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fftw3_wrapper

fftw3_wrapper is a Fortran wrapper library around FFTW, whose official introduction states that:

FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST).

fftw3_wrapper provides easy-to-use Fortran interfaces that take the burdens of cross-language interoperability, memory management, and implementation details of FFTW away from ordinary users. fftw3_wrapper tries to mimic the syntax of fft(), ifft()... from Matlab and numpy.fft.fft(), numpy.fft.ifft()... from Python NumPy. Users familiar with those programming languages should already know how to use this library.

Author

Kuan-Chih "Stargazer" Wang

Generic Interfaces

  • subroutine fft(out, inp, num)

    Compute the one-, two-, three-, or four-dimensional forward discrete Fourier transform (DFT) of input array inp into output array out by using a fast Fourier transform (FFT) algorithm.

    • out: Array; type and kind of complex(real32) or complex(real64); rank of 1, 2, 3, or 4; allocatable

      Output array containing the Fourier coefficients. It has the same kind and rank as the input array inp. Its shape is determined by the transform length num.

    • inp: Array; type and kind of complex(real32), complex(real64), real(real32), or real(real64); rank of 1, 2, 3, or 4

      Input array containing the original data.

    • num: Array; type and kind of integer; rank of 1; optional

      Transform length along each dimension of the input array inp. If num is absent, it is equivalent to specifying shape(inp). If a particular dimension length in num is smaller than that in inp, the inp is truncated. If a particular dimension length in num is larger than that in inp, the inp is padded with trailing zeros.

  • subroutine cfft(out, inp, num)

    Same as subroutine fft(out, inp, num). However, only complex-valued input array inp is accepted.

  • subroutine rfft(out, inp, num)

    Same as subroutine fft(out, inp, num). However, only real-valued input array inp is accepted.

  • subroutine fftshift(out, inp)

    Shift the zero-frequency component to the center of spectrum.

    • out: Array; type and kind of complex(real32) or complex(real64); rank of 1, 2, 3, or 4; allocatable

      Output array.

    • inp: Array; type and kind of complex(real32) or complex(real64); rank of 1, 2, 3, or 4

      Input array.

  • subroutine ifft(out, inp, num)

    Compute the one-, two-, three-, or four-dimensional inverse discrete Fourier transform (DFT) of input array inp into output array out by using a fast Fourier transform (FFT) algorithm.

    • out: Array; type and kind of complex(real32), complex(real64), real(real32), or real(real64); rank of 1, 2, 3, or 4; allocatable

      Output array containing the original data. It has the same kind and rank as the input array inp. Its shape is determined by the transform length num.

    • inp: Array; type and kind of complex(real32) or complex(real64); rank of 1, 2, 3, or 4

      Input array containing the Fourier coefficients.

    • num: Array; type and kind of integer; rank of 1; optional

      Transform length along each dimension of the input array inp. If num is absent, it is equivalent to specifying shape(inp). If a particular dimension length in num is smaller than that in inp, the inp is truncated. If a particular dimension length in num is larger than that in inp, the inp is padded with trailing zeros.

  • subroutine icfft(out, inp, num)

    Same as subroutine ifft(out, inp, num). However, only complex-valued output array out is accepted.

  • subroutine irfft(out, inp, num)

    Same as subroutine ifft(out, inp, num). However, only real-valued output array out is accepted.

  • subroutine ifftshift(out, inp)

    Inverse the actions carried out by subroutine fftshift(out, inp).

    • out: Array; type and kind of complex(real32) or complex(real64); rank of 1, 2, 3, or 4; allocatable

      Output array.

    • inp: Array; type and kind of complex(real32) or complex(real64); rank of 1, 2, 3, or 4

      Input array.

Specific Interfaces

Ordinary users should just call generic interfaces instead of these. Anyway, specific interfaces are named according to the following patterns:

{d,s}{,i}{c,r}fft{1,2,3,4}

where

  • d indicates that the arguments are double precision. s indicates that the arguments are single precision.
  • If i is absent, then it is forward FFT. If i is present, then it is inverse FFT.
  • c indicates complex-input forward FFT or complex-output inverse FFT, depending on the presence of i. r indicates real-input forward FFT or real-output inverse FFT, depending on the presence of i.
  • 1, 2, 3, and 4 indicate the dimensionality of FFT.

For example, drfft2 is a subroutine for computing double precision, real-input, and two-dimensional forward FFT. Its inverse would be dirfft2.

Compilation

  • Dependencies: FFTW (libfftw3: Double precision version; libfftw3f: Single precision version)
  • Requirements: gcc, gfortran, make

  1. Compile and install FFTW.

    # Single precision version of FFTW
./configure --prefix=/opt/fftw \
--enable-shared --enable-static \
--enable-openmp --enable-threads \
--enable-avx2 --enable-single
make
make install

# Double precision version of FFTW
./configure --prefix=/opt/fftw \
--enable-shared --enable-static \
--enable-openmp --enable-threads \
--enable-avx2
make
make install

  2. Type make. By default, Makefile expects that FFTW is installed at /opt/fftw.

    • Supply FFTWPATH=<PATH> to override the path to FFTW.
    • Supply DEBUG=1 to compile with debugging options.

    For example, suppose that you have installed FFTW under your own home directory at $HOME/fftw. You would invoke make like:

    make FFTWPATH="$HOME/fftw"

  3. Both shared (libfftw3_wrapper.so) and static (libfftw3_wrapper.a) libraries are generated along with Fortran module files (fftw3.mod and fftw3_wrapper.mod).

Testing

  • Additional Requirements: Python, NumPy

Type make check to run the self-tests, which check the implementation correctness of fftw3_wrapper against Python NumPy under different transform types, dimensions, and lengths. All results must show "PASS".

Usage

To use fftw3_wrapper in a Fortran program unit, include the following use statement near the beginning:

use :: fftw3_wrapper

When compiling, remember to specify the include paths (e.g. -I...) and link against (e.g. -L, -l...) the libfftw3_wrapper, libfftw3, and libfftw3f libraries.

To Do

  • Support CMake
  • Support FFTW wisdom
  • Support multi-threaded FFTW