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

NAME

       PDL::Matrix -- a derived matrix class that implements column-major constructors and methods

VERSION

       This document refers to version PDL::Matrix 0.01 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. matrices can be typed in using traditional matrix convention.

       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 con-
       vention, 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 eigenvalue or matrix inversion 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.

FUNCTIONS

       mpdl, PDL::Matrix::pdl

       constructs an object of class PDL::Matrix which is a piddle child class, where the first index refers to the first column of the two-dimen-
       sional piddle.

	   $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), therefore only the first scalar argument is used.

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

       PDL::Matrix::slice, PDL::Matrix::dice

       same as slice, dice for normal piddles, but reflecting the matrix convention by swapping the first two arguments.

	   print  sequence(3,2)->slice("1:2,(0)") # piddle
	   [1 2]
	   print msequence(3,2)->slice("1:2,(0)") # PDL::Matrix
	   [2 4]

       PDL::Matrix::at

       same as at for piddles, but reflecting the matrix convention by swapping the first two arguments

       If only one scalar argument is used, we assume the object to be a vector and look only at the first column.

       PDL::Matrix::set

       set a particular value in a PDL::Matrix object. Note that this has to be called as an object method rather than a function

       print msequence(3,3)->set(2,0,-1) # ok with PDL::Matrix convention [
	[ 0  1	2]
	[ 3  4	5]
	[-1  7	8] ]

       print set msequence(3,3), 2,0,-1 # does not conform with PDL::Matrix convention [
	[ 0  1 -1]
	[ 3  4	5]
	[ 6  7	8] ]

       PDL::Matrix::reshape

       same as reshape for piddles, but reflecting the matrix convention by swapping the first two arguments

       mdims

       returns the dimensions of the PDL::Matrix object in matrix convention

       "dims" is NOT overloaded by PDL::Matrix to make sure that methods like PDL::transpose still work. So use "mdims" to get the dims in the
       PDL::Matrix notation.

	   print msequence(3,2)->mdims
	   3 2

       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 operators may be applied to piddle-matrices. The inner product is not rede-
       fined. We might have missed some functions/methods. Internal consistency of our approach needs yet to be established.

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.

perl v5.8.0							    2001-12-03								 Matrix(3)