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.\"
.IX Title "Math::Cephes::Matrix 3pm"
.TH Math::Cephes::Matrix 3pm "2021-06-22" "perl v5.32.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::Cephes::Matrix \- Perl interface to the cephes matrix routines
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 12
\&  use Math::Cephes::Matrix qw(mat);
\&  # \*(Aqmat\*(Aq 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:\en";
\&    for (my $j=0; $j<3; $j++) {
\&        print "\etcolumn $j: $Dc\->[$i]\->[$j]\en";
\&    }
\&  }
.Ve
.SH "DESCRIPTION"
.IX Header "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
.PP
.Vb 1
\&  my $M = Math::Cephes::Matrix\->new($arr_ref);
.Ve
.PP
where \f(CW$arr_ref\fR is a reference to an array of arrays, as
in the following example:
.PP
.Vb 1
\&  $arr_ref = [ [1, 2, \-1], [2, \-3, 1], [1, 0, 3] ]
.Ve
.PP
which represents
.PP
.Vb 3
\&     / 1   2  \-1  \e
\&     | 2  \-3   1  |
\&     \e 1   0   3  /
.Ve
.PP
A copy of a \fIMath::Cephes::Matrix\fR object may be done as
.PP
.Vb 1
\&  my $M_copy = $M\->new();
.Ve
.SS "Methods"
.IX Subsection "Methods"
.IP "\fIcoef\fR: get coefficients of the matrix" 4
.IX Item "coef: get coefficients of the matrix"
.Vb 1
\& SYNOPSIS:
\&
\& my $c = $M\->coef;
\&
\& DESCRIPTION:
.Ve
.Sp
This returns an reference to an array of arrays
containing the coefficients of the matrix.
.IP "\fIclr\fR: set all coefficients equal to a value." 4
.IX Item "clr: set all coefficients equal to a value."
.Vb 1
\& SYNOPSIS:
\&
\& $M\->clr($n);
\&
\& DESCRIPTION:
.Ve
.Sp
This sets all the coefficients of the matrix identically to \fI\f(CI$n\fI\fR.
If \fI\f(CI$n\fI\fR is not given, a default of 0 is used.
.IP "\fIadd\fR: add two matrices" 4
.IX Item "add: add two matrices"
.Vb 1
\& SYNOPSIS:
\&
\& $P = $M\->add($N);
\&
\& DESCRIPTION:
.Ve
.Sp
This sets \f(CW$P\fR equal to \f(CW$M\fR + \f(CW$N\fR.
.IP "\fIsub\fR: subtract two matrices" 4
.IX Item "sub: subtract two matrices"
.Vb 1
\& SYNOPSIS:
\&
\& $P = $M\->sub($N);
\&
\& DESCRIPTION:
.Ve
.Sp
This sets \f(CW$P\fR equal to \f(CW$M\fR \- \f(CW$N\fR.
.IP "\fImul\fR: multiply two matrices or a matrix and a vector" 4
.IX Item "mul: multiply two matrices or a matrix and a vector"
.Vb 1
\& SYNOPSIS:
\&
\& $P = $M\->mul($N);
\&
\& DESCRIPTION:
.Ve
.Sp
This sets \f(CW$P\fR equal to \f(CW$M\fR * \f(CW$N\fR. This method can handle
matrix multiplication, when \f(CW$N\fR is a matrix, as well
as matrix-vector multiplication, where \f(CW$N\fR is an
array reference representing a column vector.
.IP "\fIdiv\fR: divide two matrices" 4
.IX Item "div: divide two matrices"
.Vb 1
\& SYNOPSIS:
\&
\& $P = $M\->div($N);
\&
\& DESCRIPTION:
.Ve
.Sp
This sets \f(CW$P\fR equal to \f(CW$M\fR * ($N)^(\-1).
.IP "\fIinv\fR: invert a matrix" 4
.IX Item "inv: invert a matrix"
.Vb 1
\& SYNOPSIS:
\&
\& $I = $M\->inv();
\&
\& DESCRIPTION:
.Ve
.Sp
This sets \f(CW$I\fR equal to ($M)^(\-1).
.IP "\fItransp\fR: transpose a matrix" 4
.IX Item "transp: transpose a matrix"
.Vb 1
\& SYNOPSIS:
\&
\& $T = $M\->transp();
\&
\& DESCRIPTION:
.Ve
.Sp
This sets \f(CW$T\fR equal to the transpose of \f(CW$M\fR.
.IP "\fIsimq\fR: solve simultaneous equations" 4
.IX Item "simq: solve simultaneous equations"
.Vb 1
\& 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]\en";
\&  }
.Ve
.Sp
where \f(CW$M\fR is a \fIMath::Cephes::Matrix\fR object, \f(CW$B\fR
is an input array reference, and \f(CW$X\fR is an output
array reference.
.Sp
.Vb 1
\& DESCRIPTION:
.Ve
.Sp
A set of N simultaneous equations may be represented
in matrix form as
.Sp
.Vb 1
\&  M X = B
.Ve
.Sp
where M is an N x N square matrix and X and B are column
vectors of length N.
.IP "\fIeigens\fR: eigenvalues and eigenvectors of a real symmetric matrix" 4
.IX Item "eigens: eigenvalues and eigenvectors of a real symmetric matrix"
.Vb 1
\& 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]\en";
\&   my $v = [];
\&   for (my $j=0; $j<3; $j++) {
\&     $v\->[$j] = $EV\->[$i]\->[$j];
\&   }
\&   print "The eigenvector is @$v\en";
\& }
.Ve
.Sp
where \f(CW$M\fR is a \fIMath::Cephes::Matrix\fR object representing
a real symmetric matrix. \f(CW$E\fR is an array reference containing
the eigenvalues of \f(CW$M\fR, and \f(CW$EV\fR is a \fIMath::Cephes::Matrix\fR object
representing the eigenvalues, the \fIith\fR row corresponding
to the \fIith\fR eigenvalue.
.Sp
.Vb 1
\& DESCRIPTION:
.Ve
.Sp
If M is an N x N real symmetric matrix, and X is an N component
column vector, the eigenvalue problem
.Sp
.Vb 1
\&  M X = lambda X
.Ve
.Sp
will in general have N solutions, with X the eigenvectors
and lambda the eigenvalues.
.SH "BUGS"
.IX Header "BUGS"
Please report any to Randy Kobes <randy@theoryx5.uwinnipeg.ca>
.SH "COPYRIGHT"
.IX Header "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, \s-1MA 02140.\s0
.PP
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.