
Matrix(3) User Contributed Perl Documentation Matrix(3)
NAME
PDL::Matrix  a derived matrix class that implements columnmajor constructors and meth
ods
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 twodimensional 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'.
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 lookandfeel 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 twodimensional 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 spec
ify 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
piddlematrices. The inner product is not redefined. We might have missed some func
tions/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 dis
tribution. If this file is separated from the PDL distribution, the copyright notice
should be included in the file.
perl v5.8.0 20011203 Matrix(3) 
