NAME

Math::Cephes::Matrix - Perl interface to the cephes matrix routines

SYNOPSIS

use Math::Cephes::Matrix qw(mat);
# 'mat' is a shortcut for Math::Cephes::Matrix->new
my $M = mat([ [1, 2, -1], [2, -3, 1], [1, 0, 3]]);
my $C = mat([ [1, 2, 4], [2, 9, 2], [6, 2, 7]]);
my $D = $M->add($C);          # D = M + C
my $Dc = $D->coef;
for (my $i=0; $i<3; $i++) {
  print "row $i:\n";
  for (my $j=0; $j<3; $j++) {
      print "\tcolumn $j: $Dc->[$i]->[$j]\n";
  }
}

DESCRIPTION

This module is a layer on top of the basic routines in the cephes math library for operations on square matrices. In the following, a Math::Cephes::Matrix object is created as

my $M = Math::Cephes::Matrix->new($arr_ref);

where $arr_ref is a reference to an array of arrays, as in the following example:

$arr_ref = [ [1, 2, -1], [2, -3, 1], [1, 0, 3] ]

which represents

/ 1   2  -1  \
| 2  -3   1  |
\ 1   0   3  /

A copy of a Math::Cephes::Matrix object may be done as

my $M_copy = $M->new();

Methods

coef: get coefficients of the matrix

SYNOPSIS:

my $c = $M->coef;

DESCRIPTION:

This returns an reference to an array of arrays containing the coefficients of the matrix.

clr: set all coefficients equal to a value.

SYNOPSIS:

$M->clr($n);

DESCRIPTION:

This sets all the coefficients of the matrix identically to $n. If $n is not given, a default of 0 is used.

add: add two matrices

SYNOPSIS:

$P = $M->add($N);

DESCRIPTION:

This sets $P equal to $M + $N.

sub: subtract two matrices

SYNOPSIS:

$P = $M->sub($N);

DESCRIPTION:

This sets $P equal to $M - $N.

mul: multiply two matrices or a matrix and a vector

SYNOPSIS:

$P = $M->mul($N);

DESCRIPTION:

This sets $P equal to $M * $N. This method can handle matrix multiplication, when $N is a matrix, as well as matrix-vector multiplication, where $N is an array reference representing a column vector.

div: divide two matrices

SYNOPSIS:

$P = $M->div($N);

DESCRIPTION:

This sets $P equal to $M * ($N)^(-1).

inv: invert a matrix

SYNOPSIS:

$I = $M->inv();

DESCRIPTION:

This sets $I equal to ($M)^(-1).

transp: transpose a matrix

SYNOPSIS:

$T = $M->transp();

DESCRIPTION:

This sets $T equal to the transpose of $M.

simq: solve simultaneous equations

SYNOPSIS:

my $M = Math::Cephes::Matrix->new([ [1, 2, -1], [2, -3, 1], [1, 0, 3]]);
my $B = [2, -1, 10];
my $X = $M->simq($B);
for (my $i=0; $i<3; $i++) {
   print "X[$i] is $X->[$i]\n";
 }

where $M is a Math::Cephes::Matrix object, $B is an input array reference, and $X is an output array reference.

DESCRIPTION:

A set of N simultaneous equations may be represented in matrix form as

M X = B

where M is an N x N square matrix and X and B are column vectors of length N.

eigens: eigenvalues and eigenvectors of a real symmetric matrix

SYNOPSIS:

my $S = Math::Cephes::Matrix->new([ [1, 2, 3], [2, 2, 3], [3, 3, 4]]);
my ($E, $EV1) = $S->eigens();
my $EV = $EV1->coef;
for (my $i=0; $i<3; $i++) {
  print "For i=$i, with eigenvalue $E->[$i]\n";
  my $v = [];
  for (my $j=0; $j<3; $j++) {
    $v->[$j] = $EV->[$i]->[$j];
  }
  print "The eigenvector is @$v\n";
}

where $M is a Math::Cephes::Matrix object representing a real symmetric matrix. $E is an array reference containing the eigenvalues of $M, and $EV is a Math::Cephes::Matrix object representing the eigenvalues, the ith row corresponding to the ith eigenvalue.

DESCRIPTION:

If M is an N x N real symmetric matrix, and X is an N component column vector, the eigenvalue problem

M X = lambda X

will in general have N solutions, with X the eigenvectors and lambda the eigenvalues.

BUGS

Please report any to Randy Kobes <randy@theoryx5.uwinnipeg.ca>

COPYRIGHT

The C code for the Cephes Math Library is Copyright 1984, 1987, 1989, 2002 by Stephen L. Moshier, and is available at http://www.netlib.org/cephes/. Direct inquiries to 30 Frost Street, Cambridge, MA 02140.

The perl interface is copyright 2000, 2002 by Randy Kobes. This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.