#include <fftw3.h>
#include <math.h>


#define M_PI 3.14159265358979323846264338327

int main(void)
{
    int N = 16; int M = 3;

    // input data (pre transform)
    double input[N][M];
    double *in = *input;

    // result of transform (in Fourier space)
    fftw_complex output[N][M];
    fftw_complex *out = (fftw_complex *) ((void *) (*output));

    // input data (post transform) so we can compute accuracy
    double input2[N][M];
    double *in2 = *input2;


    // setup plans
    const int rank = 1; const int howmany = M;
    const int istride = M; const int ostride = M;
    const int idist = 1; const int odist = 1;

    fftw_plan fp = fftw_plan_many_dft_r2c(rank, &N, howmany,
                                          in, NULL, istride, idist,
                                          out, NULL, ostride, odist,
                                          FFTW_MEASURE);

    fftw_plan bp = fftw_plan_many_dft_c2r(rank, &N, howmany,
                                          out, NULL, istride, idist,
                                          in2, NULL, ostride, odist,
                                          FFTW_MEASURE);

    for (int j = 0; j < M; ++j)
        fprintf (stderr, "cos(%d PI x) \t\t\t", 2*(j+1));
    fprintf (stderr, "\n");

    // setup input data
    for (int i = 0; i < N; ++i)
    {
        for (int j = 0; j < M; ++j)
        {
            const double x = (double) i / (double) N;
            input[i][j] = cos(2*(j+1) * M_PI * x);
            fprintf (stderr, "input[%3d][%d] = %.9f\t", i, j, input[i][j]);
        }
        fprintf (stderr, "\n");
    }
    fprintf (stderr, "\n");



    // take the forward transform
    fftw_execute(fp); fprintf (stderr, "FFT complete!\n");

    // print output (in Fourier space)
    for (int i = 0; i <= N/2; ++i)
    {
        for (int j = 0; j < M; ++j)
        {
            fprintf (stderr, "OUT[%3d] = (%.3f + %.3fi)\t",
                    i, output[i][j][0], output[i][j][1]);
        }
        fprintf (stderr, "\n");
    }

    fprintf (stderr, "\n");



    fftw_execute(bp); fprintf (stderr, "IFFT complete!\n");

    double maxError = 0.0;

    for (int i = 0; i < N; ++i)
        for (int j = 0; j < M; ++j)
        {
            // remember that FFTW doesn't normalise
            const double error = fabs(input[i][j] - input2[i][j] / (double) N);
            if (error > maxError) maxError = error;
        }

    fprintf (stderr, "maximum error after 1 cycle: %.4g\n", maxError);

    // clean up
    fftw_destroy_plan(fp);
    fftw_destroy_plan(bp);

    return 0;
}