# 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!, :@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](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

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](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:

my $fft = Math::FFT::Libfftw3.new(data => (1..30).flat) .advanced: $rank, @dims, $howmany, @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!, :@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](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

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.

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)

$.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:

my $fft = Math::FFT::Libfftw3::R2C.new(data => (1..30).flat) .advanced: $rank, @dims, $howmany, @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!, :@dims?, Int :$flag? = FFTW_ESTIMATE, :$kind!, Int :$dim?, Int :$thread? = NONE, Int :$nthreads? = 1)

## 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

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**), 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)

$.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:

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