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QuAcK/src/utils/utils.f90

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2019-03-20 13:38:42 +01:00
!------------------------------------------------------------------------
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
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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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
subroutine print_warning(message)
! Print warning
implicit none
character(len=*),intent(in) :: message
write(*,*) message
end subroutine
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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!------------------------------------------------------------------------
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
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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
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