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.