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program test
parameter(M=2**1)
integer i,j
complex A(2*m,2*m),B(4*m,4*m),C(4*m,4*m),D(4*m,4*m)
complex AA(-m:m-1,-m:m-1),BB(-m:m-1,-m:m-1),CC(-m:m-1,-m:m-1)
do i=-m,m-1
do j=-m,m-1
if((i.ne.0).and.(j.ne.0)) then
AA(i,j)=cmplx(1.,2.*j)
else
AA(i,j)=cmplx(0.,0.)
endif
enddo
enddo
! print*,"A=",AA
do i=1,2*M
do j=1,2*M
A(i,j)=AA(i-M-1,j-M-1)
enddo
enddo
! print*,'a=',A
! Call AhFFT(30.d0,M,A,C)
call Ah(30.d0,M,AA,CC)
do i=-m,M-1
do j=-m,m-1
print*,'A*B',i,j,',',CC(i,j)
enddo
enddo
call AhFFT(30.d0,M,A,C)
do i=1,4*M
do j=1,4*M
print*,'AB',i,j,',',C(i,j)
enddo
enddo
end
subroutine AhFFT(s,MM,phi,psi)
integer i,j,j1,j2
complex phii(4*MM,4*MM),phi(2*MM,2*MM),
& psi(4*MM,4*MM),G(4*MM,4*MM),
& L(4*MM,4*MM)
double precision h,s
parameter(pi=3.141592653d0)
h=s/real(MM)
do j1=1,4*MM
do j2=1,4*MM
if((j1.ne.(2*MM+1)).and.(j2.ne.(2*MM+1))) then
G(j1,j2)=1./(pi*h*cmplx(real(j1)-real(2.*MM)-1.d0,
& real(j2)-real(2.*MM)-1.d0))
else
G(j1,j2)=cmplx(0.,0.)
endif
enddo
enddo
! print*,'G=',G
do i=1,4*MM
do j=1,4*MM
if((i.le.2*MM).and.(j.le.2*MM)) then
phii(i,j)=phi(i,j)
else
phii(i,j)=cmplx(0.,0.)
endif
enddo
enddo
! print*,'phi=',i,j,phii
Call fft2d(G,2000,4*MM)
Call fft2d(phii,2000,4*MM)
do i=1,4*MM
do j=1,4*MM
L(i,j)=G(i,j)*phii(i,j)
enddo
enddo
Call ifft2d(L,2000,4*MM)
do i=1,4*MM
do j=1,4*MM
psi(i,j)=L(i,j)*h**2
enddo
enddo
return
end
subroutine Ah(s,MM,phi,psi)
integer i,j,j1,j2
complex phi(-MM:MM-1,-MM:MM-1),psi(-MM:MM-1,-MM:MM-1)
C& ii
double precision h,s
C parameter(ii=(0.,1.))
parameter(pi=3.141592653d0)
C ii=cmplx(0.,1.)
h=2.*s/real(MM)
do j1=-MM,MM-1
do j2=-MM,MM-1
psi(j1,j2)=cmplx(0.,0.)
do l1=-MM,MM-1
do l2=-MM,MM-1
if((l1.ne.j1).and.(l2.ne.j2)) then
C psi(j1,j2)=cmplx(0.,0.)
C else
psi(j1,j2)=psi(j1,j2)+1./(pi*h*
C& (real(j1)-real(l1)+ii*(real(j2)-real(l2))))
& cmplx(real(j1)-real(l1),real(j2)-real(l2)))
& *phi(l1,l2)
endif
enddo
enddo
psi(j1,j2)=psi(j1,j2)*h**2
enddo
enddo
return
end
subroutine fft2d(field, m, n)
integer m, n, i ,j
complex field(n, n)
complex xlong(2000)
do i = 1,n
do j = 1,n
xlong(j) = field(i,j)
end do
call fft1d(xlong, m, n)
do j = 1,n
field(i,j) = xlong(j)
end do
end do
do j = 1,n
call fft1d(field(1,j), m, n)
end do
return
end
subroutine fft1d(z,m,n)
complex z(*)
complex zt,wt,w(2**15)
double precision p
integer n,m,m2
save w, m2
data m2 /-1/
if (m .eq. 0) then
return
endif
if (m .ne. m2) then
p = 6.283185307179586d0/n
do k = 1,n/2
w(k) = cmplx(cos(p*(k-1)),sin(p*(k-1)))
w(k+n/2) = conjg(w(k))
enddo
m2 = m
endif
ks = 1
n2 = n
kn2 = ks*n
ie = 1
ia1 = n/2 + 1
do k = 1,m
n1 = n2
kn1 = kn2
n2 = n2/2
kn2 = kn2/2
ia= ia1
kj = 1
do j = 1,n2
wt = w(ia)
ia = ia + ie
ki = kj
do i = j,n,n1
kl = ki + kn2
zt = z(ki) - z(kl)
z(ki) = z(ki) + z(kl)
z(kl) = wt*zt
ki = ki+kn1
end do
kj = kj+ks
end do
ie = ie+ie
end do
j = 1
n1 = n - 1
ki = 1
kj = 1
do i=1,n1
if(i.lt.j) then
zt = z(kj)
z(kj) = z(ki)
z(ki) = zt
endif
k = n/2
do while (k.lt.j)
j = j - k
k = k/2
end do
j = j + k
kj = ks*(j-1) + 1
ki = ki + ks
end do
return
end
subroutine ifft2d(field, m, n)
integer m, n, i ,j
complex field(n, n)
complex xlong(2000)
do i = 1,n
do j = 1,n
xlong(j) = field(i,j)
end do
call ifft1d(xlong, m, n)
do j = 1,n
field(i,j) = xlong(j)
end do
end do
do j = 1,n
call ifft1d(field(1,j), m, n)
end do
return
end
subroutine ifft1d(z, m, n)
complex z(*)
complex zt,wt,w(2**15)
double precision p
integer n,m,m2
save w, m2
data m2 /-1/
if (m .eq. 0) then
return
endif
if (m .ne. m2) then
p = 6.283185307179586d0/n
do k = 1,n/2
w(k) = cmplx(cos(p*(k-1)),sin(p*(k-1)))
w(k+n/2) = conjg(w(k))
end do
m2 = m
end if
ks = 1
nlast = n
n2 = n
kn2 = ks*n
ie = 1
do k = 1,m
n1 = n2
kn1 = kn2
n2 = n2/2
kn2 = kn2/2
ia = 1
kj = 1
do j = 1,n2
wt = w(ia)
ia = ia + ie
ki = kj
do i = j,n,n1
kl = ki + kn2
zt = z(ki) - z(kl)
z(ki) = z(ki) + z(kl)
z(kl) = wt*zt
ki = ki+kn1
end do
kj = kj+ks
end do
ie = ie+ie
end do
ki = 1
do i = 1,n
z(ki) = z(ki)/float(n)
ki = ki+ks
end do
j = 1
n1 = n - 1
ki = 1
kj = 1
do i=1,n1
if(i.lt.j) then
zt = z(kj)
z(kj) = z(ki)
z(ki) = zt
endif
k = n/2
do while (k.lt.j)
j = j - k
k = k/2
end do
j = j + k
kj = ks*(j-1) + 1
ki = ki + ks
end do
return
end |
