ccs_matmult2d_sdd
Signature: (
indx ixa(Two=2,NnzA); nza(NnzA); missinga();
b(O,M);
zc(O);
[o]c(O,N)
; PDL_Indx sizeN)
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(Two) must be 2.
ccs_matmult2d_sdd processes 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(Two=2,NnzA); nza(NnzA);
b(O,M);
[o]c(O,N)
; PDL_Indx sizeN)
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(Two) must be 2.
ccs_matmult2d_zdd processes 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);
; PDL_Indx 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);
PDL_Indx 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=2,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.
Install Now
Emojis