. It may be downloaded here:
|
|
! https://raw.githubusercontent.com/scemama/qmcchem/master/src/TOOLS/invert.irp.f
|
|
!
|
|
! To use it in your Fortran code, you will need to~:
|
|
! 1) rename it inverse.f90
|
|
! 2) replace all $IRP_ALIGN occurences by
|
|
! a) 16 for SSE4.2
|
|
! b) 32 for AVX or AVX2
|
|
! c) 64 for AVX-512
|
|
!
|
|
!
|
|
! GPL license :
|
|
! -------------
|
|
!
|
|
! QMC=Chem : Quantum Monte Carlo for Chemistry
|
|
! Copyright (C) 2009 Anthony SCEMAMA
|
|
!
|
|
! This program is free software; you can redistribute it and/or modify
|
|
! it under the terms of the GNU General Public License as published by
|
|
! the Free Software Foundation; either version 2 of the License, or
|
|
! (at your option) any later version.
|
|
!
|
|
! This program is distributed in the hope that it will be useful,
|
|
! but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
! GNU General Public License for more details.
|
|
!
|
|
! You should have received a copy of the GNU General Public License along
|
|
! with this program; if not, write to the Free Software Foundation, Inc.,
|
|
! 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
|
!
|
|
! Anthony Scemama
|
|
! LCPQ - IRSAMC - CNRS
|
|
! Universite Paul Sabatier
|
|
! 118, route de Narbonne
|
|
! 31062 Toulouse Cedex 4
|
|
! scemama@irsamc.ups-tlse.fr
|
|
!
|
|
!
|
|
|
|
|
|
subroutine invert(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer, intent(in) :: LDA
|
|
integer, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
|
|
integer :: i,j
|
|
select case (na)
|
|
case default
|
|
!DIR$ forceinline
|
|
call invert_general(a,LDA,na,det_l)
|
|
case (5)
|
|
!DIR$ forceinline
|
|
call invert5(a,LDA,na,det_l)
|
|
case (4)
|
|
!DIR$ forceinline
|
|
call invert4(a,LDA,na,det_l)
|
|
case (3)
|
|
!DIR$ forceinline
|
|
call invert3(a,LDA,na,det_l)
|
|
case (2)
|
|
!DIR$ forceinline
|
|
call invert2(a,LDA,na,det_l)
|
|
case (1)
|
|
!DIR$ forceinline
|
|
call invert1(a,LDA,na,det_l)
|
|
case (0)
|
|
det_l=1.d0
|
|
end select
|
|
end
|
|
|
|
subroutine invert_general(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer, intent(in) :: LDA
|
|
integer, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
|
|
double precision :: work(LDA*max(na,64))
|
|
!DIR$ ATTRIBUTES ALIGN: $IRP_ALIGN :: work
|
|
integer :: inf
|
|
integer :: ipiv(LDA)
|
|
!DIR$ ATTRIBUTES ALIGN: $IRP_ALIGN :: ipiv
|
|
integer :: lwork
|
|
integer :: i, j
|
|
call dgetrf(na, na, a, LDA, ipiv, inf )
|
|
det_l = 1.d0
|
|
j=0
|
|
!DIR$ VECTOR ALIGNED
|
|
do i=1,na
|
|
j = j+min(abs(ipiv(i)-i),1)
|
|
det_l = det_l*a(i,i)
|
|
enddo
|
|
if (iand(j,1) /= 0) then
|
|
det_l = -det_l
|
|
endif
|
|
lwork = SIZE(work)
|
|
call dgetri(na, a, LDA, ipiv, work, lwork, inf )
|
|
a = a*det_l
|
|
end
|
|
|
|
subroutine sinvert(a,LDA,na,det_l)
|
|
implicit none
|
|
real :: a (LDA,na)
|
|
integer :: LDA
|
|
integer :: na
|
|
real :: det_l
|
|
|
|
real :: work(LDA*max(na,64))
|
|
!DIR$ ATTRIBUTES ALIGN: $IRP_ALIGN :: work
|
|
integer :: inf
|
|
integer :: ipiv(LDA)
|
|
!DIR$ ATTRIBUTES ALIGN: $IRP_ALIGN :: ipiv
|
|
integer :: lwork
|
|
integer :: i, j
|
|
call sgetrf(na, na, a, LDA, ipiv, inf )
|
|
det_l = 1.d0
|
|
j=0
|
|
!DIR$ VECTOR ALIGNED
|
|
do i=1,na
|
|
if (ipiv(i) /= i) then
|
|
j = j+1
|
|
endif
|
|
det_l = det_l*a(i,i)
|
|
enddo
|
|
if (iand(j,1) /= 0) then
|
|
det_l = -det_l
|
|
endif
|
|
lwork = SIZE(work)
|
|
call sgetri(na, a, LDA, ipiv, work, lwork, inf )
|
|
a = a*det_l
|
|
end
|
|
|
|
subroutine invert1(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer, intent(in) :: LDA
|
|
integer, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
|
|
det_l = a(1,1)
|
|
a(1,1) = 1.d0
|
|
end
|
|
|
|
subroutine invert2(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision :: a (LDA,na)
|
|
integer :: LDA
|
|
integer :: 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 invert3(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer, intent(in) :: LDA
|
|
integer, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(4,3)
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: b
|
|
integer :: i
|
|
det_l = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) &
|
|
-a(1,2)*(a(2,1)*a(3,3)-a(2,3)*a(3,1)) &
|
|
+a(1,3)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
|
|
do i=1,4
|
|
b(i,1) = a(i,1)
|
|
b(i,2) = a(i,2)
|
|
b(i,3) = a(i,3)
|
|
enddo
|
|
a(1,1) = b(2,2)*b(3,3) - b(2,3)*b(3,2)
|
|
a(2,1) = b(2,3)*b(3,1) - b(2,1)*b(3,3)
|
|
a(3,1) = b(2,1)*b(3,2) - b(2,2)*b(3,1)
|
|
|
|
a(1,2) = b(1,3)*b(3,2) - b(1,2)*b(3,3)
|
|
a(2,2) = b(1,1)*b(3,3) - b(1,3)*b(3,1)
|
|
a(3,2) = b(1,2)*b(3,1) - b(1,1)*b(3,2)
|
|
|
|
a(1,3) = b(1,2)*b(2,3) - b(1,3)*b(2,2)
|
|
a(2,3) = b(1,3)*b(2,1) - b(1,1)*b(2,3)
|
|
a(3,3) = b(1,1)*b(2,2) - b(1,2)*b(2,1)
|
|
|
|
end
|
|
|
|
subroutine invert4(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer, intent(in) :: LDA
|
|
integer, intent(in) :: na
|
|
double precision, intent(inout) :: det_l
|
|
double precision :: b(4,4)
|
|
!DIR$ 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 invert5(a,LDA,na,det_l)
|
|
implicit none
|
|
double precision, intent(inout) :: a (LDA,na)
|
|
integer, intent(in) :: LDA
|
|
integer, 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
|
|
|
|
subroutine invert_update(a,LDA,na,det_l,b)
|
|
implicit none
|
|
double precision :: a (LDA,na)
|
|
double precision :: b (LDA,na)
|
|
integer :: LDA
|
|
integer :: na
|
|
double precision :: det_l
|
|
|
|
double precision :: work(LDA*max(na,64))
|
|
!DIR$ ATTRIBUTES ALIGN: $IRP_ALIGN :: work
|
|
integer :: inf
|
|
integer :: ipiv(LDA)
|
|
!DIR$ ATTRIBUTES ALIGN: $IRP_ALIGN :: ipiv
|
|
integer :: lwork
|
|
integer :: i, j
|
|
double precision :: bold(LDA,na)
|
|
double precision :: ba(LDA,na)
|
|
integer :: k
|
|
ba = a
|
|
call dgetrf(na, na, ba, LDA, ipiv, inf )
|
|
det_l = 1.d0
|
|
j=0
|
|
!DIR$ VECTOR ALIGNED
|
|
do i=1,na
|
|
if (ipiv(i) /= i) then
|
|
j = j+1
|
|
endif
|
|
det_l = det_l*a(i,i)
|
|
enddo
|
|
if (iand(j,1) /= 0) then
|
|
det_l = -det_l
|
|
endif
|
|
do k=1,3
|
|
bold = b
|
|
call dgemm('N','N',na,na,na,1.d0,a,LDA,bold,LDA, &
|
|
0.d0, ba, LDA)
|
|
call dgemm('N','N',na,na,na,-1.d0,bold,LDA,ba,LDA, &
|
|
2.d0, b, LDA)
|
|
enddo
|
|
b = b*det_l
|
|
end
|
|
|