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Bryan Jurish


PDL::CCS::Functions - Useful perl-level functions for PDL::CCS


 use PDL;
 use PDL::CCS::Functions;

 ## ... stuff happens



  Signature: (indx ptr(N+1); indx [o]len(N))

Get number of non-missing values for each axis value from a CCS-encoded offset pointer vector $ptr().


  Signature: (indx whichnd(Ndims,Nnz); nzvals(Nnz); missing(); \@Dims; [o]a(@Dims))

Decode a CCS-encoded matrix (no dataflow).

Scalar Operations

Scalar operations can be performed in parallel directly on $nzvals (and if applicable on $missing as well):

 $c = 42;

 $nzvals2 = $nzvals  + $c;        $missing2 = $missing  + $c;
 $nzvals2 = $nzvals  - $c;        $missing2 = $missing  - $c;
 $nzvals2 = $nzvals  * $c;        $missing2 = $missing  * $c;
 $nzvals2 = $nzvals  / $c;        $missing2 = $missing  / $c;

 $nzvals2 = $nzvals ** $c;        $missing2 = $missing ** $c;
 $nzvals2 = log($nzvals);         $missing2 = log($missing);
 $nzvals2 = exp($nzvals);         $missing2 = exp(missing);

 $nzvals2 = $nzvals->and2($c,0);  $missing2 = $missing->and($c,0);
 $nzvals2 = $nzvals->or2($c,0);   $missing2 = $missing->or2($c,0);
 $nzvals2 = $nzvals->not();       $missing2 = $missing->not();

Nothing prevents scalar operations from producing new "missing" values (e.g. $nzvals*0), so you might want to re-encode your compressed data after applying the operation.

Vector Operations


  Signature: (indx whichDimV(Nnz); nzvals(Nnz); vec(V); [o]nzvals_out(Nnz))

A number of row- and column-vector operations may be performed directly on encoded Nd-PDLs, without the need for decoding to a (potentially huge) dense temporary. These operations assume that "missing" values are annihilators with respect to the operation in question, i.e. that it holds for all $x in $vec that:

 ($missing __OP__ $x) == $missing

This is in line with the usual PDL semantics if your $missing value is BAD, but may produce unexpected results when e.g. adding a vector to a sparse PDL with $missing==0. If you really need to do something like the latter, then you're probably better off decoding to a dense PDL anyway.

Predefined function names for encoded-PDL vector operations are all of the form: ccs_${OPNAME}_ma, where ${OPNAME} is the base name of the operation:

 plus       ##-- addition
 minus      ##-- subtraction
 mult       ##-- multiplication (NOT matrix-multiplication)
 divide     ##-- division
 modulo     ##-- modulo
 power      ##-- potentiation

 gt         ##-- greater-than
 ge         ##-- greater-than-or-equal
 lt         ##-- less-than
 le         ##-- less-than-or-equal
 eq         ##-- equality
 ne         ##-- inequality
 spaceship  ##-- 3-way comparison

 and2       ##-- binary AND
 or2        ##-- binary OR
 xor        ##-- binary XOR
 shiftleft  ##-- left-shift
 shiftright ##-- right-shift

\&CODE = ccs_binop_vector_mia($opName, \&PDLCODE);

Returns a generic vector-operation subroutine which reports errors as $opName and uses \&PDLCODE to perform underlying computation.



  Signature: (indx which(Ndims,Nnz); nzvals(Nnz); missing(); Dim0(); indx [o]nzix(Nnz); indx [o]nzenum(Nnz))

Underlying guts for PDL::CCS::Nd::qsort() and PDL::CCS::Nd::qsorti(). Given a set of $Nnz items $i each associated with a vector-key $which(:,$i) and a value $nzvals($i), returns a vector of $Nnz item indices $nzix() such that $which(:,$nzix) is vector-sorted in ascending order and $nzvals(:,$nzix) are sorted in ascending order for each unique key-vector in $which(), and an enumeration $nzenum() of items for each unique key-vector in terms of the sorted data: $nzenum($j) is the logical position of the item $nzix($j).

If $missing and $Dim0 are defined, items $i=$nzix($j) with values $nzvals($i) > $missing will be logically enumerated at the end of the range [0,$Dim0-1] and there will be a gap between $nzenum() values for a $which()-key with fewer than $Dim0 instances; otherwise $nzenum() values will be enumerated in ascending order starting from 0.

For an unsorted index+value dataset ($which0,$nzvals0) with

 ($nzix,$nzenum) = ccs_qsort($which0("1:-1,"),$nzvals0,$missing,$which0("0,")->max+1)

qsort() can be implemented as:

 $which  = $nzenum("*1,")->glue(0,$which0("1:-1,")->dice_axis(1,$nzix));
 $nzvals = $nzvals0->index($nzix);

and qsorti() as:

 $which  = $nzenum("*1,")->glue(0,$which0("1:-1,")->dice_axis(1,$nzix));
 $nzvals = $which0("(0),")->index($nzix);


Perl by Larry Wall.

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


Bryan Jurish <moocow@cpan.org>

Copyright (C) 2007-2013, 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.


perl(1), PDL(3perl), PDL::CCS::Nd(3perl),