mirror of
https://github.com/pfloos/quack
synced 2024-06-25 22:52:18 +02:00
340 lines
6.3 KiB
Fortran
340 lines
6.3 KiB
Fortran
!------------------------------------------------------------------------
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function Kronecker_delta(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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double precision :: delta
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if(i == j) then
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delta = 1d0
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else
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delta = 0d0
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endif
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end function Kronecker_delta
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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(9X,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 trace_vector(n,v,Tr)
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! Calculate the trace of the vector v of length n
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!!! Please use the intrinsic fortran sum() !!!
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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) :: v(n)
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! Local variables
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integer :: i
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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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Tr = Tr + v(i)
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enddo
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end subroutine trace_vector
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!------------------------------------------------------------------------
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function trace_matrix(n,A) result(Tr)
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! Calculate the trace of the square matrix A
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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)
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! Local variables
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integer :: i
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! Output variables
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double precision :: Tr
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Tr = 0d0
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do i=1,n
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Tr = Tr + A(i,i)
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enddo
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end function trace_matrix
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!------------------------------------------------------------------------
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subroutine compute_error(nData,Mean,Var,Error)
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! Calculate the statistical error
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implicit none
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! Input variables
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double precision,intent(in) :: nData,Mean(3)
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! Output variables
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double precision,intent(out) :: Error(3)
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double precision,intent(inout):: Var(3)
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Error = sqrt((Var-Mean**2/nData)/nData/(nData-1d0))
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end subroutine compute_error
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!------------------------------------------------------------------------
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subroutine identity_matrix(N,A)
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! Set the matrix A to the identity matrix
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implicit none
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! Input variables
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integer,intent(in) :: N
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! Local viaruabkes
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integer :: i
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! Output variables
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double precision,intent(out) :: A(N,N)
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A = 0d0
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do i=1,N
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A(i,i) = 1d0
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enddo
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end subroutine identity_matrix
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!------------------------------------------------------------------------
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subroutine prepend(N,M,A,b)
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! Prepend the vector b of size N into the matrix A of size NxM
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implicit none
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! Input variables
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integer,intent(in) :: N,M
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double precision,intent(in) :: b(N)
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! Local viaruabkes
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integer :: i,j
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! Output variables
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double precision,intent(out) :: A(N,M)
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! print*,'b in append'
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! call matout(N,1,b)
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do i=1,N
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do j=M-1,1,-1
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A(i,j+1) = A(i,j)
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enddo
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A(i,1) = b(i)
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enddo
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end subroutine prepend
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!------------------------------------------------------------------------
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subroutine append(N,M,A,b)
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! Append the vector b of size N into the matrix A of size NxM
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implicit none
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! Input variables
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integer,intent(in) :: N,M
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double precision,intent(in) :: b(N)
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! Local viaruabkes
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integer :: i,j
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! Output variables
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double precision,intent(out) :: A(N,M)
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do i=1,N
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do j=2,M
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A(i,j-1) = A(i,j)
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enddo
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A(i,M) = b(i)
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enddo
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end subroutine append
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!------------------------------------------------------------------------
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subroutine AtDA(N,A,D,B)
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! Perform B = At.D.A where A is a NxN matrix and D is a diagonal matrix given
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! as a vector of length N
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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),D(N)
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! Local viaruabkes
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integer :: i,j,k
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! Output variables
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double precision,intent(out) :: B(N,N)
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B = 0d0
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do i=1,N
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do j=1,N
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do k=1,N
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B(i,k) = B(i,k) + A(j,i)*D(j)*A(j,k)
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enddo
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enddo
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enddo
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end subroutine AtDA
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!------------------------------------------------------------------------
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subroutine ADAt(N,A,D,B)
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! Perform B = A.D.At where A is a NxN matrix and D is a diagonal matrix given
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! as a vector of length N
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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),D(N)
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! Local viaruabkes
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integer :: i,j,k
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! Output variables
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double precision,intent(out) :: B(N,N)
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B = 0d0
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do i=1,N
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do j=1,N
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do k=1,N
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B(i,k) = B(i,k) + A(i,j)*D(j)*A(k,j)
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enddo
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enddo
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enddo
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end subroutine ADAt
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!------------------------------------------------------------------------
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subroutine DA(N,D,A)
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! Perform A <- D.A where A is a NxN matrix and D is a diagonal matrix given
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! as a vector of length N
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implicit none
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integer,intent(in) :: N
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integer :: i,j,k
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double precision,intent(in) :: D(N)
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double precision,intent(inout):: A(N,N)
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do i=1,N
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do j=1,N
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A(i,j) = D(i)*A(i,j)
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enddo
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enddo
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end subroutine DA
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!------------------------------------------------------------------------
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subroutine AD(N,A,D)
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! Perform A <- A.D where A is a NxN matrix and D is a diagonal matrix given
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! as a vector of length N
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implicit none
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integer,intent(in) :: N
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integer :: i,j,k
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double precision,intent(in) :: D(N)
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double precision,intent(inout):: A(N,N)
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do i=1,N
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do j=1,N
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A(i,j) = A(i,j)*D(j)
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enddo
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enddo
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end subroutine AD
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!------------------------------------------------------------------------
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subroutine print_warning(message)
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! Print warning
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implicit none
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character(len=*),intent(in) :: message
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write(*,*) message
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end subroutine print_warning
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