PDL::Matrix

Matrix(3pm)           User Contributed Perl Documentation          Matrix(3pm)



NAME
       PDL::Matrix -- a convenience matrix class for column-major access

VERSION
       This document refers to version PDL::Matrix 0.5 of PDL::Matrix

SYNOPSIS
         use PDL::Matrix;

         $m = mpdl [[1,2,3],[4,5,6]];
         $m = PDL::Matrix->pdl([[1,2,3],[4,5,6]]);
         $m = msequence(4,3);
         @dimsa = $a->mdims; # 'dims' is not overloaded

         $v = vpdl [0,1,2,3]
         $v = vzeroes(4);

DESCRIPTION
       Overview

       This package tries to help people who want to use PDL for 2D matrix
       computation with lots of indexing involved. It provides a PDL subclass
       so one- and two-dimensional piddles that are used as vectors resp and
       matrices can be typed in using traditional matrix convention.

       If you want to know more about matrix operation support in PDL, you
       want to read PDL::MatrixOps or PDL::Slatec.

       The original pdl class refers to the first index as the first row, the
       second index as the first column of a matrix. Consider

         print $B = sequence(3,2)
         [
          [0 1 2]
          [3 4 5]
         ]

       which gives a 2x3 matrix in terms of the matrix convention, but the
       constructor used (3,2). This might get more confusing when using slices
       like sequence(3,2)->slice("1:2,(0)") : with traditional matrix conven-
       tion one would expect [2 4] instead of [1 2].

       This subclass PDL::Matrix overloads the constructors and indexing func-
       tions of pdls so that they are compatible with the usual matrix conven-
       tion, where the first dimension refers to the row of a matrix. So now,
       the above example would be written as

         print $B = PDL::Matrix->sequence(3,2) # or $B = msequence(3,2)
         [
          [0 1]
          [2 3]
          [4 5]
         ]

       Routines like eigens or inv can be used without any changes.

       Furthermore one can construct and use vectors as n x 1 matrices without
       mentioning the second index '1'.

       Implementation

       "PDL::Matrix" works by overloading a number of PDL constructors and
       methods such that first and second args (corresponding to first and
       second dims of corresponding matrices) are effectively swapped.  It is
       not yet clear if PDL::Matrix achieves a consistent column-major look-
       and-feel in this way.

NOTES
       As of version 0.5 (rewrite by CED) the matrices are stored in the usual
       way, just constructed and stringified differently.  That way indexing
       and everything else works the way you think it should.

FUNCTIONS
       mpdl, PDL::Matrix::pdl

       constructs an object of class PDL::Matrix which is a piddle child
       class.

           $m = mpdl [[1,2,3],[4,5,6]];
           $m = PDL::Matrix->pdl([[1,2,3],[4,5,6]]);

       mzeroes, mones, msequence

       constructs a PDL::Matrix object similar to the piddle constructors
       zeroes, ones, sequence.

       vpdl

       constructs an object of class PDL::Matrix which is of matrix dimensions
       (n x 1)

           print $v = vpdl [0,1];
           [
            [0]
            [1]
           ]

       vzeroes, vones, vsequence

       constructs a PDL::Matrix object with matrix dimensions (n x 1), there-
       fore only the first scalar argument is used.

           print $v = vsequence(2);
           [
            [0]
            [1]
           ]

       kroneckerproduct

       returns kroneckerproduct of two matrices. This is not efficiently
       implemented.

       det_general

       returns a generalized determinant of a matrix. If the matrix is not
       regular, one can specify the rank of the matrix and the corresponding
       subdeterminant is returned. This is implemented using the "eigens"
       function.

       trace

       returns the trace of a matrix (sum of diagonals)

       vcrossp, PDL::Matrix::crossp

       similar to PDL::crossp, however reflecting PDL::Matrix notations

BUGS AND PROBLEMS
       Because we change the way piddles are constructed, not all pdl opera-
       tors may be applied to piddle-matrices. The inner product is not rede-
       fined. We might have missed some functions/methods. Internal consis-
       tency of our approach needs yet to be established.

       Because PDL::Matrix changes the way slicing behaves, it breaks many
       operators, notably those in MatrixOps.

TODO
       check all PDL functions, benchmarks, optimization, lots of other things
       ...

AUTHOR(S)
       Stephan Heuel (stephan AT heuel.org), Christian Soeller (c.soeller@auck-
       land.ac.nz).

COPYRIGHT
       All rights reserved. There is no warranty. You are allowed to redis-
       tribute this software / documentation under certain conditions. For
       details, see the file COPYING in the PDL distribution. If this file is
       separated from the PDL distribution, the copyright notice should be
       included in the file.



perl v5.8.8                       2004-09-07                       Matrix(3pm)