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## Math::FFT::Libfftw3 cpan:FRITH last updated on 2019-11-30

Math-FFT-Libfftw3-0.3.4/

## Math::FFT::Libfftw3

Math::FFT::Libfftw3 - An interface to libfftw3.

## Build Status

Operating System Build Status CI Provider
Linux Travis CI

## Example

```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);
```

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!, 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) 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).

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
• 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)
• \$.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.

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;
```

### 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. The manual is available here.

## 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 "perl6 -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 Perl 6 module. If you need a pure Perl 6 module, Math::FourierTransform works just fine.

This module needs Perl 6 ≥ 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 `\$*PERL.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

The Artistic License 2.0