I'd like to use FFTW's "advanced" interface to compute the Fourier transform of the "fast" and "slow" axis of a 2D array individually. The input data are real. An in-place transform is required. I will attach a simple Fortran 90 test program which illustrates a problem that I'm having. The program initializes a FFTW "padded" real array to a constant value of 1.0. It runs the r2c/c2r FFTW advanced planner, accouting (or attempting to account) for the requisite doubling of the output stride and halving of the output distance for the r2c transform. It computes the forward FFT and shows the first three transformed vectors in the output. As the only nonzero Fourier component should be the DC, the program sums the DC components of each transformed vector and sums the remaining components. Then the program computes the inverse FFT and sums the output, checking consistency with input. !----------------------------------------------------------------------- program FFTW_2D_R2C_Decomp implicit none include 'fftw3.f' integer :: n1, n1p, n2, s1, d1, h1 integer*8 :: pf1, pb1, pf2, pb2 real, dimension(:,:), allocatable :: data ! n1-> "fast" axis, n2-> "slow" axis, n1p-> padding on "fast" axis n1=300 n2=500 n1p=2*(n1/2+1) allocate( data(n1p,n2) ) ! Input data = constant value of 1.0 for all x,y data(1:n1,:) = 1.0 ! "howmany", "dist", and "stride" for FFTW advanced interface h1 = n2; d1 = n1p; s1 = 1 !--------------------------------------------------------------------- ! First run forward/inverse 1-D FFT along "fast" axis of 2-D data !--------------------------------------------------------------------- call sfftw_plan_many_dft_r2c(pf1, 1, n1, h1, data, n1, s1, d1, data, & n1, s1*2, d1/2, FFTW_ESTIMATE) call sfftw_plan_many_dft_c2r(pb1, 1, n1, h1, data, n1, s1*2, d1/2, & data, n1, s1, d1, FFTW_ESTIMATE) call sfftw_execute(pf1) write(0,*) '--------------------------------------------' write(0,*) 'Running 1-D Forward FFT of 1-axis of 2D data' write(0,*) '--------------------------------------------' write(0,'(a,10i3)') ' 5 (real,imag) pairs for 3 1-axis FFTd vectors; each should be: ',n1,0,0,0,0,0,0,0,0,0 write(0,'(" ",10f6.2)') data(1:10,1) write(0,'(" ",10f6.2)') data(1:10,2) write(0,'(" ",10f6.2)') data(1:10,3) write(0,'(" DC sum (should be",i7,"):",f10.2)') n1*n2,sum(data(1,:)) write(0,'(" non-DC sum (should be 0):",f10.2)') sum(data(2:,:)) call sfftw_execute(pb1) data = data/n1 write(0,*) '--------------------------------------------' write(0,*) 'Running 1-D Inverse FFT of 1-axis of 2D data' write(0,*) '--------------------------------------------' write(0,'(a,5i3)') ' 5 real values for 3 1-axis reconstructed vectors; each should be: ',1,1,1,1,1 write(0,'(" ",5f6.2)') data(1:5,1) write(0,'(" ",5f6.2)') data(1:5,2) write(0,'(" ",5f6.2)') data(1:5,3) write(0,'(" sum (should be",i7,"):",f10.2)') n1*n2,sum(data) call sfftw_destroy_plan(pf1) call sfftw_destroy_plan(pb1) deallocate(data) call exit(0) end program FFTW_2D_R2C_Decomp !------------------------------------------------------------------------------- If you save this program as FFTW_2D_R2C_Decomp.f90, you can compile it with the following ifort command, provided you define "/usr/local/ include" and "/usr/local/lib" to point to your FFTW include and lib directories, respectively. ifort -O3 -vms -w -WB -I/usr/local/include FFTW_2D_R2C_Decomp.f90 -L/ usr/local/lib -lfftw3f -lfftw3 -lfftw3f_threads -lpthread -lm -o When I run ./FFTW_2D_R2C_Decomp, I obtain the following: -------------------------------------------- Running 1-D Forward FFT of 1-axis of 2D data -------------------------------------------- 5 (real,imag) pairs for 3 1-axis FFTd vectors; each should be: 300 0 0 0 0 0 0 0 0 0 300.00 0.00 1.00 1.00 0.00 0.00 1.00 1.00 0.00 0.00 300.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 300.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 DC sum (should be 150000): 150000.00 non-DC sum (should be 0): 150.00 -------------------------------------------- Running 1-D Inverse FFT of 1-axis of 2D data -------------------------------------------- 5 real values for 3 1-axis reconstructed vectors; each should be: 1 1 1 1 1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 sum (should be 150000): 149999.98 -------------------------------------------- In other words, the transformed vectors look fine, except for the first vector, which appears to have something resembling the FT of a cosine around Nyquist. The DC components have the correct magnitude. Oddly, the inverse FFT perfectly reconstructs the input. To pre-empt some questions: yes, I have RTFM'd ;-). I have run the same test program using complex-to-complex FFTs and obtain the correct result. I was even able to use the "guru" planner to compute the c2c FFT of the 2-axis of a 3D array! Although I have read the salient sections of the FFTW manual, from my results, I suspect that I've still got an "off by 1" bug in one of my dimensions. I'd appreciate it if someone who's successfully implemented this transform pair could help me out. Morgan Brown

# r2c/c2r FFTW advanced interface question/example

Started by ●December 21, 2007