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 = $x->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 ndarrays 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 convention one would expect [2
       4] instead of [1 2].

       This subclass PDL::Matrix overloads the constructors and indexing functions of pdls so
       that they are compatible with the usual matrix convention, 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 an ndarray 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 ndarray 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), therefore 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)

BUGS AND PROBLEMS

       Because we change the way ndarrays are constructed, not all pdl operators may be applied
       to ndarray-matrices. The inner product is not redefined. We might have missed some
       functions/methods. Internal consistency 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@heuel.org), Christian Soeller (c.soeller@auckland.ac.nz).

COPYRIGHT

       All rights reserved. There is no warranty. You are allowed to redistribute 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.