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 ndarrays if the flag is set for any of the input ndarrays.

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 ndarrays if the flag is set for any of the input ndarrays.

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 parameter $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 parameter $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.

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All other parts Copyright (C) 2009-2022, 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.