mirror of
https://github.com/pfloos/quack
synced 2025-04-02 06:51:37 +02:00
386 lines
9.8 KiB
Fortran
386 lines
9.8 KiB
Fortran
!------------------------------------------------------------------------
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function KroneckerDelta(i,j) result(delta)
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! Kronecker Delta
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implicit none
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! Input variables
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integer,intent(in) :: i,j
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! Output variables
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integer :: delta
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if(i == j) then
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delta = 1
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else
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delta = 0
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endif
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end function KroneckerDelta
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!------------------------------------------------------------------------
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subroutine matout(m,n,A)
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! Print the MxN array A
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implicit none
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integer,parameter :: ncol = 5
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double precision,parameter :: small = 1d-10
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integer,intent(in) :: m,n
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double precision,intent(in) :: A(m,n)
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double precision :: B(ncol)
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integer :: ilower,iupper,num,i,j
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do ilower=1,n,ncol
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iupper = min(ilower + ncol - 1,n)
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num = iupper - ilower + 1
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write(*,'(3X,10(7X,I6))') (j,j=ilower,iupper)
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do i=1,m
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do j=ilower,iupper
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B(j-ilower+1) = A(i,j)
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enddo
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do j=1,num
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if(abs(B(j)) < small) B(j) = 0d0
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enddo
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write(*,'(I7,10F15.8)') i,(B(j),j=1,num)
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enddo
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enddo
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end subroutine matout
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!------------------------------------------------------------------------
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subroutine CalcTrAB(n,A,B,Tr)
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! Calculate the trace of the square matrix A.B
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implicit none
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! Input variables
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integer,intent(in) :: n
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double precision,intent(in) :: A(n,n),B(n,n)
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! Local variables
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integer :: i,j
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! Output variables
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double precision,intent(out) :: Tr
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Tr = 0d0
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do i=1,n
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do j=1,n
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Tr = Tr + A(i,j)*B(j,i)
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enddo
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enddo
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end subroutine CalcTrAB
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!------------------------------------------------------------------------
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function EpsilonSwitch(i,j) result(delta)
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! Epsilon function
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implicit none
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! Input variables
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integer,intent(in) :: i,j
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integer :: delta
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if(i <= j) then
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delta = 1
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else
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delta = -1
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endif
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end function EpsilonSwitch
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!------------------------------------------------------------------------
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function KappaCross(i,j,k) result(kappa)
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! kappa(i,j,k) = eps(i,j) delta(i,k) - eps(k,i) delta(i,j)
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implicit none
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! Input variables
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integer,intent(in) :: i,j,k
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! Local variables
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integer :: EpsilonSwitch,KroneckerDelta
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double precision :: kappa
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kappa = dble(EpsilonSwitch(i,j)*KroneckerDelta(i,k) - EpsilonSwitch(k,i)*KroneckerDelta(i,j))
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end function KappaCross
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!------------------------------------------------------------------------
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subroutine CalcInv3(a,det)
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! Calculate the inverse and the determinant of a 3x3 matrix
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implicit none
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double precision,intent(inout) :: a(3,3)
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double precision, intent(inout) :: det
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double precision :: b(3,3)
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integer :: i,j
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det = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) &
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- a(1,2)*(a(2,1)*a(3,3)-a(2,3)*a(3,1)) &
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+ a(1,3)*(a(2,1)*a(3,2)-a(2,2)*a(3,1))
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do i=1,3
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b(i,1) = a(i,1)
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b(i,2) = a(i,2)
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b(i,3) = a(i,3)
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enddo
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a(1,1) = b(2,2)*b(3,3) - b(2,3)*b(3,2)
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a(2,1) = b(2,3)*b(3,1) - b(2,1)*b(3,3)
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a(3,1) = b(2,1)*b(3,2) - b(2,2)*b(3,1)
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a(1,2) = b(1,3)*b(3,2) - b(1,2)*b(3,3)
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a(2,2) = b(1,1)*b(3,3) - b(1,3)*b(3,1)
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a(3,2) = b(1,2)*b(3,1) - b(1,1)*b(3,2)
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a(1,3) = b(1,2)*b(2,3) - b(1,3)*b(2,2)
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a(2,3) = b(1,3)*b(2,1) - b(1,1)*b(2,3)
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a(3,3) = b(1,1)*b(2,2) - b(1,2)*b(2,1)
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do i=1,3
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do j=1,3
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a(i,j) = a(i,j)/det
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enddo
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enddo
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end subroutine CalcInv3
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!------------------------------------------------------------------------
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subroutine CalcInv4(a,det)
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implicit none
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double precision,intent(inout) :: a(4,4)
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double precision,intent(inout) :: det
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double precision :: b(4,4)
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integer :: i,j
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det = a(1,1)*(a(2,2)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
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-a(2,3)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
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+a(2,4)*(a(3,2)*a(4,3)-a(3,3)*a(4,2))) &
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- a(1,2)*(a(2,1)*(a(3,3)*a(4,4)-a(3,4)*a(4,3)) &
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-a(2,3)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
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+a(2,4)*(a(3,1)*a(4,3)-a(3,3)*a(4,1))) &
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+ a(1,3)*(a(2,1)*(a(3,2)*a(4,4)-a(3,4)*a(4,2)) &
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-a(2,2)*(a(3,1)*a(4,4)-a(3,4)*a(4,1)) &
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+a(2,4)*(a(3,1)*a(4,2)-a(3,2)*a(4,1))) &
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- a(1,4)*(a(2,1)*(a(3,2)*a(4,3)-a(3,3)*a(4,2)) &
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-a(2,2)*(a(3,1)*a(4,3)-a(3,3)*a(4,1)) &
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+a(2,3)*(a(3,1)*a(4,2)-a(3,2)*a(4,1)))
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do i=1,4
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b(1,i) = a(1,i)
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b(2,i) = a(2,i)
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b(3,i) = a(3,i)
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b(4,i) = a(4,i)
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enddo
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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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))
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do i=1,4
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do j=1,4
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a(i,j) = a(i,j)/det
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enddo
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enddo
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end subroutine CalcInv4
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!double precision function binom(i,j)
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! implicit none
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! integer,intent(in) :: i,j
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! double precision :: logfact
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! integer, save :: ifirst
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! double precision, save :: memo(0:15,0:15)
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! integer :: k,l
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! if (ifirst == 0) then
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! ifirst = 1
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! do k=0,15
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! do l=0,15
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! memo(k,l) = dexp( logfact(k)-logfact(l)-logfact(k-l) )
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! enddo
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! enddo
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! endif
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! if ( (i<=15).and.(j<=15) ) then
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! binom = memo(i,j)
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! else
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! binom = dexp( logfact(i)-logfact(j)-logfact(i-j) )
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! endif
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!end
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!
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!double precision function fact(n)
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! implicit none
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! integer :: n
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! double precision, save :: memo(1:100)
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! integer, save :: memomax = 1
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!
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! if (n<=memomax) then
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! if (n<2) then
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! fact = 1.d0
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! else
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! fact = memo(n)
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! endif
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! return
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! endif
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!
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! integer :: i
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! memo(1) = 1.d0
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! do i=memomax+1,min(n,100)
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! memo(i) = memo(i-1)*dble(i)
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! enddo
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! memomax = min(n,100)
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! double precision :: logfact
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! fact = dexp(logfact(n))
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!end function
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!
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!double precision function logfact(n)
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! implicit none
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! integer :: n
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! double precision, save :: memo(1:100)
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! integer, save :: memomax = 1
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!
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! if (n<=memomax) then
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! if (n<2) then
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! logfact = 0.d0
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! else
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! logfact = memo(n)
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! endif
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! return
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! endif
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!
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! integer :: i
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! memo(1) = 0.d0
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! do i=memomax+1,min(n,100)
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! memo(i) = memo(i-1)+dlog(dble(i))
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! enddo
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! memomax = min(n,100)
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! logfact = memo(memomax)
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! do i=101,n
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! logfact += dlog(dble(i))
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! enddo
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!end function
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!
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!double precision function dble_fact(n)
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! implicit none
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! integer :: n
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! double precision :: dble_fact_even, dble_fact_odd
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!
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! dble_fact = 1.d0
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!
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! if(n.lt.0) return
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!
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! if(iand(n,1).eq.0)then
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! dble_fact = dble_fact_even(n)
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! else
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! dble_fact= dble_fact_odd(n)
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! endif
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!
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!end function
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!
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!double precision function dble_fact_even(n) result(fact2)
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! implicit none
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! integer :: n,k
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! double precision, save :: memo(0:100)
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! integer, save :: memomax = 0
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! double precision :: prod
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!
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!
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! if (n <= memomax) then
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! if (n < 2) then
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! fact2 = 1.d0
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! else
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! fact2 = memo(n)
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! endif
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! return
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! endif
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!
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! integer :: i
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! memo(0)=1.d0
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! memo(1)=1.d0
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! do i=memomax+2,min(n,100),2
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! memo(i) = memo(i-2)* dble(i)
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! enddo
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! memomax = min(n,100)
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! fact2 = memo(memomax)
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!
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! if (n > 100) then
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! double precision :: dble_logfact
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! fact2 = dexp(dble_logfact(n))
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! endif
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!
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!end function
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!
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!double precision function dble_fact_odd(n) result(fact2)
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! implicit none
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! integer :: n
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! double precision, save :: memo(1:100)
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! integer, save :: memomax = 1
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!
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! if (n<=memomax) then
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! if (n<3) then
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! fact2 = 1.d0
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! else
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! fact2 = memo(n)
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! endif
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! return
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! endif
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!
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! integer :: i
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! memo(1) = 1.d0
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! do i=memomax+2,min(n,99),2
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! memo(i) = memo(i-2)* dble(i)
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! enddo
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! memomax = min(n,99)
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! fact2 = memo(memomax)
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!
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! if (n > 99) then
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! double precision :: dble_logfact
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! fact2 = dexp(dble_logfact(n))
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! endif
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!
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!end function
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