Compat(3pm)

NAME
PDL::CCS::Compat - Backwards-compatibility module for PDL::CCS

SYNOPSIS
 use PDL;
 use PDL::CCS::Compat;

 ##-- source pdl
 $a = random($N=8,$M=7);

 ##---------------------------------------------------------------------
 ## Non-missing value counts
 $nnz    = $a->flat->nnz;         ##-- "missing" == 0
 $nnaz   = $a->flat->nnza(1e-6);  ##-- "missing" ~= 0
 #$ngood = $a->ngood;             ##-- "missing" == BAD (see PDL::Bad)

 ##---------------------------------------------------------------------
 ## CCS Encoding
 ($ptr,$rowids,$vals) = ccsencode_nz ($a);             # missing == 0
 ($ptr,$rowids,$vals) = ccsencode_naz($a,$eps);        # missing ~= 0
 ($ptr,$rowids,$vals) = ccsencode_g  ($a);             # missing == BAD
 ($ptr,$rowids,$vals) = ccsencode_i  ($i,$ivals,$N);   # generic flat
 ($ptr,$rowids,$vals) = ccsencode_i2d($xi,$yi,$ivals); # generic 2d

 ##---------------------------------------------------------------------
 ## CCS Decoding
 $cols = ccsdecodecols($ptr,$rowids,$nzvals, $xvals
 $a2   = ccsdecode  ($ptr,$rowids,$vals);              # missing == 0
 $a2   = ccsdecode_g($ptr,$rowids,$vals);              # missing == BAD

 ##---------------------------------------------------------------------
 ## CCS Index Conversion
 $nzi  = ccsitonzi  ($ptr,$rowids, $ix,     $missing); # ix => nzi
 $nzi  = ccsi2dtonzi($ptr,$rowids, $xi,$yi, $missing); # 2d => nzi

 $ix       = ccswhich  ($ptr,$rowids,$vals);           # CCS => ix
 ($xi,$yi) = ccswhichND($ptr,$rowids,$vals);           # CCS => 2d
 $xyi      = ccswhichND($ptr,$rowids,$vals);           # ...as scalar

 ##---------------------------------------------------------------------
 ## CCS Lookup

 $ixvals = ccsget  ($ptr,$rowids,$vals, $ix,$missing);     # ix => values
 $ixvals = ccsget2d($ptr,$rowids,$vals, $xi,$yi,$missing); # 2d => values

 ##---------------------------------------------------------------------
 ## CCS Operations
 ($ptrT,$rowidsT,$valsT) = ccstranspose($ptr,$rowids,$vals); # CCS<->CRS

 ##---------------------------------------------------------------------
 ## Vector Operations, by column
 $nzvals_out = ccsadd_cv ($ptr,$rowids,$nzvals, $colvec);
 $nzvals_out = ccsdiff_cv($ptr,$rowids,$nzvals, $colvec);
 $nzvals_out = ccsmult_cv($ptr,$rowids,$nzvals, $colvec);
 $nzvals_out = ccsdiv_cv ($ptr,$rowids,$nzvals, $colvec);

 ##---------------------------------------------------------------------
 ## Vector Operations, by row
 $nzvals_out = ccsadd_rv ($ptr,$rowids,$nzvals, $rowvec);
 $nzvals_out = ccsdiff_rv($ptr,$rowids,$nzvals, $rowvec);
 $nzvals_out = ccsmult_rv($ptr,$rowids,$nzvals, $rowvec);
 $nzvals_out = ccsdiv_rv ($ptr,$rowids,$nzvals, $rowvec);

 ##---------------------------------------------------------------------
 ## Scalar Operations
 $nzvals_out = $nzvals * 42;  # ... or whatever

 ##---------------------------------------------------------------------
 ## Accumulators
 $rowsumover  = ccssumover ($ptr,$rowids,$nzvals); ##-- like $a->sumover()
 $colsumovert = ccssumovert($ptr,$rowids,$nzvals); ##-- like $a->xchg(0,1)->sumover

Encoding

  ccs_encode_compat
  Signature: (indx awhich(2,Nnz); avals(Nnz);
              indx $N; indx $M;
              indx [o]ptr(N); indx [o]rowids(Nnz); [o]nzvals(Nnz))

Generic wrapper for backwards-compatible ccsencode() variants.

  ccsencode

  ccsencode_nz
  Signature: (a(N,M); indx [o]ptr(N); indx [o]rowids(Nnz); [o]nzvals(Nnz))

Encodes matrix $a() in compressed column format, interpreting zeroes as "missing" values.

Allocates output vectors if required.

  ccsencodea

  ccsencode_naz
  Signature: (a(N,M); eps(); indx [o]ptr(N); indx [o]rowids(Nnz); [o]nzvals(Nnz))

Encodes matrix $a() in CCS format interpreting approximate zeroes as "missing" values. This function is just like ccsencode_nz(), but uses the tolerance parameter $eps() to determine which elements are to be treated as zeroes.

Allocates output vectors if required.

  ccsencodeg

  ccsencode_g
  Signature: (a(N,M); indx [o]ptr(N); indx [o]rowids(Nnz); [o]nzvals(Nnz))

Encodes matrix $a() in CCS format interpreting BAD values as "missing". Requires bad-value support built into PDL.

Allocates output vectors if required.

  ccsencode_i
  Signature: (indx ix(Nnz); nzvals(Nnz); indx $N; int [o]ptr(N); indx [o]rowids(Nnz); [o]nzvals_enc(Nnz))

General-purpose CCS encoding method for flat indices. Encodes values $nzvals() from flat-index locations $ix() into a CCS matrix ($ptr(), $rowids(), $nzvals_enc()).

Allocates output vectors if required.

$N (~ $a->dim(0)) must be specified.

  ccsencode_i2d
  Signature: (
              indx    xvals(Nnz)     ;
              indx    yvals(Nnz)     ;
                      nzvals(Nnz)    ;
              indx    $N             ; ##-- optional
              indx [o]ptr(N)         ;
              indx [o]rowids(Nnz)    ;
                   [o]nzvals_enc(Nnz);
             )

General-purpose encoding method. Encodes values $nzvals() from 2d-index locations ($xvals(), $yvals()) in an $N-by-(whatever) PDL into a CCS matrix $ptr(), $rowids(), $nzvals_enc().

Allocates output vectors if required. If $N is omitted, it defaults to the maximum column index given in $xvals().

Decoding

  ccsdecodecols
  Signature: (
              indx   ptr    (N)  ;
              indx   rowids (Nnz);
                     nzvals (Nnz);
              indx   xvals  (I)  ; # default=sequence($N)
                     missing()   ; # default=0
                     M      ()   ; # default=rowids->max+1
                  [o]cols   (I,M); # default=new
              )

Extract dense columns from a CCS-encoded matrix (no dataflow). Allocates output matrix if required. If $a(N,M) was the dense source matrix for the CCS-encoding, and if missing values are zeros, then the following two calls are equivalent (modulo data flow):

  $cols = $a->dice_axis(1,$col_ix);
  $cols = ccsdecodecols($ptr,$rowids,$nzvals, $col_ix,0);

  ccsdecode
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); $M; [o]dense(N,M))

Decodes compressed column format vectors $ptr(), $rowids(), and $nzvals() into dense output matrix $a(). Allocates the output matrix if required.

Note that if the original matrix (pre-encoding) contained trailing rows with no nonzero elements, such rows will not be allocated by this method (unless you specify either $M or $dense). In such cases, you might prefer to call ccsdecodecols() directly.

  ccsdecode_g
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); $M; [o]dense(N,M))

Convenience method. Like ccsdecode() but sets "missing" values to BAD.

Index Conversion
  Signature: (indx ptr(N); indx rowids(Nnz); indx ind(2,I); indx missing(); indx [o]nzix(I))

  ccsiNDtonzi
Convert N-dimensional index values $ind() appropriate for a dense matrix (N,M) into indices $nzix() appropriate for the $rowids() and/or $nzvals() components of the CCS-encoded matrix ($ptr(),$rowids(),$nzvals()). Missing values are returned in $nzix() as $missing().

  ccsi2dtonzi
  Signaure: (indx ptr(N); indx rowids(Nnz); indx col_ix(I); indx row_ix(I); indx missing(); indx [o]nzix(I))

Convert 2d index values $col_ix() and $row_ix() appropriate for a dense matrix (N,M) into indices $nzix() appropriate for the $rowids() and/or $nzvals() components of the CCS-encoded matrix ($ptr(),$rowids(),$nzvals()). Missing values are returned in $nzix() as $missing().

  Signature: (indx ptr(N); indx rowids(Nnz); indx ix(I); indx missing(); indx [o]nzix(I))

  ccsitonzi
Convert flat index values $ix() appropriate for a dense matrix (N,M) into indices $nzix() appropriate for the $rowids() and/or $nzvals() components of the CCS-encoded matrix ($ptr(),$rowids(),$nzvals()). Missing values are returned in $nzix() as $missing().

  ccswhichND

  ccswhich2d

  ccswhichfull
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); indx [o]which_cols(Nnz); indx [o]which_rows(Nnz)',

In scalar context, returns concatenation of $which_cols() and $which_rows(), similar to the builtin whichND(). Note however that ccswhichND() may return its index PDLs sorted in a different order than the builtin whichND() method for dense matrices. Use the qsort() or qsorti() methods if you need sorted index PDLs.

  ccswhich
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); indx [o]which(Nnz); indx [t]wcols(Nnz)',

Convenience method. Calls ccswhichfull(), and scales the output PDLs to correspond to a flat enumeration. The output PDL $which() is not guaranteed to be sorted in any meaningful order. Use the qsort() method if you need sorted output.

  ccstranspose
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); indx [o]ptrT(M); indx [o]rowidsT(Nnz); [o]nzvalsT(Nnz)',

Transpose a compressed matrix.

Lookup

  ccsget2d
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); indx xvals(I); indx yvals(I); missing(); [o]ixvals(I))

Lookup values in a CCS-encoded PDL by 2d source index (no dataflow). Pretty much like ccsi2dtonzi(), but returns values instead of indices. If you know that your index PDLs $xvals() and $yvals() do not refer to any missing values in the CCS-encoded matrix, then the following two calls are equivalent (modulo dataflow):

  $ixvals =                ccsget2d   ($ptr,$rowids,$nzvals, $xvals,$yvals,0);
  $ixvals = index($nzvals, ccsi2dtonzi($ptr,$rowids,         $xvals,$yvals,0));

The difference is that only the second incantation will cause subsequent changes to $ixvals to be propagated back into $nzvals.

  ccsget
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals(Nnz); indx ix(I); missing(); [o]ixvals(I))

Lookup values in a CCS-encoded PDL by flat source index (no dataflow). Pretty much like ccsitonzi(), but returns values instead of indices. If you know that your index PDL $ix() does not refer to any missing values in the CCS-encoded matrix, then the following two calls are equivalent (modulo dataflow):

  $ixvals =                ccsget   ($ptr,$rowids,$nzvals, $ix,0);
  $ixvals = index($nzvals, ccsitonzi($ptr,$rowids,         $ix,0))

The difference is that only the second incantation will cause subsequent changes to $ixvals to be propagated back into $nzvals.

Vector Operations

  ccs${OP}_cv
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals_in(Nnz);  colvec(M);  [o]nzvals_out(Nnz))

Column-vector operation ${OP} on CCS-encoded PDL.

Should do something like the following (without decoding the CCS matrix):

 ($colvec ${OP} ccsdecode(\$ptr,\$rowids,\$nzvals))->ccsencode;

Missing values in the CCS-encoded PDL are not affected by this operation.

${OP} is one of the following:

 plus       ##-- addition    (alias: 'add')
 minus      ##-- subtraction (alias: 'diff')
 mult       ##-- multiplication (NOT matrix-multiplication)
 divide     ##-- division    (alias: 'div')
 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

  ccs${OP}_rv
  Signature: (indx ptr(N); indx rowids(Nnz); nzvals_in(Nnz);  rowvec(N);  [o]nzvals_out(Nnz))

Row-vector operation ${OP} on CCS-encoded PDL. Should do something like the following (without decoding the CCS matrix):

 ($column->slice("*1,") ${OP} ccsdecode($ptr,$rowids,$nzvals))->ccsencode;

Missing values in the CCS-encoded PDL are not effected by this operation.

See ccs${OP}_cv() above for supported operations.

EXAMPLES

  Compressed Column Format Example
 $a = pdl([
           [10, 0, 0, 0,-2,  0],
           [3,  9, 0, 0, 0,  3],
           [0,  7, 8, 7, 0,  0],
           [3,  0, 8, 7, 5,  0],
           [0,  8, 0, 9, 9, 13],
           [0,  4, 0, 0, 2, -1]
          ]);

 ($ptr,$rowids,$nzvals) = ccsencode($a);

 print join("\n", "ptr=$ptr", "rowids=$rowids", "nzvals=$nzvals");

... prints something like:

 ptr=[0 3 7 9 12 16]
 rowids=[ 0 1 3 1 2 4 5 2 3 2 3 4  0 3 4 5 1  4  5]
 nzvals=[10 3 3 9 7 8 4 8 8 7 7 9 -2 5 9 2 3 13 -1]

  Sparse Matrix Example
 ##-- create a random sparse matrix
 $a  = random(100,100);
 $a *= ($a>.9);

 ##-- encode it
 ($ptr,$rowids,$nzvals) = ccsencode($a);

 ##-- what did we save?
 sub pdlsize { return PDL::howbig($_[0]->type)*$_[0]->nelem; }
 print "Encoding saves us ",
       ($saved = pdlsize($a) - pdlsize($ptr) - pdlsize($rowids) - pdlsize($nzvals)),
       " bytes (", (100.0*$saved/pdlsize($a)), "%)\n";

... prints something like:

 Encoding saves us 71416 bytes (89.27%)

  Decoding Example
 ##-- random matrix
 $a = random(100,100);

 ##-- make an expensive copy of $a by encoding & decoding
 ($ptr,$rowids,$nzvals) = ccsencode($a);
 $a2 = ccsdecode($ptr,$rowids,$nzvals);

 ##-- ...and make sure it's good
 print all($a==$a2) ? "Decoding is good!\n" : "Nasty icky bug!\n";

ACKNOWLEDGEMENTS
Perl by Larry Wall.

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

Original inspiration and algorithms from the SVDLIBC C library by Douglas Rohde; which is itself based on SVDPACKC by Michael Berry, Theresa Do, Gavin O'Brien, Vijay Krishna and Sowmini Varadhan.

KNOWN BUGS
Many.

AUTHOR
Bryan Jurish <moocow@cpan.org>

  Copyright Policy
Copyright (C) 2005-2024, 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), PDL::SVDLIBC(3perl), PDL::CCS::Nd(3perl),

SVDLIBC: http://tedlab.mit.edu/~dr/SVDLIBC/

SVDPACKC: http://www.netlib.org/svdpack/