.\" Automatically generated by Pod::Man 4.10 (Pod::Simple 3.35)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" Set up some character translations and predefined strings.  \*(-- will
.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
.\" double quote, and \*(R" will give a right double quote.  \*(C+ will
.\" give a nicer C++.  Capital omega is used to do unbreakable dashes and
.\" therefore won't be available.  \*(C` and \*(C' expand to `' in nroff,
.\" nothing in troff, for use with C<>.
.tr \(*W-
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.ie n \{\
.    ds -- \(*W-
.    ds PI pi
.    if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
.    if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\"  diablo 12 pitch
.    ds L" ""
.    ds R" ""
.    ds C` ""
.    ds C' ""
'br\}
.el\{\
.    ds -- \|\(em\|
.    ds PI \(*p
.    ds L" ``
.    ds R" ''
.    ds C`
.    ds C'
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el       .ds Aq '
.\"
.\" If the F register is >0, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.\"
.\" Avoid warning from groff about undefined register 'F'.
.de IX
..
.nr rF 0
.if \n(.g .if rF .nr rF 1
.if (\n(rF:(\n(.g==0)) \{\
.    if \nF \{\
.        de IX
.        tm Index:\\$1\t\\n%\t"\\$2"
..
.        if !\nF==2 \{\
.            nr % 0
.            nr F 2
.        \}
.    \}
.\}
.rr rF
.\" ========================================================================
.\"
.IX Title "MatrixOps 3pm"
.TH MatrixOps 3pm "2018-11-02" "perl v5.28.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
PDL::CCS::MatrixOps \- Low\-level matrix operations for compressed storage sparse PDLs
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 2
\& use PDL;
\& use PDL::CCS::MatrixOps;
\&
\& ##\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
\& ## ... stuff happens
.Ve
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "ccs_matmult2d_sdd"
.IX Subsection "ccs_matmult2d_sdd"
.Vb 6
\&  Signature: (
\&    indx ixa(NdimsA,NnzA); nza(NnzA); missinga();
\&    b(O,M);
\&    zc(O);
\&    [o]c(O,N)
\&    )
.Ve
.PP
Two-dimensional matrix multiplication of a sparse index-encoded \s-1PDL\s0
$a() with a dense pdl $b(), with output to a dense pdl $c().
.PP
The sparse input \s-1PDL\s0 $a() should be passed here with 0th
dimension \*(L"M\*(R" and 1st dimension \*(L"N\*(R", just as for the
built-in \fBPDL::Primitive::matmult()\fR.
.PP
\&\*(L"Missing\*(R" values in $a() are treated as $\fBmissinga()\fR, which shouldn't
be \s-1BAD\s0 or infinite, but otherwise ought to be handled correctly.
The input pdl $\fBzc()\fR is used to pass the cached contribution of
a $\fBmissinga()\fR\-row (\*(L"M\*(R") to an output column (\*(L"O\*(R"), i.e.
.PP
.Vb 1
\& $zc = ((zeroes($M,1)+$missinga) x $b)\->flat;
.Ve
.PP
\&\f(CW$SIZ\fRE(Ndimsa) is assumed to be 2.
.PP
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.
.SS "ccs_matmult2d_zdd"
.IX Subsection "ccs_matmult2d_zdd"
.Vb 5
\&  Signature: (
\&    indx ixa(Ndimsa,NnzA); nza(NnzA);
\&    b(O,M);
\&    [o]c(O,N)
\&    )
.Ve
.PP
Two-dimensional matrix multiplication of a sparse index-encoded \s-1PDL\s0
$a() with a dense pdl $b(), with output to a dense pdl $c().
.PP
The sparse input \s-1PDL\s0 $a() should be passed here with 0th
dimension \*(L"M\*(R" and 1st dimension \*(L"N\*(R", just as for the
built-in \fBPDL::Primitive::matmult()\fR.
.PP
\&\*(L"Missing\*(R" values in $a() are treated as zero.
\&\f(CW$SIZ\fRE(Ndimsa) is assumed to be 2.
.PP
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.
.SS "ccs_vnorm"
.IX Subsection "ccs_vnorm"
.Vb 4
\&  Signature: (
\&    indx acols(NnzA); avals(NnzA);
\&    float+ [o]vnorm(M);
\&    ; int sizeM=>M)
.Ve
.PP
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 $\fBvnorm()\fR.
\&\*(L"Missing\*(R" values in $a() are treated as zero,
and $\fBacols()\fR specifies the (unsorted) indices along the logical dimension M of the corresponding non-missing
values in $\fBavals()\fR.
This is basically the same thing as:
.PP
.Vb 1
\& $vnorm = ($a**2)\->xchg(0,1)\->sumover\->sqrt;
.Ve
.PP
\&... but should be must faster to compute for sparse index-encoded piddles.
.PP
\&\fBccs_vnorm()\fR always clears the bad-status flag on $\fBvnorm()\fR.
.SS "ccs_vcos_zdd"
.IX Subsection "ccs_vcos_zdd"
.Vb 7
\&  Signature: (
\&    indx ixa(2,NnzA); nza(NnzA);
\&    b(N);
\&    float+ [o]vcos(M);
\&    float+ [t]anorm(M);
\&    int sizeM=>M;
\&  )
.Ve
.PP
Computes the vector cosine similarity of a dense row-vector $b(N) with respect to each column $a(i,*)
of a sparse index-encoded \s-1PDL\s0 $a() of logical dimensions (M,N), with output to a dense piddle
\&\f(CW$vco\fRs(M).
\&\*(L"Missing\*(R" values in $a() are treated as zero,
and magnitudes for $a() are passed in the optional parameter $\fBanorm()\fR, which will be implicitly
computed using ccs_vnorm if the $\fBanorm()\fR parameter is omitted or empty.
This is basically the same thing as:
.PP
.Vb 2
\& $anorm //= ($a**2)\->xchg(0,1)\->sumover\->sqrt;
\& $vcos    = ($a * $b\->slice("*1,"))\->xchg(0,1)\->sumover / ($anorm * ($b**2)\->sumover\->sqrt);
.Ve
.PP
\&... but should be must faster to compute.
.PP
Output values in $\fBvcos()\fR are cosine similarities in the range [\-1,1],
except for zero-magnitude vectors which will result in NaN values in $\fBvcos()\fR.
If you need non-negative distances, follow this up with a:
.PP
.Vb 2
\& $vcos\->minus(1,$vcos,1)
\& $vcos\->inplace\->setnantobad\->inplace\->setbadtoval(0); ##\-\- minimum distance for NaN values
.Ve
.PP
to get distances values in the range [0,2].  You can use \s-1PDL\s0 threading to batch-compute distances for
multiple $b() vectors simultaneously:
.PP
.Vb 2
\&  $bx   = random($N, $NB);                   ##\-\- get $NB random vectors of size $N
\&  $vcos = ccs_vcos_zdd($ixa,$nza, $bx, $M);  ##\-\- $vcos is now ($M,$NB)
.Ve
.PP
\&\fBccs_vcos_zdd()\fR always clears the bad status flag on the output piddle \f(CW$vcos\fR.
.SS "_ccs_vcos_zdd"
.IX Subsection "_ccs_vcos_zdd"
.Vb 5
\&  Signature: (
\&    indx ixa(Two,NnzA); nza(NnzA);
\&    b(N);
\&    float+ anorm(M);
\&    float+ [o]vcos(M);)
.Ve
.PP
Guts for \fBccs_vcos_zdd()\fR, with slightly different calling conventions.
.PP
Always clears the bad status flag on the output piddle \f(CW$vcos\fR.
.SS "ccs_vcos_pzd"
.IX Subsection "ccs_vcos_pzd"
.Vb 5
\&  Signature: (
\&    indx aptr(Nplus1); indx acols(NnzA); avals(NnzA);
\&    indx brows(NnzB);                     bvals(NnzB);
\&    anorm(M);
\&    float+ [o]vcos(M);)
.Ve
.PP
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 \s-1PDL\s0 $a() of logical dimensions (M,N),
with output to a dense piddle \f(CW$vco\fRs(M).
\&\*(L"Missing\*(R" values in $a() are treated as zero,
and magnitudes for $a() are passed in the obligatory parameter $\fBanorm()\fR.
Usually much faster than \fBccs_vcos_zdd()\fR if a \s-1CRS\s0 pointer over logical dimension (N) is available
for $a().
.PP
\&\fBccs_vcos_pzd()\fR always clears the bad status flag on the output piddle \f(CW$vcos\fR.
.SH "ACKNOWLEDGEMENTS"
.IX Header "ACKNOWLEDGEMENTS"
Perl by Larry Wall.
.PP
\&\s-1PDL\s0 by Karl Glazebrook, Tuomas J. Lukka, Christian Soeller, and others.
.SH "KNOWN BUGS"
.IX Header "KNOWN BUGS"
We should really implement matrix multiplication in terms of
inner product, and have a good sparse-matrix only implementation
of the former.
.SH "AUTHOR"
.IX Header "AUTHOR"
Bryan Jurish <moocow@cpan.org>
.SS "Copyright Policy"
.IX Subsection "Copyright Policy"
All other parts Copyright (C) 2009\-2015, Bryan Jurish. All rights reserved.
.PP
This package is free software, and entirely without warranty.
You may redistribute it and/or modify it under the same terms
as Perl itself.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBperl\fR\|(1), \s-1\fBPDL\s0\fR\|(3perl)