c++ - inverse fft of fft not returning expected data -

i'm trying make sure fftw think should do, having problems. i'm using opencv's cv::mat. made test program that, given mat f, computes ifft(fft(f)) , compares result f. expect difference between 2 negligible, there's strange pattern in data..

in case, f initialized 8x8 array of floats positive values less 1.

here's test program code:

mat f = .. //populate f if (f.type() != cv_32fc1)     dlog << "bad f type"; const int y = f.rows; const int x = f.cols; double* input = fftw_alloc_real(y * 2*(x/2 + 1)); // forward fft fftw_plan plan = fftw_plan_dft_r2c_2d(x, y, input, (fftw_complex*)input, fftw_measure); // inverse fft fftw_plan iplan = fftw_plan_dft_c2r_2d(x, y, (fftw_complex*)input, input, fftw_measure);  // populate fftw data f (int yi = 0; yi < y; ++yi) {     const float* yptr = f.ptr<float>(yi);     (int xi = 0; xi < x; ++xi)         input[yi*x + xi] = (double)yptr[xi]; }  fftw_execute(plan);  fftw_execute(iplan);  // put data cv::mat comparison mat check(y, x, f.type()); (int yi = 0; yi < y; ++yi) {     float* yptr = check.ptr<float>(yi);     (int xi = 0; xi < x ; ++xi)         yptr[xi] = (float)input[yi*x + xi]; }  dlog << util::summary(f, "f"); dlog << f; dlog << util::summary(check, "check"); dlog << check; mat diff = f*x*y - check; dlog << util::summary(diff, "diff"); dlog << diff; 

where dlog logger , util::summary(cv::mat m) prints passed string , dimensions, channels, min, , max of mat.

here's data looks (output):

f: rows:8 cols:8 chans:1 min:0.00257996 max:0.4   [0.050668437, 0.04509116, 0.033668514, 0.10986148, 0.12855141, 0.048241843, 0.12613985,.09731093;   0.028602425, 0.0092236707, 0.037089188, 0.118964, 0.075040311, 0.40000001, 0.11959606, 0.071930833;   0.0025799556, 0.051522054, 0.22233701, 0.052993439, 0.032000393, 0.12673819, 0.015244827, 0.044803992;   0.13946071, 0.019708242, 0.0112687, 0.047459811, 0.019342113, 0.030085485, 0.018739942, 0.0098618753;   0.041809395, 0.029681522, 0.026837418, 0.16038358, 0.29034778, 0.17247421, 0.1789207, 0.042179305;   0.025630442, 0.017192598, 0.060540862, 0.1854037, 0.21287154, 0.04813192, 0.042614728, 0.034764063;   0.0030835248, 0.018511582, 0.0071733585, 0.017076733, 0.064545207, 0.0026390438, 0.088922881, 0.045725599; 0.12798512, 0.23215951, 0.027465452, 0.03174505, 0.04352935, 0.025079668, 0.044403922, 0.035459157]  check: rows:8 cols:8 chans:1 min:-3.26489 max:25.6   [3.24278, 2.8858342, 2.1547849, 7.0311346, 8.2272902, 3.0874779, 8.0729504, 6.2278996;   0.30818239, 0, 2.373708, 7.6136961, 4.8025799, 25.6, 7.6541481, 4.6035733;   0.16511716, 3.2974114, -3.2648909, 0, 2.0480251, 8.1112442, 0.97566891, 2.8674555;   8.9254856, 1.2613275, 0.72119683, 3.0374279, -0.32588482, 0, 1.1993563, 0.63116002;   2.6758013, 1.8996174, 1.7175947, 10.264549, 18.582258, 11.038349, 0.042666838, 0;   1.6403483, 1.1003263, 3.8746152, 11.865837, 13.623778, 3.0804429, 2.7273426, 2.2249;   0.44932228, 0, 0.45909494, 1.0929109, 4.1308932, 0.16889881, 5.6910644, 2.9264383;   8.1910477, 14.858209, -0.071794562, 0, 2.7858784, 1.6050987, 2.841851, 2.2693861]    diff: rows:8 cols:8 chans:1 min:-0.251977 max:17.4945   [0, 0, 0, 0, 0, 0, 0, 0;   1.5223728, 0.59031492, 0, 0, 0, 0, 0, 0;   0, 0, 17.494459, 3.3915801, 0, 0, 0, 0;   0, 0, 0, 0, 1.5637801, 1.9254711, 0, 0;   0, 0, 0, 0, 0, 0, 11.408258, 2.6994755;   0, 0, 0, 0, 0, 0, 0, 0;   -0.2519767, 1.1847413, 0, 0, 0, 0, 0, 0;   0, 0, 1.8295834, 2.0316832, 0, 0, 0, 0] 

the difficult part me nonzero entries in diff matrix. i've accounted scaling fftw on values , padding needed in-place fft on real data; missing?

i find surprising data off value of 17 (which 66% of max value), when there many zeros. also, data irregularities seem form diagonal pattern.

as may have noticed when writting fftw_alloc_real(y * 2*(x/2 + 1)); fftw needs space in x direction store complex data. in case, x=8, needs 2*(x/2+1)=10 reals.

http://www.fftw.org/doc/real_002ddata-dft-array-format.html#real_002ddata-dft-array-format

so...you should take care of populate input array or retreive values it.

you way change

 input[yi*x + xi] = (double)yptr[xi]; 

for

 int xfft=2*(x/2 + 1);  ...  input[yi*xfft + xi] = (double)yptr[xi]; 

and

 yptr[xi] = (float)input[yi*x + xi]; 

for

 yptr[xi] = (float)input[yi*xfft + xi]; 

it should solve problem since non-nul points in diff correspond padding.

bye,