C2C
NAME
Math::FFT::Libfftw3::C2C - High-level bindings to libfftw3 Complex-to-Complex transform
SYNOPSIS
use v6;
use Math::FFT::Libfftw3::C2C;
use Math::FFT::Libfftw3::Constants; # needed for the FFTW_BACKWARD constant
my @in = (0, π/100 … 2*π)».sin;
put @in».Complex».round(10⁻¹²); # print the original array as complex values rounded to 10⁻¹²
my Math::FFT::Libfftw3::C2C $fft .= new: data => @in;
my @out = $fft.execute;
put @out; # print the direct transform output
my Math::FFT::Libfftw3::C2C $fftr .= new: data => @out, direction => FFTW_BACKWARD;
my @outr = $fftr.execute;
put @outr».round(10⁻¹²); # print the backward transform output rounded to 10⁻¹²
use v6;
use Math::FFT::Libfftw3::C2C;
use Math::FFT::Libfftw3::Constants; # needed for the FFTW_BACKWARD constant
# direct 2D transform
my Math::FFT::Libfftw3::C2C $fft .= new: data => 1..18, dims => (6, 3);
my @out = $fft.execute;
put @out;
# reverse 2D transform
my Math::FFT::Libfftw3::C2C $fftr .= new: data => @out, dims => (6,3), direction => FFTW_BACKWARD;
my @outr = $fftr.execute;
put @outr».round(10⁻¹²);
DESCRIPTION
Math::FFT::Libfftw3::C2C provides an OO interface to libfftw3 and allows you to perform Complex-to-Complex Fast Fourier Transforms.
new(:@data!, :@dims?, Int :$direction? = FFTW_FORWARD, Int :$flag? = FFTW_ESTIMATE, Int :$dim?, Int :$thread? = NONE, Int :$nthreads? = 1)
new(:$data!, Int :$direction? = FFTW_FORWARD, Int :$flag? = FFTW_ESTIMATE, Int :$dim?, Int :$thread? = NONE, Int :$nthreads? = 1)
The first constructor accepts any Positional of type Int, Rat, Num, Complex (and IntStr, RatStr, NumStr, ComplexStr); it allows List of Ints, Array of Complex, Seq of Rat, shaped arrays of any base type, etc.
The only mandatory argument is @data. Multidimensional data are expressed in row-major order (see C Library Documentation) and the array @dims must be passed to the constructor, or the data will be interpreted as a 1D array. If one uses a shaped array, there's no need to pass the @dims array, because the dimensions will be read from the array itself.
The $direction parameter is used to specify a direct or backward transform; it defaults to FFTW_FORWARD.
The $flag parameter specifies the way the underlying library has to analyze the data in order to create a plan for the transform; it defaults to FFTW_ESTIMATE (see C Library Documentation).
The $dim parameter asks for an optimization for a specific matrix rank. The parameter is optional and if present must be in the range 1..3.
The $thread parameter specifies the kind of threaded operation one wants to get; this argument is optional and if not specified is assumed as NONE. There are three possibile values:
NONE
THREAD
OPENMP
THREAD will use specific POSIX thread library while OPENMP will select an OpenMP library.
The $nthreads specifies the number of threads to use; it defaults to 1.
The second constructor accepts a scalar: an object of type Math::Matrix (if that module is installed, otherwise it returns a Failure); the meaning of all the other parameters is the same as in the other constructor.
execute(Int :$output? = OUT-COMPLEX --> Positional)
Executes the transform and returns the output array of values as a normalized row-major array. The parameter $output can be optionally used to specify how the array is to be returned:
OUT-COMPLEX
OUT-REIM
OUT-NUM
The default (OUT-COMPLEX) is to return an array of Complex.
OUT-REIM makes the execute method return the native representation of the data: an array of couples of
real/imaginary values.
OUT-NUM makes the execute method return just the real part of the complex values.
Attributes
Some of this class' attributes are readable:
@.out
$.rank
@.dims
$.direction
$.dim (used when a specialized tranform has been requested)
$.flag (how to compute a plan)
$.adv (normal or advanced interface)
$.howmany (only for the advanced interface)
$.istride (only for the advanced interface)
$.ostride (only for the advanced interface)
$.idist (only for the advanced interface)
$.odist (only for the advanced interface)
@.inembed (only for the advanced interface)
@.onembed (only for the advanced interface)
$.thread (only for the threaded model)
Wisdom interface
This interface allows to save and load a plan associated to a transform (There are some caveats. See C Library Documentation).
plan-save(Str $filename --> True)
Saves the plan into a file. Returns True if successful and a Failure object otherwise.
plan-load(Str $filename --> True)
Loads the plan from a file. Returns True if successful and a Failure object otherwise.
Advanced interface
This interface allows to compose several transformations in one pass. See C Library Documentation.
advanced(Int $rank!, @dims!, Int $howmany!, @inembed!, Int $istride!, Int $idist!, @onembed!, Int $ostride!, Int $odist!)
This method activates the advanced interface. The meaning of the arguments are detailed in the C Library Documentation.
This method returns self, so it can be concatenated to the .new() method:
my $fft = Math::FFT::Libfftw3::C2C.new(data => (1..30).flat)
.advanced: $rank, @dims, $howmany,
@inembed, $istride, $idist,
@onembed, $ostride, $odist;
C Library Documentation
For more details on libfftw see http://www.fftw.org/. The manual is available here http://www.fftw.org/fftw3.pdf
Prerequisites
This module requires the libfftw3 library to be installed. Please follow the instructions below based on your platform:
Debian Linux
sudo apt-get install libfftw3-double3
The module looks for a library called libfftw3.so.
Installation
To install it using zef (a module management tool):
$ zef install Math::FFT::Libfftw3
Testing
To run the tests:
$ prove -e "raku -Ilib"
Notes
Math::FFT::Libfftw3 relies on a C library which might not be present in one's installation, so it's not a substitute for a pure Raku module. If you need a pure Raku module, Math::FourierTransform works just fine.
This module needs Raku ≥ 2018.09 only if one wants to use shaped arrays as input data. An attempt to feed a shaped
array to the new method using $*RAKU.compiler.version < v2018.09 results in an exception.
Author
Fernando Santagata
License
The Artistic License 2.0