mirror of https://github.com/pfloos/quack
386 lines
9.8 KiB
Fortran
386 lines
9.8 KiB
Fortran
!------------------------------------------------------------------------
|
|
|
|
function KroneckerDelta(i,j) result(delta)
|
|
|
|
! Kronecker Delta
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: i,j
|
|
|
|
|
|
! Output variables
|
|
|
|
integer :: delta
|
|
|
|
if(i == j) then
|
|
delta = 1
|
|
else
|
|
delta = 0
|
|
endif
|
|
|
|
end function KroneckerDelta
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
subroutine matout(m,n,A)
|
|
|
|
! Print the MxN array A
|
|
|
|
implicit none
|
|
|
|
integer,parameter :: ncol = 5
|
|
double precision,parameter :: small = 1d-10
|
|
integer,intent(in) :: m,n
|
|
double precision,intent(in) :: A(m,n)
|
|
double precision :: B(ncol)
|
|
integer :: ilower,iupper,num,i,j
|
|
|
|
do ilower=1,n,ncol
|
|
iupper = min(ilower + ncol - 1,n)
|
|
num = iupper - ilower + 1
|
|
write(*,'(3X,10(7X,I6))') (j,j=ilower,iupper)
|
|
do i=1,m
|
|
do j=ilower,iupper
|
|
B(j-ilower+1) = A(i,j)
|
|
enddo
|
|
do j=1,num
|
|
if(abs(B(j)) < small) B(j) = 0d0
|
|
enddo
|
|
write(*,'(I7,10F15.8)') i,(B(j),j=1,num)
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine matout
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
subroutine CalcTrAB(n,A,B,Tr)
|
|
|
|
! Calculate the trace of the square matrix A.B
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: n
|
|
double precision,intent(in) :: A(n,n),B(n,n)
|
|
|
|
! Local variables
|
|
|
|
integer :: i,j
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: Tr
|
|
|
|
Tr = 0d0
|
|
do i=1,n
|
|
do j=1,n
|
|
Tr = Tr + A(i,j)*B(j,i)
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine CalcTrAB
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
function EpsilonSwitch(i,j) result(delta)
|
|
|
|
! Epsilon function
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: i,j
|
|
integer :: delta
|
|
|
|
if(i <= j) then
|
|
delta = 1
|
|
else
|
|
delta = -1
|
|
endif
|
|
|
|
end function EpsilonSwitch
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
function KappaCross(i,j,k) result(kappa)
|
|
|
|
! kappa(i,j,k) = eps(i,j) delta(i,k) - eps(k,i) delta(i,j)
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: i,j,k
|
|
|
|
! Local variables
|
|
|
|
integer :: EpsilonSwitch,KroneckerDelta
|
|
double precision :: kappa
|
|
|
|
kappa = dble(EpsilonSwitch(i,j)*KroneckerDelta(i,k) - EpsilonSwitch(k,i)*KroneckerDelta(i,j))
|
|
|
|
end function KappaCross
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
subroutine CalcInv3(a,det)
|
|
|
|
! Calculate the inverse and the determinant of a 3x3 matrix
|
|
|
|
implicit none
|
|
|
|
double precision,intent(inout) :: a(3,3)
|
|
double precision, intent(inout) :: det
|
|
double precision :: b(3,3)
|
|
integer :: i,j
|
|
|
|
det = 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=1,3
|
|
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)
|
|
|
|
do i=1,3
|
|
do j=1,3
|
|
a(i,j) = a(i,j)/det
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine CalcInv3
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
subroutine CalcInv4(a,det)
|
|
|
|
implicit none
|
|
|
|
double precision,intent(inout) :: a(4,4)
|
|
double precision,intent(inout) :: det
|
|
double precision :: b(4,4)
|
|
integer :: i,j
|
|
|
|
det = 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))
|
|
|
|
do i=1,4
|
|
do j=1,4
|
|
a(i,j) = a(i,j)/det
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine CalcInv4
|
|
|
|
|
|
!double precision function binom(i,j)
|
|
! implicit none
|
|
! integer,intent(in) :: i,j
|
|
! double precision :: logfact
|
|
! integer, save :: ifirst
|
|
! double precision, save :: memo(0:15,0:15)
|
|
! integer :: k,l
|
|
! if (ifirst == 0) then
|
|
! ifirst = 1
|
|
! do k=0,15
|
|
! do l=0,15
|
|
! memo(k,l) = dexp( logfact(k)-logfact(l)-logfact(k-l) )
|
|
! enddo
|
|
! enddo
|
|
! endif
|
|
! if ( (i<=15).and.(j<=15) ) then
|
|
! binom = memo(i,j)
|
|
! else
|
|
! binom = dexp( logfact(i)-logfact(j)-logfact(i-j) )
|
|
! endif
|
|
!end
|
|
!
|
|
!double precision function fact(n)
|
|
! implicit none
|
|
! integer :: n
|
|
! double precision, save :: memo(1:100)
|
|
! integer, save :: memomax = 1
|
|
!
|
|
! if (n<=memomax) then
|
|
! if (n<2) then
|
|
! fact = 1.d0
|
|
! else
|
|
! fact = memo(n)
|
|
! endif
|
|
! return
|
|
! endif
|
|
!
|
|
! integer :: i
|
|
! memo(1) = 1.d0
|
|
! do i=memomax+1,min(n,100)
|
|
! memo(i) = memo(i-1)*dble(i)
|
|
! enddo
|
|
! memomax = min(n,100)
|
|
! double precision :: logfact
|
|
! fact = dexp(logfact(n))
|
|
!end function
|
|
!
|
|
!double precision function logfact(n)
|
|
! implicit none
|
|
! integer :: n
|
|
! double precision, save :: memo(1:100)
|
|
! integer, save :: memomax = 1
|
|
!
|
|
! if (n<=memomax) then
|
|
! if (n<2) then
|
|
! logfact = 0.d0
|
|
! else
|
|
! logfact = memo(n)
|
|
! endif
|
|
! return
|
|
! endif
|
|
!
|
|
! integer :: i
|
|
! memo(1) = 0.d0
|
|
! do i=memomax+1,min(n,100)
|
|
! memo(i) = memo(i-1)+dlog(dble(i))
|
|
! enddo
|
|
! memomax = min(n,100)
|
|
! logfact = memo(memomax)
|
|
! do i=101,n
|
|
! logfact += dlog(dble(i))
|
|
! enddo
|
|
!end function
|
|
!
|
|
!double precision function dble_fact(n)
|
|
! implicit none
|
|
! integer :: n
|
|
! double precision :: dble_fact_even, dble_fact_odd
|
|
!
|
|
! dble_fact = 1.d0
|
|
!
|
|
! if(n.lt.0) return
|
|
!
|
|
! if(iand(n,1).eq.0)then
|
|
! dble_fact = dble_fact_even(n)
|
|
! else
|
|
! dble_fact= dble_fact_odd(n)
|
|
! endif
|
|
!
|
|
!end function
|
|
!
|
|
!double precision function dble_fact_even(n) result(fact2)
|
|
! implicit none
|
|
! integer :: n,k
|
|
! double precision, save :: memo(0:100)
|
|
! integer, save :: memomax = 0
|
|
! double precision :: prod
|
|
!
|
|
!
|
|
! if (n <= memomax) then
|
|
! if (n < 2) then
|
|
! fact2 = 1.d0
|
|
! else
|
|
! fact2 = memo(n)
|
|
! endif
|
|
! return
|
|
! endif
|
|
!
|
|
! integer :: i
|
|
! memo(0)=1.d0
|
|
! memo(1)=1.d0
|
|
! do i=memomax+2,min(n,100),2
|
|
! memo(i) = memo(i-2)* dble(i)
|
|
! enddo
|
|
! memomax = min(n,100)
|
|
! fact2 = memo(memomax)
|
|
!
|
|
! if (n > 100) then
|
|
! double precision :: dble_logfact
|
|
! fact2 = dexp(dble_logfact(n))
|
|
! endif
|
|
!
|
|
!end function
|
|
!
|
|
!double precision function dble_fact_odd(n) result(fact2)
|
|
! implicit none
|
|
! integer :: n
|
|
! double precision, save :: memo(1:100)
|
|
! integer, save :: memomax = 1
|
|
!
|
|
! if (n<=memomax) then
|
|
! if (n<3) then
|
|
! fact2 = 1.d0
|
|
! else
|
|
! fact2 = memo(n)
|
|
! endif
|
|
! return
|
|
! endif
|
|
!
|
|
! integer :: i
|
|
! memo(1) = 1.d0
|
|
! do i=memomax+2,min(n,99),2
|
|
! memo(i) = memo(i-2)* dble(i)
|
|
! enddo
|
|
! memomax = min(n,99)
|
|
! fact2 = memo(memomax)
|
|
!
|
|
! if (n > 99) then
|
|
! double precision :: dble_logfact
|
|
! fact2 = dexp(dble_logfact(n))
|
|
! endif
|
|
!
|
|
!end function
|
|
|