mirror of
https://github.com/pfloos/quack
synced 2024-10-31 03:03:49 +01:00
629 lines
14 KiB
Fortran
629 lines
14 KiB
Fortran
!------------------------------------------------------------------------
|
|
function Kronecker_delta(i,j) result(delta)
|
|
|
|
! Kronecker Delta
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: i,j
|
|
|
|
! Output variables
|
|
|
|
double precision :: delta
|
|
|
|
if(i == j) then
|
|
delta = 1d0
|
|
else
|
|
delta = 0d0
|
|
endif
|
|
|
|
end function
|
|
|
|
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
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine diagonal_matrix(N,D,A)
|
|
|
|
! Construct diagonal matrix A from vector D
|
|
|
|
implicit none
|
|
|
|
integer,intent(in) :: N
|
|
double precision,intent(in) :: D(N)
|
|
double precision,intent(out) :: A(N,N)
|
|
|
|
integer :: i
|
|
|
|
A(:,:) = 0d0
|
|
do i=1,N
|
|
A(i,i) = D(i)
|
|
end do
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine matrix_exponential(N,A,ExpA)
|
|
|
|
! Compute Exp(A)
|
|
|
|
implicit none
|
|
|
|
integer,intent(in) :: N
|
|
integer :: i
|
|
double precision,intent(in) :: A(N,N)
|
|
double precision,allocatable :: W(:,:)
|
|
double precision,allocatable :: tau(:)
|
|
double precision,allocatable :: t(:,:)
|
|
double precision,intent(out) :: ExpA(N,N)
|
|
|
|
! Memory allocation
|
|
|
|
allocate(W(N,N),tau(N),t(N,N))
|
|
|
|
! Initialize
|
|
|
|
ExpA(:,:) = 0d0
|
|
|
|
! Diagonalize
|
|
|
|
W(:,:) = - matmul(A,A)
|
|
call diagonalize_matrix(N,W,tau)
|
|
|
|
! do i=1,N
|
|
! tau(i) = max(abs(tau(i)),1d-14)
|
|
! end do
|
|
tau(:) = sqrt(abs(tau(:)))
|
|
|
|
! Construct cos part
|
|
|
|
call diagonal_matrix(N,cos(tau),t)
|
|
t(:,:) = matmul(t,transpose(W))
|
|
ExpA(:,:) = ExpA(:,:) + matmul(W,t)
|
|
|
|
! Construct sin part
|
|
|
|
call diagonal_matrix(N,sin(tau)/tau,t)
|
|
t(:,:) = matmul(t,transpose(W))
|
|
t(:,:) = matmul(t,A)
|
|
ExpA(:,:) = ExpA(:,:) + matmul(W,t)
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
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(9X,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
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine vecout(m,A)
|
|
|
|
! Print the N vector A
|
|
|
|
implicit none
|
|
|
|
integer,intent(in) :: m
|
|
double precision,intent(in) :: A(m)
|
|
|
|
call matout(m,1,A)
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine trace_vector(n,v,Tr)
|
|
|
|
! Calculate the trace of the vector v of length n
|
|
!!! Please use the intrinsic fortran sum() !!!
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: n
|
|
double precision,intent(in) :: v(n)
|
|
|
|
! Local variables
|
|
|
|
integer :: i
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: Tr
|
|
|
|
Tr = 0d0
|
|
do i=1,n
|
|
Tr = Tr + v(i)
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
function trace_matrix(n,A) result(Tr)
|
|
|
|
! Calculate the trace of the square matrix A
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: n
|
|
double precision,intent(in) :: A(n,n)
|
|
|
|
! Local variables
|
|
|
|
integer :: i
|
|
|
|
! Output variables
|
|
|
|
double precision :: Tr
|
|
|
|
Tr = 0d0
|
|
do i=1,n
|
|
Tr = Tr + A(i,i)
|
|
enddo
|
|
|
|
end function
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine compute_error(nData,Mean,Var,Error)
|
|
|
|
! Calculate the statistical error
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
double precision,intent(in) :: nData,Mean(3)
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: Error(3)
|
|
double precision,intent(inout):: Var(3)
|
|
|
|
Error = sqrt((Var-Mean**2/nData)/nData/(nData-1d0))
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine identity_matrix(N,A)
|
|
|
|
! Set the matrix A to the identity matrix
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: N
|
|
|
|
! Local viaruabkes
|
|
|
|
integer :: i
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: A(N,N)
|
|
|
|
A = 0d0
|
|
|
|
do i=1,N
|
|
A(i,i) = 1d0
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine prepend(N,M,A,b)
|
|
|
|
! Prepend the vector b of size N into the matrix A of size NxM
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: N,M
|
|
double precision,intent(in) :: b(N)
|
|
|
|
! Local viaruabkes
|
|
|
|
integer :: i,j
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: A(N,M)
|
|
|
|
|
|
! print*,'b in append'
|
|
! call matout(N,1,b)
|
|
|
|
do i=1,N
|
|
do j=M-1,1,-1
|
|
A(i,j+1) = A(i,j)
|
|
enddo
|
|
A(i,1) = b(i)
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine append(N,M,A,b)
|
|
|
|
! Append the vector b of size N into the matrix A of size NxM
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: N,M
|
|
double precision,intent(in) :: b(N)
|
|
|
|
! Local viaruabkes
|
|
|
|
integer :: i,j
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: A(N,M)
|
|
|
|
do i=1,N
|
|
do j=2,M
|
|
A(i,j-1) = A(i,j)
|
|
enddo
|
|
A(i,M) = b(i)
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine AtDA(N,A,D,B)
|
|
|
|
! Perform B = At.D.A where A is a NxN matrix and D is a diagonal matrix given
|
|
! as a vector of length N
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: N
|
|
double precision,intent(in) :: A(N,N),D(N)
|
|
|
|
! Local viaruabkes
|
|
|
|
integer :: i,j,k
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: B(N,N)
|
|
|
|
B = 0d0
|
|
|
|
do i=1,N
|
|
do j=1,N
|
|
do k=1,N
|
|
B(i,k) = B(i,k) + A(j,i)*D(j)*A(j,k)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine ADAt(N,A,D,B)
|
|
|
|
! Perform B = A.D.At where A is a NxN matrix and D is a diagonal matrix given
|
|
! as a vector of length N
|
|
|
|
implicit none
|
|
|
|
! Input variables
|
|
|
|
integer,intent(in) :: N
|
|
double precision,intent(in) :: A(N,N),D(N)
|
|
|
|
! Local viaruabkes
|
|
|
|
integer :: i,j,k
|
|
|
|
! Output variables
|
|
|
|
double precision,intent(out) :: B(N,N)
|
|
|
|
B = 0d0
|
|
|
|
do i=1,N
|
|
do j=1,N
|
|
do k=1,N
|
|
B(i,k) = B(i,k) + A(i,j)*D(j)*A(k,j)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine
|
|
!------------------------------------------------------------------------
|
|
subroutine DA(N,D,A)
|
|
|
|
! Perform A <- D.A where A is a NxN matrix and D is a diagonal matrix given
|
|
! as a vector of length N
|
|
|
|
implicit none
|
|
|
|
integer,intent(in) :: N
|
|
integer :: i,j,k
|
|
double precision,intent(in) :: D(N)
|
|
double precision,intent(inout):: A(N,N)
|
|
|
|
do i=1,N
|
|
do j=1,N
|
|
A(i,j) = D(i)*A(i,j)
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine AD(N,A,D)
|
|
|
|
! Perform A <- A.D where A is a NxN matrix and D is a diagonal matrix given
|
|
! as a vector of length N
|
|
|
|
implicit none
|
|
|
|
integer,intent(in) :: N
|
|
integer :: i,j,k
|
|
double precision,intent(in) :: D(N)
|
|
double precision,intent(inout):: A(N,N)
|
|
|
|
do i=1,N
|
|
do j=1,N
|
|
A(i,j) = A(i,j)*D(j)
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
subroutine print_warning(message)
|
|
|
|
! Print warning
|
|
|
|
implicit none
|
|
|
|
character(len=*),intent(in) :: message
|
|
|
|
write(*,*) message
|
|
|
|
end subroutine
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
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
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
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
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
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
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
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
|
|
|
|
!------------------------------------------------------------------------
|
|
|
|
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
|
|
|
|
subroutine wall_time(t)
|
|
implicit none
|
|
double precision, intent(out) :: t
|
|
integer*8 :: c
|
|
integer*8, save :: rate = 0
|
|
if (rate == 0) then
|
|
CALL SYSTEM_CLOCK(count_rate=rate)
|
|
endif
|
|
CALL SYSTEM_CLOCK(count=c)
|
|
t = dble(c)/dble(rate)
|
|
end subroutine
|
|
|