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
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 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), 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 piddles are constructed, not all pdl operators may be
applied to piddle-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.