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## Math::FFT::Libfftw3 zef:FRITH last updated on 2022-11-27

3c5976a8f2eab0f0c13ae8702fb456a750a936db/

# NAME

Math::FFT::Libfftw3::C2C - High-level bindings to libfftw3 Complex-to-Complex transform

```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!, 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(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(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

• \$.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)

## 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.

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(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:

```my \$fft = Math::FFT::Libfftw3.new(data => (1..30).flat)
@inembed, \$istride, \$idist,
@onembed, \$ostride, \$odist;
```

# NAME

Math::FFT::Libfftw3::R2C - High-level bindings to libfftw3 Real-to-Complex transform

```use v6;

use Math::FFT::Libfftw3::R2C;
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::R2C \$fft .= new: data => @in;
my @out = \$fft.execute;
put @out; # print the direct transform output
my Math::FFT::Libfftw3::R2C \$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::R2C;
use Math::FFT::Libfftw3::Constants; # needed for the FFTW_BACKWARD constant

# direct 2D transform
my Math::FFT::Libfftw3::R2C \$fft .= new: data => 1..18, dims => (6, 3);
my @out = \$fft.execute;
put @out;
# reverse 2D transform
my Math::FFT::Libfftw3::R2C \$fftr .= new: data => @out, dims => (6,3), direction => FFTW_BACKWARD;
my @outr = \$fftr.execute;
put @outr».round(10⁻¹²);
```

# DESCRIPTION

Math::FFT::Libfftw3::R2C provides an OO interface to libfftw3 and allows you to perform Real-to-Complex Fast Fourier Transforms.

The direct transform accepts an array of real numbers and outputs a half-Hermitian array of complex numbers. The reverse transform accepts a half-Hermitian array of complex numbers and outputs an array of real numbers.

## 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(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(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.

When performing the reverse transform, the output array has only real values, so the `:\$output` parameter is ignored.

## Attributes

Some of this class' attributes are readable:

• @.out

• \$.rank

• @.dims

• \$.direction

• \$.dim (used when a specialized tranform has been requested)

• \$.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)

## 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.

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(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:

```my \$fft = Math::FFT::Libfftw3::R2C.new(data => (1..30).flat)
@inembed, \$istride, \$idist,
@onembed, \$ostride, \$odist;
```

# NAME

Math::FFT::Libfftw3::R2R - High-level bindings to libfftw3 Real-to-Complex transform

```use v6;

use Math::FFT::Libfftw3::R2R;
use Math::FFT::Libfftw3::Constants; # needed for the FFTW_R2HC and FFTW_HC2R constants

my @in = (0, π/100 … 2*π)».sin;
put @in».round(10⁻¹²); # print the original array as complex values rounded to 10⁻¹²
my Math::FFT::Libfftw3::R2R \$fft .= new: data => @in, kind => FFTW_R2HC;
my @out = \$fft.execute;
put @out; # print the direct transform output
my Math::FFT::Libfftw3::R2R \$fftr .= new: data => @out, kind => FFTW_HC2R;
my @outr = \$fftr.execute;
put @outr».round(10⁻¹²); # print the backward transform output rounded to 10⁻¹²
```
```use v6;

use Math::FFT::Libfftw3::R2R;
use Math::FFT::Libfftw3::Constants; # needed for the FFTW_R2HC and FFTW_HC2R constants

# direct 2D transform
my Math::FFT::Libfftw3::R2R \$fft .= new: data => 1..18, dims => (6, 3), kind => FFTW_R2HC;
my @out = \$fft.execute;
put @out;
# reverse 2D transform
my Math::FFT::Libfftw3::R2R \$fftr .= new: data => @out, dims => (6, 3), kind => FFTW_HC2R;
my @outr = \$fftr.execute;
put @outr».round(10⁻¹²);
```

# DESCRIPTION

Math::FFT::Libfftw3::R2R provides an OO interface to libfftw3 and allows you to perform Real-to-Real Halfcomplex Fast Fourier Transforms.

The direct transform accepts an array of real numbers and outputs a half-complex array of real numbers. The reverse transform accepts a half-complex array of real numbers and outputs an array of real numbers.

## new(:\$data!, Int :\$flag? = FFTW_ESTIMATE, :\$kind!, Int :\$dim?, Int :\$thread? = NONE, Int :\$nthreads? = 1)

The first constructor accepts any Positional of type Int, Rat, Num (and IntStr, RatStr, NumStr); it allows List of Ints, Seq of Rat, shaped arrays of any base type, etc.

The only mandatory argument are @data and \$kind. Multidimensional data are expressed in row-major order (see 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 kind argument, of type fftw_r2r_kind, specifies what kind of trasform will be performed on the input data. fftw_r2r_kind constants are defined as an enum in Math::FFT::Libfftw3::Constants. The values of the fftw_r2r_kind enum are:

• FFTW_R2HC

• FFTW_HC2R

• FFTW_DHT

• FFTW_REDFT00

• FFTW_REDFT01

• FFTW_REDFT10

• FFTW_REDFT11

• FFTW_RODFT00

• FFTW_RODFT01

• FFTW_RODFT10

• FFTW_RODFT11

The Half-Complex transform uses the symbol FFTW_R2HC for a Real to Half-Complex (direct) transform, while the corresponding Half-Complex to Real (reverse) transform is specified by the symbol FFTW_HC2R. The reverse transform of FFTW_R*DFT10 is FFTW_R*DFT01 and vice versa, of FFTW_R*DFT11 is FFTW_R*DFT11, and of FFTW_R*DFT00 is FFTW_R*DFT00.

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(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), a \$flag, and a list of the kind of trasform one wants to be performed on each dimension; the meaning of all the other parameters is the same as in the other constructor.

## execute(--> Positional)

Executes the transform and returns the output array of values as a normalized row-major array.

## Attributes

Some of this class' attributes are readable:

• @.out

• \$.rank

• @.dims

• \$.direction

• @.kind

• \$.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)

## 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.

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(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:

```my \$fft = Math::FFT::Libfftw3::R2R.new(data => 1..30)
@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