modern_fftpack - A modern Fortran (2008+) library of fast Fourier transforms

An object-oriented modernization of NCAR's FFTPACK5.1.

The original work, written in fixed-form FORTRAN 77, was extensively refactored to incorporate features of free-form modern Fortran (2008+).
The library is fully Fortran 2008 (ISO/IEC 1539-1:2010) compliant;
all instances of go to's are replaced with modern control structures.
Numerous do loops are replaced with array operations to improve readability.
Potentially large automatic arrays are replaced with allocatable arrays for heap access.
Test programs are provided for the transforms. Each serves two purposes: as a template to guide you in writing your own codes utilizing the fttpack library, and as a demonstration that you can correctly produce the executables.
Ideally, type(FFTpack)'s functionality and usage will evolve into something similar to scipy.fftpack

Usage


    use, intrinsic :: ISO_C_binding, only: &
        wp => C_DOUBLE

    use fftpack_library, only: &
        FFTpack

    ! Explicit typing only
    implicit none

    type (FFTpack)            :: foo
    complex (wp), allocatable :: my_data(:)

    !.... generate some data

    ! Forward transform
    foo%fft(my_data)

    ! Backward transform
    foo%ifft(my_data)

Requirements

The GNU Make tool https://www.gnu.org/software/make/
The GNU gfortran compiler https://gcc.gnu.org/wiki/GFortran

To build the project

Type the following command line arguments


    git clone https://github.com/jlokimlin/modern_fftpack.git

    cd modern_fftpack; make all

Contributing

This project is still a work in progress and anyone is free to contribute under the proviso that they abstain from using the dreaded go to.

For bug reports or feature requests please open an issue on github.

Bibliography

[1] Swarztrauber, Paul N. "Symmetric FFTs." Mathematics of Computation 47.175 (1986): 323-346.

[2] Swarztrauber, Paul N. "FFT algorithms for vector computers." Parallel Computing 1.1 (1984): 45-63.

Result

```

program tcfft1 and related messages:
cfft1 backward-forward max error = 0.794798730345622E-015
program tcfft1 and related messages:
cfft1 forward-backward max error = 0.867111901826273E-015
end program tcfft1 and related messages

program trfft1 and related messages:
rfft1 forward-backward max error = 0.555111512312578E-015
rfft1 backward-forward max error = 0.777156117237610E-015
end program trfft1 and related messages

program tcosq1 and related messages:
cosq1 forward-backward max error = 0.777156117237610E-015
cosq1 backward-forward max error = 0.666133814775094E-015
end program tcosq1 and related messages

program tcost1 and related messages:
cost1 forward-backward max error = 0.233146835171283E-013
cost1 backward-forward max error = 0.224265050974282E-013
end program tcost1 and related messages

program tsinq1 and related messages:
sinq1 forward-backward max error = 0.777156117237610E-015
sinq1 backward-forward max error = 0.777156117237610E-015
end program tsinq1 and related messages

program tsint1 and related messages:
sint1 forward-backward max error = 0.455191440096314E-013
sint1 backward-forward max error = 0.395239396766556E-013
end program tsint1 and related messages

program tcfft2 and related messages:
cfft2 forward-backward max error = 0.948574968053509E-015
cfft2 backward-forward max error = 0.915513359704447E-015
end program tcfft2 and related messages

program trfft2 and related messages:
rfft2 forward-backward max error = 0.777156117237610E-015
rfft2 backward-forward max error = 0.832667268468867E-015
end program trfft2 and related messages

This result was compiled by GCC version 5.3.1 20160409 using the options -I ../lib -mtune=generic -march=x86-64 -O3 -Wall -J ../lib

```

jlokimlin / modern_fftpack