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# Matrix

## 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];
[


]
```

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);
[


]
```

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 AT heuel DOT org), Christian Soeller (c DOT soeller AT auckland DOT ac DOT nz).