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[![Actions Status](https://github.com/frithnanth/perl6-Math-FFT-Libfftw3/workflows/test/badge.svg)](https://github.com/frithnanth/perl6-Math-FFT-Libfftw3/actions) ## NAME Math::FFT::Libfftw3 - An interface to libfftw3. ## SYNOPSIS ```raku 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 ``` ```raku 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 = $fftr.execute; put @outr».round(10⁻¹²); ``` For more examples see the `example` directory. ## Description Math::FFT::Libfftw3 provides an interface to libfftw3 and allows you to perform Fast Fourier Transforms. ## Documentation ### Math::FFT::Libfftw3::C2C Complex-to-Complex transform #### new(:@data!, :@dims?, Int :$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 the [C Library Documentation](#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 the [C Library Documentation](#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 * @.kind (available only in the R2R transform) * $.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](#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](#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](#c-library-documentation). This method returns `self`, so it can be concatenated to the `.new()` method: ```raku my $fft = Math::FFT::Libfftw3::C2C.new(data => (1..30).flat) .advanced: $rank, @dims, $howmany, @inembed, $istride, $idist, @onembed, $ostride, $odist; ``` ### Math::FFT::Libfftw3::R2C Real-to-Complex transform The interface for the R2C transform is slightly different. In particular: * in the `execute` method, when performing the reverse transform, the output array has only real values, so the `:$output` parameter is ignored. See the `pod` documentation inside the module for further details. ### Math::FFT::Libfftw3::R2R Real-to-Real transform This module implements several R2R transforms. The major difference is that the constructor has a new `$kind` argument, which specifies the kind of trasform that will be performed on the input data. See the `pod` documentation inside the module for further details. ## C Library documentation For more details on libfftw see [the FFTW home](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 update $ 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. ## TODO There are some alternative interfaces to implement: * The *guru* interface to apply the same plan to different data. * The *distributed-memory* interface, for parallel systems supporting the MPI message-passing interface. ## Author Fernando Santagata ## Copyright and license The Artistic License 2.0