在 Fortran 中使用 r2c 和 c2r FFTW 时，前向和后向维度是否相同？
When using r2c and c2r FFTW in Fortran, are the forward and backward dimensions same?
Blow是主档
PROGRAM SPHEROID
USE nrtype
USE SUB_INFO
INCLUDE "/usr/local/include/fftw3.f"
INTEGER(I8B) :: plan_forward, plan_backward
INTEGER(I4B) :: i, t, int_N
REAL(DP) :: cth_i, sth_i, real_i, perturbation
REAL(DP) :: PolarEffect, dummy, x1, x2, x3
REAL(DP), DIMENSION(4096) :: dummy1, dummy2, gam, th, ph
REAL(DP), DIMENSION(4096) :: k1, k2, k3, k4, l1, l2, l3, l4, f_in
COMPLEX(DPC), DIMENSION(2049) :: output1, output2, f_out
CHARACTER(1024) :: baseOutputFilename
CHARACTER(1024) :: outputFile, format_string
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
int_N = 4096
! File Open Section
format_string = '(I5.5)'
! Write the coodinates at t = 0
do i = 1, N
real_i = real(i)
gam(i) = 2d0*pi/real_N
perturbation = 0.01d0*dsin(2d0*pi*real_i/real_N)
ph(i) = 2d0*pi*real_i/real_N + perturbation
th(i) = pi/3d0 + perturbation
end do
! Initialization Section for FFTW PLANS
call dfftw_plan_dft_r2c_1d(plan_forward, int_N, f_in, f_out, FFTW_ESTIMATE)
call dfftw_plan_dft_c2r_1d(plan_backward, int_N, f_out, f_in, FFTW_ESTIMATE)
! Runge-Kutta 4th Order Method Section
do t = 1, Iter_N
call integration(th, ph, gam, k1, l1)
do i = 1, N
dummy1(i) = th(i) + 0.5d0*dt*k1(i)
end do
do i = 1, N
dummy2(i) = ph(i) + 0.5d0*dt*l1(i)
end do
call integration(dummy1, dummy2, gam, k2, l2)
do i = 1, N
dummy1(i) = th(i) + 0.5d0*dt*k2(i)
end do
do i = 1, N
dummy2(i) = ph(i) + 0.5d0*dt*l2(i)
end do
call integration(dummy1, dummy2, gam, k3, l3)
do i = 1, N
dummy1(i) = th(i) + dt*k3(i)
end do
do i = 1, N
dummy2(i) = ph(i) + dt*l3(i)
end do
call integration(dummy1, dummy2, gam, k4, l4)
do i = 1, N
cth_i = dcos(th(i))
sth_i = dsin(th(i))
PolarEffect = (nv-sv)*dsqrt(1d0+a*sth_i**2) + (nv+sv)*cth_i
PolarEffect = PolarEffect/(sth_i**2)
th(i) = th(i) + dt*(k1(i) + 2d0*k2(i) + 2d0*k3(i) + k4(i))/6d0
ph(i) = ph(i) + dt*(l1(i) + 2d0*l2(i) + 2d0*l3(i) + l4(i))/6d0
ph(i) = ph(i) + dt*0.25d0*PolarEffect/pi
end do
!! Fourier Filtering Section
call dfftw_execute_dft_r2c(plan_forward, th, output1)
do i = 1, N/2+1
dummy = abs(output1(i))
if (dummy.lt.threshhold) then
output1(i) = dcmplx(0.0d0)
end if
end do
call dfftw_execute_dft_c2r(plan_backward, output1, th)
do i = 1, N
th(i) = th(i)/real_N
end do
call dfftw_execute_dft_r2c(plan_forward, ph, output2)
do i = 1, N/2+1
dummy = abs(output2(i))
if (dummy.lt.threshhold) then
output2(i) = dcmplx(0.0d0)
end if
end do
call dfftw_execute_dft_c2r(plan_backward, output2, ph)
do i = 1, N
ph(i) = ph(i)/real_N
end do
!! Data Writing Section
write(baseOutputFilename, format_string) t
outputFile = "xyz" // baseOutputFilename
open(unit=7, file=outputFile)
outputFile = "Fsptrm" // baseOutputFilename
open(unit=8, file=outputFile)
do i = 1, N
x1 = dsin(th(i))*dcos(ph(i))
x2 = dsin(th(i))*dsin(ph(i))
x3 = dsqrt(1d0+a)*dcos(th(i))
write(7,*) x1, x2, x3
end do
do i = 1, N/2+1
write(8,*) abs(output1(i)), abs(output2(i))
end do
close(7)
close(8)
do i = 1, N/2+1
output1(i) = dcmplx(0.0d0)
end do
do i = 1, N/2+1
output2(i) = dcmplx(0.0d0)
end do
end do
! Destroying Process for FFTW PLANS
call dfftw_destroy_plan(plan_forward)
call dfftw_destroy_plan(plan_backward)
END PROGRAM
下面是集成的子程序文件
! We implemented Shelly's spectrally accurate convergence method
SUBROUTINE integration(in1,in2,in3,out1,out2)
USE nrtype
USE SUB_INFO
INTEGER(I4B) :: i, j
REAL(DP) :: th_i, th_j, gi, ph_i, ph_j, gam_j, v1, v2
REAL(DP), DIMENSION(N), INTENT(INOUT) :: in1, in2, in3, out1, out2
REAL(DP) :: ui, uj, part1, part2, gj, cph, sph
REAL(DP) :: denom, numer, temp
do i = 1, N
out1(i) = 0d0
end do
do i = 1, N
out2(i) = 0d0
end do
do i = 1, N
th_i = in1(i)
ph_i = in2(i)
ui = dcos(th_i)
part1 = dsqrt(1d0+a)/(dsqrt(-a)*ui+dsqrt(1d0+a-a*ui*ui))
part1 = part1**(dsqrt(-a))
part2 = (dsqrt(1d0+a-a*ui*ui)+ui)/(dsqrt(1d0+a-a*ui*ui)-ui)
part2 = dsqrt(part2)
gi = dsqrt(1d0-ui*ui)*part1*part2
do j = 1, N
if (mod(i+j,2).eq.1) then
th_j = in1(j)
ph_j = in2(j)
gam_j = in3(j)
uj = dcos(th_j)
part1 = dsqrt(1d0+a)/(dsqrt(-a)*uj+dsqrt(1d0+a-a*uj*uj))
part1 = part1**(dsqrt(-a))
part2 = (dsqrt(1d0+a-a*uj*uj)+uj)/(dsqrt(1d0+a-a*uj*uj)-uj)
part2 = dsqrt(part2)
gj = dsqrt(1d0-ui*ui)*part1*part2
cph = dcos(ph_i-ph_j)
sph = dsin(ph_i-ph_j)
numer = dsqrt(1d0-uj*uj)*sph
denom = (gj/gi*(1d0-ui*ui) + gi/gj*(1d0-uj*uj))*0.5d0
denom = denom - dsqrt((1d0-ui*ui)*(1d0-uj*uj))*cph
denom = denom + krasny_delta
v1 = -0.25d0*gam_j*numer/denom/pi
temp = dsqrt(1d0+(1d0-ui*ui)*a)
numer = -(gj/gi)*(temp+ui)
numer = numer + (gi/gj)*((1d0-uj*uj)/(1d0-ui*ui))*(temp-ui)
numer = numer + 2d0*ui*dsqrt((1d0-uj*uj)/(1d0-ui*ui))*cph
numer = 0.5d0*numer
v2 = -0.25d0*gam_j*numer/denom/pi
out1(i) = out1(i) + 2d0*v1
out2(i) = out2(i) + 2d0*v2
end if
end do
end do
END
下面是模块文件
module nrtype
Implicit none
!integer
INTEGER, PARAMETER :: I8B = SELECTED_INT_KIND(20)
INTEGER, PARAMETER :: I4B = SELECTED_INT_KIND(9)
INTEGER, PARAMETER :: I2B = SELECTED_INT_KIND(4)
INTEGER, PARAMETER :: I1B = SELECTED_INT_KIND(2)
!real
INTEGER, PARAMETER :: SP = KIND(1.0)
INTEGER, PARAMETER :: DP = KIND(1.0D0)
!complex
INTEGER, PARAMETER :: SPC = KIND((1.0,1.0))
INTEGER, PARAMETER :: DPC = KIND((1.0D0,1.0D0))
!defualt logical
INTEGER, PARAMETER :: LGT = KIND(.true.)
!mathematical constants
REAL(DP), PARAMETER :: pi = 3.141592653589793238462643383279502884197_dp
!derived data type s for sparse matrices,single and double precision
!User-Defined Constants
INTEGER(I4B), PARAMETER :: N = 4096, Iter_N = 20000
REAL(DP), PARAMETER :: real_N = 4096d0
REAL(DP), PARAMETER :: a = -0.1d0, dt = 0.001d0, krasny_delta = 0.01d0
REAL(DP), PARAMETER :: nv = 0d0, sv = 0d0, threshhold = 0.00000000001d0
!N : The Number of Point Vortices, Iter_N * dt = Total time, dt : Time Step
!krasny_delta : Smoothing Parameter introduced by R.Krasny
!nv : Northern Vortex Strength, sv : Southern Vortex Strength
!a : The Eccentricity in the direction of z , threshhold : Filtering Threshhold
end module nrtype
下面是一个子程序信息文件
MODULE SUB_INFO
INTERFACE
SUBROUTINE integration(in1,in2,in3,out1,out2)
USE nrtype
INTEGER(I4B) :: i, j
REAL(DP) :: th_i, th_j, gi, ph_i, ph_j, gam_j, v1, v2
REAL(DP), DIMENSION(N), INTENT(INOUT) :: in1, in2, in3, out1, out2
REAL(DP) :: ui, uj, part1, part2, gj, cph, sph
REAL(DP) :: denom, numer, temp
END SUBROUTINE
END INTERFACE
END MODULE
我使用以下命令编译了它们
gfortran -o p0 -fbounds-check nrtype.f90 spheroid_sub_info.f90 spheroid_sub_integration.f90 spheroid_main.f90 -lfftw3 -lm -Wall -pedantic -pg
nohup./p0 &
注意 2049 = 4096 / 2 + 1
做plan_backward的时候，输出的维度是2049，所以用2049代替4096不对吗？
但是当我这样做的时候，它爆炸了。 （炸毁表示NAN错误）
如果我用4096制作plan_backward，一切都很好，除了一些傅里叶系数异常大，这是不应该发生的。
请帮助我在 Fortran 中正确使用 FFTW。这个问题郁闷了我好久
首先，虽然你说你的例子是最小的，但它仍然很大，我没有时间研究它。
但我更新了要点代码 https://gist.github.com/LadaF/73eb430682ef527eea9972ceb96116c5 以显示反向变换并回答有关变换维度的标题问题。
变换的逻辑大小是实际数组的大小 (Real-data DFT Array Format)，但由于固有的对称性，复数部分较小。
但是，当您首先将 r2c 从大小为 n 的实数数组转换为大小为 n/2+1 的复数数组时。然后反向变换，真实数组的大小应该再次为 n.
这是我的要点中的最小示例：
module FFTW3
use, intrinsic :: iso_c_binding
include "fftw3.f03"
end module
use FFTW3
implicit none
integer, parameter :: n = 100
real(c_double), allocatable :: data_in(:)
complex(c_double_complex), allocatable :: data_out(:)
type(c_ptr) :: planf, planb
allocate(data_in(n))
allocate(data_out(n/2+1))
call random_number(data_in)
planf = fftw_plan_dft_r2c_1d(size(data_in), data_in, data_out, FFTW_ESTIMATE+FFTW_UNALIGNED)
planb = fftw_plan_dft_c2r_1d(size(data_in), data_out, data_in, FFTW_ESTIMATE+FFTW_UNALIGNED)
print *, "real input:", real(data_in)
call fftw_execute_dft_r2c(planf, data_in, data_out)
print *, "result real part:", real(data_out)
print *, "result imaginary part:", aimag(data_out)
call fftw_execute_dft_c2r(planb, data_out, data_in)
print *, "real output:", real(data_in)/n
call fftw_destroy_plan(planf)
call fftw_destroy_plan(planb)
end
请注意，我使用的是现代 Fortran 界面。我不喜欢用旧的。
一个问题可能是 dfftw_execute_dft_c2r 会破坏输入数组的内容，如 page 中所述。关键摘录是
FFTW_PRESERVE_INPUT specifies that an out-of-place transform must not change its input array. This is ordinarily the default, except for c2r and hc2r (i.e. complex-to-real) transforms for which FFTW_DESTROY_INPUTis the default...
我们可以验证这一点，例如，通过修改@VladimirF 的示例代码，使其在第一次 FFT(r2c) 调用后立即将 data_out 保存到 data_save，然后计算它们第二次 FFT (c2r) 调用后的差异。因此，对于 OP 的代码，在进入第二个 FFT（c2r）之前将 output1 和 output2 保存到不同的数组似乎更安全。
Blow是主档
PROGRAM SPHEROID
USE nrtype
USE SUB_INFO
INCLUDE "/usr/local/include/fftw3.f"
INTEGER(I8B) :: plan_forward, plan_backward
INTEGER(I4B) :: i, t, int_N
REAL(DP) :: cth_i, sth_i, real_i, perturbation
REAL(DP) :: PolarEffect, dummy, x1, x2, x3
REAL(DP), DIMENSION(4096) :: dummy1, dummy2, gam, th, ph
REAL(DP), DIMENSION(4096) :: k1, k2, k3, k4, l1, l2, l3, l4, f_in
COMPLEX(DPC), DIMENSION(2049) :: output1, output2, f_out
CHARACTER(1024) :: baseOutputFilename
CHARACTER(1024) :: outputFile, format_string
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
int_N = 4096
! File Open Section
format_string = '(I5.5)'
! Write the coodinates at t = 0
do i = 1, N
real_i = real(i)
gam(i) = 2d0*pi/real_N
perturbation = 0.01d0*dsin(2d0*pi*real_i/real_N)
ph(i) = 2d0*pi*real_i/real_N + perturbation
th(i) = pi/3d0 + perturbation
end do
! Initialization Section for FFTW PLANS
call dfftw_plan_dft_r2c_1d(plan_forward, int_N, f_in, f_out, FFTW_ESTIMATE)
call dfftw_plan_dft_c2r_1d(plan_backward, int_N, f_out, f_in, FFTW_ESTIMATE)
! Runge-Kutta 4th Order Method Section
do t = 1, Iter_N
call integration(th, ph, gam, k1, l1)
do i = 1, N
dummy1(i) = th(i) + 0.5d0*dt*k1(i)
end do
do i = 1, N
dummy2(i) = ph(i) + 0.5d0*dt*l1(i)
end do
call integration(dummy1, dummy2, gam, k2, l2)
do i = 1, N
dummy1(i) = th(i) + 0.5d0*dt*k2(i)
end do
do i = 1, N
dummy2(i) = ph(i) + 0.5d0*dt*l2(i)
end do
call integration(dummy1, dummy2, gam, k3, l3)
do i = 1, N
dummy1(i) = th(i) + dt*k3(i)
end do
do i = 1, N
dummy2(i) = ph(i) + dt*l3(i)
end do
call integration(dummy1, dummy2, gam, k4, l4)
do i = 1, N
cth_i = dcos(th(i))
sth_i = dsin(th(i))
PolarEffect = (nv-sv)*dsqrt(1d0+a*sth_i**2) + (nv+sv)*cth_i
PolarEffect = PolarEffect/(sth_i**2)
th(i) = th(i) + dt*(k1(i) + 2d0*k2(i) + 2d0*k3(i) + k4(i))/6d0
ph(i) = ph(i) + dt*(l1(i) + 2d0*l2(i) + 2d0*l3(i) + l4(i))/6d0
ph(i) = ph(i) + dt*0.25d0*PolarEffect/pi
end do
!! Fourier Filtering Section
call dfftw_execute_dft_r2c(plan_forward, th, output1)
do i = 1, N/2+1
dummy = abs(output1(i))
if (dummy.lt.threshhold) then
output1(i) = dcmplx(0.0d0)
end if
end do
call dfftw_execute_dft_c2r(plan_backward, output1, th)
do i = 1, N
th(i) = th(i)/real_N
end do
call dfftw_execute_dft_r2c(plan_forward, ph, output2)
do i = 1, N/2+1
dummy = abs(output2(i))
if (dummy.lt.threshhold) then
output2(i) = dcmplx(0.0d0)
end if
end do
call dfftw_execute_dft_c2r(plan_backward, output2, ph)
do i = 1, N
ph(i) = ph(i)/real_N
end do
!! Data Writing Section
write(baseOutputFilename, format_string) t
outputFile = "xyz" // baseOutputFilename
open(unit=7, file=outputFile)
outputFile = "Fsptrm" // baseOutputFilename
open(unit=8, file=outputFile)
do i = 1, N
x1 = dsin(th(i))*dcos(ph(i))
x2 = dsin(th(i))*dsin(ph(i))
x3 = dsqrt(1d0+a)*dcos(th(i))
write(7,*) x1, x2, x3
end do
do i = 1, N/2+1
write(8,*) abs(output1(i)), abs(output2(i))
end do
close(7)
close(8)
do i = 1, N/2+1
output1(i) = dcmplx(0.0d0)
end do
do i = 1, N/2+1
output2(i) = dcmplx(0.0d0)
end do
end do
! Destroying Process for FFTW PLANS
call dfftw_destroy_plan(plan_forward)
call dfftw_destroy_plan(plan_backward)
END PROGRAM
下面是集成的子程序文件
! We implemented Shelly's spectrally accurate convergence method
SUBROUTINE integration(in1,in2,in3,out1,out2)
USE nrtype
USE SUB_INFO
INTEGER(I4B) :: i, j
REAL(DP) :: th_i, th_j, gi, ph_i, ph_j, gam_j, v1, v2
REAL(DP), DIMENSION(N), INTENT(INOUT) :: in1, in2, in3, out1, out2
REAL(DP) :: ui, uj, part1, part2, gj, cph, sph
REAL(DP) :: denom, numer, temp
do i = 1, N
out1(i) = 0d0
end do
do i = 1, N
out2(i) = 0d0
end do
do i = 1, N
th_i = in1(i)
ph_i = in2(i)
ui = dcos(th_i)
part1 = dsqrt(1d0+a)/(dsqrt(-a)*ui+dsqrt(1d0+a-a*ui*ui))
part1 = part1**(dsqrt(-a))
part2 = (dsqrt(1d0+a-a*ui*ui)+ui)/(dsqrt(1d0+a-a*ui*ui)-ui)
part2 = dsqrt(part2)
gi = dsqrt(1d0-ui*ui)*part1*part2
do j = 1, N
if (mod(i+j,2).eq.1) then
th_j = in1(j)
ph_j = in2(j)
gam_j = in3(j)
uj = dcos(th_j)
part1 = dsqrt(1d0+a)/(dsqrt(-a)*uj+dsqrt(1d0+a-a*uj*uj))
part1 = part1**(dsqrt(-a))
part2 = (dsqrt(1d0+a-a*uj*uj)+uj)/(dsqrt(1d0+a-a*uj*uj)-uj)
part2 = dsqrt(part2)
gj = dsqrt(1d0-ui*ui)*part1*part2
cph = dcos(ph_i-ph_j)
sph = dsin(ph_i-ph_j)
numer = dsqrt(1d0-uj*uj)*sph
denom = (gj/gi*(1d0-ui*ui) + gi/gj*(1d0-uj*uj))*0.5d0
denom = denom - dsqrt((1d0-ui*ui)*(1d0-uj*uj))*cph
denom = denom + krasny_delta
v1 = -0.25d0*gam_j*numer/denom/pi
temp = dsqrt(1d0+(1d0-ui*ui)*a)
numer = -(gj/gi)*(temp+ui)
numer = numer + (gi/gj)*((1d0-uj*uj)/(1d0-ui*ui))*(temp-ui)
numer = numer + 2d0*ui*dsqrt((1d0-uj*uj)/(1d0-ui*ui))*cph
numer = 0.5d0*numer
v2 = -0.25d0*gam_j*numer/denom/pi
out1(i) = out1(i) + 2d0*v1
out2(i) = out2(i) + 2d0*v2
end if
end do
end do
END
下面是模块文件
module nrtype
Implicit none
!integer
INTEGER, PARAMETER :: I8B = SELECTED_INT_KIND(20)
INTEGER, PARAMETER :: I4B = SELECTED_INT_KIND(9)
INTEGER, PARAMETER :: I2B = SELECTED_INT_KIND(4)
INTEGER, PARAMETER :: I1B = SELECTED_INT_KIND(2)
!real
INTEGER, PARAMETER :: SP = KIND(1.0)
INTEGER, PARAMETER :: DP = KIND(1.0D0)
!complex
INTEGER, PARAMETER :: SPC = KIND((1.0,1.0))
INTEGER, PARAMETER :: DPC = KIND((1.0D0,1.0D0))
!defualt logical
INTEGER, PARAMETER :: LGT = KIND(.true.)
!mathematical constants
REAL(DP), PARAMETER :: pi = 3.141592653589793238462643383279502884197_dp
!derived data type s for sparse matrices,single and double precision
!User-Defined Constants
INTEGER(I4B), PARAMETER :: N = 4096, Iter_N = 20000
REAL(DP), PARAMETER :: real_N = 4096d0
REAL(DP), PARAMETER :: a = -0.1d0, dt = 0.001d0, krasny_delta = 0.01d0
REAL(DP), PARAMETER :: nv = 0d0, sv = 0d0, threshhold = 0.00000000001d0
!N : The Number of Point Vortices, Iter_N * dt = Total time, dt : Time Step
!krasny_delta : Smoothing Parameter introduced by R.Krasny
!nv : Northern Vortex Strength, sv : Southern Vortex Strength
!a : The Eccentricity in the direction of z , threshhold : Filtering Threshhold
end module nrtype
下面是一个子程序信息文件
MODULE SUB_INFO
INTERFACE
SUBROUTINE integration(in1,in2,in3,out1,out2)
USE nrtype
INTEGER(I4B) :: i, j
REAL(DP) :: th_i, th_j, gi, ph_i, ph_j, gam_j, v1, v2
REAL(DP), DIMENSION(N), INTENT(INOUT) :: in1, in2, in3, out1, out2
REAL(DP) :: ui, uj, part1, part2, gj, cph, sph
REAL(DP) :: denom, numer, temp
END SUBROUTINE
END INTERFACE
END MODULE
我使用以下命令编译了它们
gfortran -o p0 -fbounds-check nrtype.f90 spheroid_sub_info.f90 spheroid_sub_integration.f90 spheroid_main.f90 -lfftw3 -lm -Wall -pedantic -pg
nohup./p0 &
注意 2049 = 4096 / 2 + 1
做plan_backward的时候，输出的维度是2049，所以用2049代替4096不对吗？
但是当我这样做的时候，它爆炸了。 （炸毁表示NAN错误）
如果我用4096制作plan_backward，一切都很好，除了一些傅里叶系数异常大，这是不应该发生的。
请帮助我在 Fortran 中正确使用 FFTW。这个问题郁闷了我好久
首先，虽然你说你的例子是最小的，但它仍然很大，我没有时间研究它。
但我更新了要点代码 https://gist.github.com/LadaF/73eb430682ef527eea9972ceb96116c5 以显示反向变换并回答有关变换维度的标题问题。
变换的逻辑大小是实际数组的大小 (Real-data DFT Array Format)，但由于固有的对称性，复数部分较小。
但是，当您首先将 r2c 从大小为 n 的实数数组转换为大小为 n/2+1 的复数数组时。然后反向变换，真实数组的大小应该再次为 n.
这是我的要点中的最小示例：
module FFTW3
use, intrinsic :: iso_c_binding
include "fftw3.f03"
end module
use FFTW3
implicit none
integer, parameter :: n = 100
real(c_double), allocatable :: data_in(:)
complex(c_double_complex), allocatable :: data_out(:)
type(c_ptr) :: planf, planb
allocate(data_in(n))
allocate(data_out(n/2+1))
call random_number(data_in)
planf = fftw_plan_dft_r2c_1d(size(data_in), data_in, data_out, FFTW_ESTIMATE+FFTW_UNALIGNED)
planb = fftw_plan_dft_c2r_1d(size(data_in), data_out, data_in, FFTW_ESTIMATE+FFTW_UNALIGNED)
print *, "real input:", real(data_in)
call fftw_execute_dft_r2c(planf, data_in, data_out)
print *, "result real part:", real(data_out)
print *, "result imaginary part:", aimag(data_out)
call fftw_execute_dft_c2r(planb, data_out, data_in)
print *, "real output:", real(data_in)/n
call fftw_destroy_plan(planf)
call fftw_destroy_plan(planb)
end
请注意，我使用的是现代 Fortran 界面。我不喜欢用旧的。
一个问题可能是 dfftw_execute_dft_c2r 会破坏输入数组的内容，如 page 中所述。关键摘录是
FFTW_PRESERVE_INPUTspecifies that an out-of-place transform must not change its input array. This is ordinarily the default, except for c2r and hc2r (i.e. complex-to-real) transforms for whichFFTW_DESTROY_INPUTis the default...
我们可以验证这一点，例如，通过修改@VladimirF 的示例代码，使其在第一次 FFT(r2c) 调用后立即将 data_out 保存到 data_save，然后计算它们第二次 FFT (c2r) 调用后的差异。因此，对于 OP 的代码，在进入第二个 FFT（c2r）之前将 output1 和 output2 保存到不同的数组似乎更安全。