Math::Symbolic::Custom::Matrix
==============================
Matrix routines for Math::Symbolic.
Provides some routines for manipulating matrices of Math::Symbolic expressions. A matrix here is just a 2D array of
elements. Passing in matrices with elements which are not already Math::Symbolic objects will cause them to be
converted to Math::Symbolic objects.
EXAMPLE
use strict;
use Math::Symbolic 0.613 qw/:all/;
use Math::Symbolic::MiscAlgebra qw/:all/;
use Math::Symbolic::Custom::Matrix 0.2;
use Math::Symbolic::Custom::Polynomial 0.3;
use Math::Symbolic::Custom::CollectSimplify 0.2;
Math::Symbolic::Custom::CollectSimplify->register();
# Say we want the eigenvalues of some matrix with a parameter.
# 1. A = | 4, 3-k |
# | 2, 3 |
my @matrix = ([4,'3-k'],[2,3]);
my $A = make_symbolic_matrix(\@matrix);
# 2. get an identity matrix
my $I = identity_matrix(2);
# 3. multiply it with lambda
my $lambda_I = scalar_multiply_matrix("lambda", $I);
# 4. subtract it from matrix A
my $B = sub_matrix($A, $lambda_I);
# 5. form the characteristic polynomial, |A-lambda*I|
my $c_poly = det(@{$B})->simplify();
print "Characteristic polynomial is: $c_poly\n";
# 6. analyze the polynomial to get roots
my ($var, $coeffs, $disc, $roots) = $c_poly->test_polynomial('lambda');
print "Expressions for the roots are:\n\t$roots->[0]\n\t$roots->[1]\n";
# 7. Check for some values of parameter k
foreach my $k (0..3) {
print "For k = $k: lambda_1 = ",
$roots->[0]->value('k' => $k), "; lambda_2 = ",
$roots->[1]->value('k' => $k), "\n";
}
INSTALLATION
To install this module, run the following commands:
perl Makefile.PL
make
make test
make install
SUPPORT AND DOCUMENTATION
After installing, you can find documentation for this module with the
perldoc command.
perldoc Math::Symbolic::Custom::Matrix
You can also look for information at:
RT, CPAN's request tracker (report bugs here)
CPAN Ratings
Search CPAN
LICENSE AND COPYRIGHT
This software is copyright (c) 2024 by Matt Johnson.
This is free software; you can redistribute it and/or modify it under
the same terms as the Perl 5 programming language system itself.