fftw and online DFT calculator get different results

Question

I calculated the FFT of array {1,2,3,4,5,6} with fftw/C++ and an online calculator (http://calculator-fx.com/calculator/fast-fourier-transform-calculator-fft/1d-discrete-fourier-transform). And the results seemed to be a bit different.

fftw output:

0     21.000000      0.000000
1     -3.000000      5.196152
2     -3.000000      1.732051
3     -3.000000      0.000000
4      0.000000      0.000000
5      0.000000      0.000000

Online calculator output:

 21 + 0j
 -3 + 5.196152j
 -3 + 1.732051j
 -3 + 0j
 -3 - 1.732051j
 -3 - 5.196152j

As is shown above, the latter two results of fftw turned to be zero. Can't figure out why. Could anybody help me out? Thanks.

[EDITED] cpp code:

int main()
{
    fftw_complex *out;
    fftw_plan plan;

    double arr[]={1,2,3,4,5,6};
    int n = sizeof(arr)/sizeof(double);

    out = (fftw_complex*)fftw_malloc ( sizeof ( fftw_complex ) * n );
    plan = fftw_plan_dft_r2c_1d ( n, arr, out, FFTW_ESTIMATE );
    fftw_execute ( plan );

    for (int i = 0; i < n; i++ )
    {
        printf ( "  %3d  %12lf  %12lf\n", i, out[i][0], out[i][1] );
    }

    fftw_free(out);
    fftw_destroy_plan(plan);
    return 0;
}

Answer 1

Oh, you're using the R2C mode (don't know why I didn't think of that before). That only writes n/2 + 1 results, because of the symmetry.

This behaviour is documented: http://www.fftw.org/doc/One_002dDimensional-DFTs-of-Real-Data.html.