Blitz++ & FFTW

Shakes
2006-06-27
2013-05-09
  • Shakes
    Shakes
    2006-06-27

    The following is the code for getting FFT's on Blitz Arrays using the mature and highly recognised FFTW C Library.

    template <typename type, int size>
    void FourierTransform<type,size>::FFTW(Array<complex<double>,2> &field, Array<complex<double>,2> &fftOfField)
    {
        complex<double> *ptrField, *ptrFFT;
        fftw_plan plan;

        ptrField = field.data();
        ptrFFT = fftOfField.data();
        plan = fftw_plan_dft_2d(field.rows(),field.cols(),reinterpret_cast<fftw_complex*>(ptrField),reinterpret_cast<fftw_complex*>(ptrFFT),FFTW_FORWARD,FFTW_ESTIMATE);

        fftw_execute(plan);

        fftw_destroy_plan(plan);
    }

    I have tested and its does work. Note that this works because as FFTW points out:
    "C++ has its own complex<T> template class, defined in the standard <complex> header file.
    Reportedly, the C++ standards committee has recently agreed to mandate that the storage
    format used for this type be binary-compatible with the C99 type, i.e. an array T[2] with
    consecutive real [0] and imaginary [1] parts. (See report WG21/N1388.) Although not
    part of the official standard as of this writing, the proposal stated that: “This solution has
    been tested with all current major implementations of the standard library and shown to
    be working.” To the extent that this is true, if you have a variable complex<double> *x,
    you can pass it directly to FFTW via reinterpret_cast<fftw_complex*>(x)."

    Also data reordering has to be done if DC is wanted in the centre (http://www.fftw.org/faq/section3.html#centerorigin). I have done it in the following:
    void FourierTransform<type,size>::centerDC(Array<complex<double>,2> &field, Array<complex<double>,2> &result)
    {
        Array<complex<double>,2> tmp(field.rows(),field.cols());

        for(int k = 0; k < field.cols(); k ++)
            for(int j = 0; j < field.rows(); j ++)
                tmp((j+field.rows()/2)%field.rows(),(k+field.cols()/2)%field.cols()) = field(j,k);

        result = tmp;
    }

    Code Excerpt is taken from the FourierTransform Class in the up and coming Quantum Mechanics and Discrete Geometry Toolkit based on Blitz++ and Qt - qC++ (qcplusplus.sourceforge.net). It currently supports BEC simulations and the Fourier class can be found in the Subversion area.

    Keep up the good work guys, more work on the tiny stuff would be appreciated :)

    Cheers
    Shakes
    PS: Subversion migration? :P