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PDL::Matrix -- a convenience matrix class for column-major access |
AUTHOR(S)
PDL::Matrix -- a convenience matrix class for column-major access
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 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 the PDL::MatrixOps manpage or the PDL::Slatec manpage.
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'.
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.
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]]);
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];
[
[0]
[1]
]
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]
]
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 arguments
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 specify 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)
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 functions/methods. Internal consistency of our approach needs yet to be established.
check all PDL functions, benchmarks, optimization, lots of other things ...
AUTHOR(S)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 distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.
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PDL::Matrix -- a convenience matrix class for column-major access |