txt: ## dist_cpan-FRITH-Math-Libgsl-DigitalFiltering.md
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  ![Impulse filter](examples/04-impulse.svg)
  
  # NAME
  
  Math::Libgsl::DigitalFiltering - An interface to libgsl, the Gnu Scientific Library - Digital Filtering
  
  # SYNOPSIS
  
  ```
  use Math::Libgsl::Vector;
  use Math::Libgsl::DigitalFiltering;
  
  my constant $N = 1000;
  my constant $K = 21;
  my Math::Libgsl::Vector $x .= new: :size($N);
  $x.scanf('data.dat');
  my Math::Libgsl::DigitalFiltering::Gaussian $gauss .= new: :size($K);
  my $y = $gauss.filter(2.5, $x);
  
  ```
  
  # DESCRIPTION
  
  Math::Libgsl::DigitalFiltering is an interface to the Digital Filtering functions of libgsl, the Gnu Scientific Library.
  
  This module exports four classes:
  
  * Math::Libgsl::DigitalFiltering::Gaussian
  * Math::Libgsl::DigitalFiltering::Median
  * Math::Libgsl::DigitalFiltering::RMedian
  * Math::Libgsl::DigitalFiltering::Impulse
  
  each encapsulates the methods and the buffers needed to create and use the filter on the data stored in a Math::Libgsl::Vector object.
  
  ## Math::Libgsl::DigitalFiltering::Gaussian
  
  This class encapsulate a Gaussian filter.
  
  ### multi method new(Int $size!)
  
  ### multi method new(Int :$size!)
  
  The constructor accepts one simple or named argument: the kernel size.
  
  ### filter(Num() $alpha!, Math::Libgsl::Vector $x!, Int :$order = 0, Int :$endtype = GSL\_MOVSTAT\_END\_PADZERO, Bool :$inplace? --> Math::Libgsl::Vector)
  
  This method applies a Gaussian filter parameterized by **$alpha** to the input vector **$x**. The optional named argument **:$order** specifies the derivative order, with `0` corresponding to a Gaussian, `1` corresponding to a first derivative Gaussian, and so on. The optional named argument **:$endtype** specifies how the signal end points are handled. The symbolic names for this argument are listed in the Math::Libgsl::Constants module as follows:
  
  * **GSL\_MOVSTAT\_END\_PADZERO**: inserts zeros into the window near the signal end points
  * **GSL\_MOVSTAT\_END\_PADVALUE**: pads the window with the first and last sample in the input signal
  * **GSL\_MOVSTAT\_END\_TRUNCATE**: no padding is performed: the windows are truncated as the end points are approached
  
  The boolean named argument **:$inplace** directs the method to apply the filter in-place. This method returns the filter output as a **Math::Libgsl::Vector** object.
  
  ### kernel(Num() $alpha!, Int $size, Int :$order = 0, Int :$normalize = 0 --> Math::Libgsl::Vector)
  
  This method constructs a Gaussian kernel parameterized by **$alpha**, of size **$size**. The optional named argument **:$order** specifies the derivative order. The optional named argument **:$normalize** specifies if the kernel is to be normalized to sum to one on output. This method returns the filter output as a **Math::Libgsl::Vector** object.
  
  ## Math::Libgsl::DigitalFiltering::Median
  
  This class encapsulate a Median filter.
  
  ### multi method new(Int $size!)
  
  ### multi method new(Int :$size!)
  
  The constructor accepts one simple or named argument: the kernel size.
  
  ### filter(Math::Libgsl::Vector $x!, Int :$endtype = GSL\_MOVSTAT\_END\_PADZERO, Bool :$inplace? --> Math::Libgsl::Vector)
  
  This method applies a Median filter to the input vector **$x**. The optional named argument **:$endtype** specifies how the signal end points are handled. The optional boolean named argument **:$inplace** directs the method to apply the filter in-place. This method returns the filter output as a **Math::Libgsl::Vector** object.
  
  ## Math::Libgsl::DigitalFiltering::RMedian
  
  This class encapsulate a recursive Median filter.
  
  ### multi method new(Int $size!)
  
  ### multi method new(Int :$size!)
  
  The constructor accepts one simple or named argument: the kernel size.
  
  ### filter(Math::Libgsl::Vector $x!, Int :$endtype = GSL\_MOVSTAT\_END\_PADZERO, Bool :$inplace? --> Math::Libgsl::Vector)
  
  This method applies a Median filter to the input vector **$x**. The optional named argument **:$endtype** specifies how the signal end points are handled. The optional boolean named argument **:$inplace** directs the method to apply the filter in-place. This method returns the filter output as a **Math::Libgsl::Vector** object.
  
  ## Math::Libgsl::DigitalFiltering::Impulse
  
  This class encapsulate an Impulse detection filter.
  
  ### multi method new(Int $size!)
  
  ### multi method new(Int :$size!)
  
  The constructor accepts one simple or named argument: the kernel size.
  
  ### filter(Math::Libgsl::Vector $x!, Num() $tuning, Int :$endtype = GSL\_MOVSTAT\_END\_PADZERO, Int :$scaletype = GSL\_FILTER\_SCALE\_MAD, Bool :$inplace? --> List)
  
  This method applies an Impulse filter to the input vector **$x**, using the tuning parameter **$tuning**. The optional named argument **:$endtype** specifies how the signal end points are handled. The optional named argument **:$scaletype** specifies how the scale estimate Sₙ of the window is calculated. The symbolic names for this argument are listed in the Math::Libgsl::Constants module as follows:
  
  * **GSL\_FILTER\_SCALE\_MAD**: specifies the median absolute deviation (MAD) scale estimate
  * **GSL\_FILTER\_SCALE\_IQR**: specifies the interquartile range (IQR) scale estimate
  * **GSL\_FILTER\_SCALE\_SN**: specifies the so-called Sₙ statistic
  * **GSL\_FILTER\_SCALE\_QN**: specifies the so-called Qₙ statistic
  
  The optional boolean named argument **:$inplace** directs the method to apply the filter in-place. This method returns a List of values:
  
  * the window medians, as a **Math::Libgsl::Vector** object
  * the window Sₙ, as a **Math::Libgsl::Vector** object
  * the number of outliers as an Int
  * the location of the outliers as a **Math::Libgsl::Vector::Int32** object
  
  # C Library Documentation
  
  For more details on libgsl see <https://www.gnu.org/software/gsl/>. The excellent C Library manual is available here <https://www.gnu.org/software/gsl/doc/html/index.html>, or here <https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf> in PDF format.
  
  # Prerequisites
  
  This module requires the libgsl library to be installed. Please follow the instructions below based on your platform:
  
  ## Debian Linux and Ubuntu 20.04
  
  ```
  sudo apt install libgsl23 libgsl-dev libgslcblas0
  
  ```
  
  That command will install libgslcblas0 as well, since it's used by the GSL.
  
  ## Ubuntu 18.04
  
  libgsl23 and libgslcblas0 have a missing symbol on Ubuntu 18.04. I solved the issue installing the Debian Buster version of those three libraries:
  
  * <http://http.us.debian.org/debian/pool/main/g/gsl/libgslcblas0_2.5+dfsg-6_amd64.deb>
  * <http://http.us.debian.org/debian/pool/main/g/gsl/libgsl23_2.5+dfsg-6_amd64.deb>
  * <http://http.us.debian.org/debian/pool/main/g/gsl/libgsl-dev_2.5+dfsg-6_amd64.deb>
  
  # Installation
  
  To install it using zef (a module management tool):
  
  ```
  $ zef install Math::Libgsl::DigitalFiltering
  
  ```
  
  # AUTHOR
  
  Fernando Santagata [nando.santagata@gmail.com](mailto:nando.santagata@gmail.com)
  
  # COPYRIGHT AND LICENSE
  
  Copyright 2020 Fernando Santagata
  
  This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.
  