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Math::Libgsl::Eigensystem cpan:FRITH last updated on 2021-01-22

Math-Libgsl-Eigensystem-0.0.1/

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NAME

Math::Libgsl::Eigensystem - An interface to libgsl, the Gnu Scientific Library - Eigensystems

SYNOPSIS

use Math::Libgsl::Matrix;
use Math::Libgsl::Eigensystem;

my Math::Libgsl::Eigensystem::RealSymm $e .= new: 2;

my Math::Libgsl::Matrix $vm .= new: 2, 2;
$vm[0;0] = 2; $vm[0;1] = 1;
$vm[1;0] = 1; $vm[1;1] = 2

my ($eval) = $e.compute($vm);
put $eval;

DESCRIPTION

Math::Libgsl::Eigensystem is an interface to the Eigensystem functions of libgsl, the Gnu Scientific Library.

This module exports six classes:

each encapsulates the methods and the buffers needed to create and compute the eigenvalues and the eigenvectors of different kind of matrices.

All these classes share the same constructor schema:

multi method new(Int $size!, Bool $vectors?)

multi method new(Int :$size!, Bool :$vectors?)

The constructor accepts two simple or named arguments: the size of the system we want to compute and the request to compute the eigenvectors besides the eigenvalues.

All the classes have a compute method; they differ for the number and type of arguments and the return value(s).

Math::Libgsl::Eigensystem::RealSymm

This class acts on a real symmetrix matrix.

method compute(Math::Libgsl::Matrix $A where .matrix.size1 == .matrix.size2, gsl_eigen_sort_t :$sort --> List)

This method computes the eigenvalues and the eigenvectors, if selected during the initialization. The optional named argument :$sort specifies the required sort order. The symbolic names for this argument are listed in the Math::Libgsl::Constants module as follows:

This method outputs a List of values: a single Math::Libgsl::Vector, which contains the eigenvalues, and an optional Math::Libgsl::Matrix, which contains the eigenvectors if they were requested.

Math::Libgsl::Eigensystem::ComplexHerm

This class acts on a complex hermitian matrix.

method compute(Math::Libgsl::Matrix::Complex64 $A where .matrix.size1 == .matrix.size2, gsl_eigen_sort_t :$sort --> List)

This method computes the eigenvalues and the eigenvectors, if selected during the initialization. The optional named argument :$sort specifies the required sort order.

This method outputs a List of values: a single Math::Libgsl::Vector, which contains the eigenvalues, and an optional Math::Libgsl::Matrix::Complex64, which contains the eigenvectors if they were requested.

Math::Libgsl::Eigensystem::RealNonSymm

This class acts on a complex hermitian matrix.

method compute(Math::Libgsl::Matrix $A where .matrix.size1 == .matrix.size2, Bool :$balance = False, gsl_eigen_sort_t :$sort, Bool :$schur-vectors = False, Bool :$schur = False --> List)

This method computes the eigenvalues and the eigenvectors, if selected during the initialization. The optional named argument :$balance requires that a balancing transformation is applied to the matrix prior to computing eigenvalues. The optional named argument :$schur requires that it computes the full Schur form T. The optional named argument :$schur-vectors requires that it also computes the Schur vectors. The optional named argument :$sort specifies the required sort order.

This method outputs a List of values: a single Math::Libgsl::Vector::Complex64, which contains the eigenvalues, an optional Math::Libgsl::Matrix::Complex64, which contains the eigenvectors if they were requested, and an optional Math::Libgsl::Matrix if the Schur vectors were requested.

Math::Libgsl::Eigensystem::RealGenSymm

method compute(Math::Libgsl::Matrix $A where .matrix.size1 == .matrix.size2, Math::Libgsl::Matrix $B where .matrix.size1 == .matrix.size2 && .matrix.size1 == $A.matrix.size1, gsl_eigen_sort_t :$sort --> List)

This method computes the eigenvalues and the eigenvectors, if selected during the initialization. It requires two mandatory Math::Libgsl::Matrix objects (refer to the very good C Library documentation for the meaning of those two matrices and the computation details). The optional named argument :$sort specifies the required sort order.

This method outputs a List of values: a single Math::Libgsl::Vector, which contains the eigenvalues, an optional Math::Libgsl::Matrix, which contains the eigenvectors if they were requested. On exit the first matrix $A is destroyed and the second one $B will contain the Cholesky decomposition of the eigenvector matrix.

Math::Libgsl::Eigensystem::ComplexGenHerm

method compute(Math::Libgsl::Matrix::Complex64 $A where .matrix.size1 == .matrix.size2, Math::Libgsl::Matrix::Complex64 $B where .matrix.size1 == .matrix.size2 && .matrix.size1 == $A.matrix.size1, gsl_eigen_sort_t :$sort --> List)

This method computes the eigenvalues and the eigenvectors, if selected during the initialization. It requires two mandatory Math::Libgsl::Matrix::Complex64 objects (refer to the very good C Library documentation for the meaning of those two matrices and the details of the computation). The optional named argument :$sort specifies the required sort order.

This method outputs a List of values: a single Math::Libgsl::Vector, which contains the eigenvalues, an optional Math::Libgsl::Matrix::Complex64, which contains the eigenvectors if they were requested. On exit the first matrix $A is destroyed and the second one $B will contain the Cholesky decomposition of the eigenvector matrix.

Math::Libgsl::Eigensystem::RealGenNonSymm

method compute(Math::Libgsl::Matrix $A where .matrix.size1 == .matrix.size2, Math::Libgsl::Matrix $B where .matrix.size1 == .matrix.size2 && .matrix.size1 == $A.matrix.size1, Bool :$schur-S = False, Bool :$schur-T = False, Bool :$balance = False, Bool :$schur-vectors = False, gsl_eigen_sort_t :$sort --> List)

This method computes the eigenvalues and the eigenvectors, if selected during the initialization. It requires two mandatory Math::Libgsl::Matrix objects (refer to the amazing C Library documentation for the meaning of those two matrices and the details of the computation). The optional named argument :$schur-S requires that it computes the full Schur form S. The optional named argument :$schur-T requires that it computes the full Schur form T. The optional named argument :$balance requires that a balancing transformation is applied to the matrix prior to computing eigenvalues (currently ignored by the underlying C library; TBI). The optional named argument :$schur-vectors requires that it also computes the Schur vectors. The optional named argument :$sort specifies the required sort order.

This method outputs a List of values: one Math::Libgsl::Vector::Complex64 and one Math::Libgsl::Vector object, which contain the eigenvalues (see the C library documentation for the meaning of these two vectors), an optional Math::Libgsl::Matrix::Complex64, which contains the eigenvectors if they were requested. If the Schur vectors were requested the left and right Schur vectors are returned as Math::Libgsl::Matrix objects. On exit, if $schur-S is True, the first matrix $A will contain the Schur form S; if $schur-T is True, the second matrix $B will contain the Schur form T.

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:

Installation

To install it using zef (a module management tool):

$ zef install Math::Libgsl::Eigensystem

AUTHOR

Fernando Santagata [email protected]

COPYRIGHT AND LICENSE

Copyright 2021 Fernando Santagata

This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.