---
name: "Math::Cephes::Matrix"
section: "3pm"
platform: "linux"
package: "libmath-cephes-perl"
version: "0.5307-1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Math::Cephes::Matrix"
---

# Math::Cephes::Matrix(3pm)

Perl interface to the cephes matrix routines

## 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.