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

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

       This document refers to version PDL::Matrix 0.01 of PDL::Matrix

	 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);


       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 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 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'.


       "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.

       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-dimensional 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


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

	   print $v = vpdl [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);

       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]


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

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


       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] ]


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


       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


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


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


       returns the trace of a matrix (sum of diagonals)

       vcrossp, PDL::Matrix::crossp

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

       Because we change the way piddles are constructed, not all pdl operators may be applied to
       piddle-matrices. The inner product is not redefined. We might have missed some func-
       tions/methods. Internal consistency of our approach needs yet to be established.

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

       Stephan Heuel (stephan@heuel.org), Christian Soeller (c.soeller@auckland.ac.nz).

       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 dis-
       tribution. 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)
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