# NAME

PDL::CCS::MatrixOps - Low-level matrix operations for compressed storage sparse PDLs

# SYNOPSIS

```
use PDL;
use PDL::CCS::MatrixOps;
##---------------------------------------------------------------------
## ... stuff happens
```

# FUNCTIONS

## ccs_matmult2d_sdd

```
Signature: (
indx ixa(NdimsA,NnzA); nza(NnzA); missinga();
b(O,M);
zc(O);
[o]c(O,N)
)
```

Two-dimensional matrix multiplication of a sparse index-encoded PDL $a() with a dense pdl $b(), with output to a dense pdl $c().

The sparse input PDL $a() should be passed here with 0th dimension "M" and 1st dimension "N", just as for the built-in PDL::Primitive::matmult().

"Missing" values in $a() are treated as $missinga(), which shouldn't be BAD or infinite, but otherwise ought to be handled correctly. The input pdl $zc() is used to pass the cached contribution of a $missinga()-row ("M") to an output column ("O"), i.e.

` $zc = ((zeroes($M,1)+$missinga) x $b)->flat;`

$SIZE(Ndimsa) is assumed to be 2.

ccs_matmult2d_sdd does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## ccs_matmult2d_zdd

```
Signature: (
indx ixa(Ndimsa,NnzA); nza(NnzA);
b(O,M);
[o]c(O,N)
)
```

Two-dimensional matrix multiplication of a sparse index-encoded PDL $a() with a dense pdl $b(), with output to a dense pdl $c().

The sparse input PDL $a() should be passed here with 0th dimension "M" and 1st dimension "N", just as for the built-in PDL::Primitive::matmult().

"Missing" values in $a() are treated as zero. $SIZE(Ndimsa) is assumed to be 2.

ccs_matmult2d_zdd does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## ccs_vnorm

```
Signature: (
indx acols(NnzA); avals(NnzA);
float+ [o]vnorm(M);
; int sizeM=>M)
```

Computes the Euclidean lengths of each column-vector $a(i,*) of a sparse index-encoded pdl $a() of logical dimensions (M,N), with output to a dense piddle $vnorm(). "Missing" values in $a() are treated as zero, and $acols() specifies the (unsorted) indices along the logical dimension M of the corresponding non-missing values in $avals(). This is basically the same thing as:

` $vnorm = ($a**2)->xchg(0,1)->sumover->sqrt;`

... but should be must faster to compute for sparse index-encoded piddles.

ccs_vnorm() always clears the bad-status flag on $vnorm().

## ccs_vcos_zdd

```
Signature: (
indx ixa(2,NnzA); nza(NnzA);
b(N);
float+ [o]vcos(M);
float+ [t]anorm(M);
int sizeM=>M;
)
```

Computes the vector cosine similarity of a dense row-vector $b(N) with respect to each column $a(i,*) of a sparse index-encoded PDL $a() of logical dimensions (M,N), with output to a dense piddle $vcos(M). "Missing" values in $a() are treated as zero, and magnitudes for $a() are passed in the optional paramter $anorm(), which will be implicitly computed using ccs_vnorm if the $anorm() parameter is omitted or empty. This is basically the same thing as:

```
$anorm //= ($a**2)->xchg(0,1)->sumover->sqrt;
$vcos = ($a * $b->slice("*1,"))->xchg(0,1)->sumover / ($anorm * ($b**2)->sumover->sqrt);
```

... but should be must faster to compute.

Output values in $vcos() are cosine similarities in the range [-1,1], except for zero-magnitude vectors which will result in NaN values in $vcos(). If you need non-negative distances, follow this up with a:

```
$vcos->minus(1,$vcos,1)
$vcos->inplace->setnantobad->inplace->setbadtoval(0); ##-- minimum distance for NaN values
```

to get distances values in the range [0,2]. You can use PDL threading to batch-compute distances for multiple $b() vectors simultaneously:

```
$bx = random($N, $NB); ##-- get $NB random vectors of size $N
$vcos = ccs_vcos_zdd($ixa,$nza, $bx, $M); ##-- $vcos is now ($M,$NB)
```

ccs_vcos_zdd() always clears the bad status flag on the output piddle $vcos.

## _ccs_vcos_zdd

```
Signature: (
indx ixa(Two,NnzA); nza(NnzA);
b(N);
float+ anorm(M);
float+ [o]vcos(M);)
```

Guts for ccs_vcos_zdd(), with slightly different calling conventions.

Always clears the bad status flag on the output piddle $vcos.

## ccs_vcos_pzd

```
Signature: (
indx aptr(Nplus1); indx acols(NnzA); avals(NnzA);
indx brows(NnzB); bvals(NnzB);
anorm(M);
float+ [o]vcos(M);)
```

Computes the vector cosine similarity of a sparse index-encoded row-vector $b() of logical dimension (N) with respect to each column $a(i,*) a sparse Harwell-Boeing row-encoded PDL $a() of logical dimensions (M,N), with output to a dense piddle $vcos(M). "Missing" values in $a() are treated as zero, and magnitudes for $a() are passed in the obligatory paramter $anorm(). Usually much faster than ccs_vcos_zdd() if a CRS pointer over logical dimension (N) is available for $a().

ccs_vcos_pzd() always clears the bad status flag on the output piddle $vcos.

# ACKNOWLEDGEMENTS

Perl by Larry Wall.

PDL by Karl Glazebrook, Tuomas J. Lukka, Christian Soeller, and others.

# KNOWN BUGS

We should really implement matrix multiplication in terms of inner product, and have a good sparse-matrix only implementation of the former.

# AUTHOR

Bryan Jurish <moocow@cpan.org>

## Copyright Policy

All other parts Copyright (C) 2009-2015, Bryan Jurish. All rights reserved.

This package is free software, and entirely without warranty. You may redistribute it and/or modify it under the same terms as Perl itself.

# SEE ALSO

perl(1), PDL(3perl)