++ed by:
ZMUGHAL AERO

2 PAUSE users

Bryan Jurish

NAME

PDL::SVDLIBC - PDL interface to Doug Rohde's SVD C Library

SYNOPSIS

 use PDL;
 use PDL::SVDLIBC;

 ##---------------------------------------------------------------------
 ## Input matrix (dense)
 ##---------------------------------------------------------------------
 $n = 100;                  ##-- number of columns
 $m = 50;                   ##-- number of rows
 $a = random(double,$n,$m); ##-- random matrix

 ##---------------------------------------------------------------------
 ## Output pdls
 ##---------------------------------------------------------------------
 $d  = $n;                   ##-- max number of output dimensions
 $ut = zeroes(double,$m,$d); ##-- left singular components
 $s  = zeroes(double,$d);    ##-- singular values (diagnonal vector)
 $vt = zeroes(double,$n,$d); ##-- right singular components

 ##---------------------------------------------------------------------
 ## Singular Value Decomposition (dense)
 ##---------------------------------------------------------------------
 svdlas2d($a, $maxiters, $end, $kappa, $ut, $s, $vt);

 ##---------------------------------------------------------------------
 ## Singular Value Decomposition (sparse, using direct whichND()-encoding)
 ##---------------------------------------------------------------------
 $which  = whichND($a)->qsortvec();
 $nzvals = indexND($a,$which);

 svdlas2w($which, $nzvals, $n, $m, $maxiters, $end, $kappa, $ut, $s, $vt);

 ##---------------------------------------------------------------------
 ## Singular Value Decomposition (sparse, using PDL::CCS encoding)
 ##---------------------------------------------------------------------
 use PDL::CCS;
 ($ptr,$rowids,$nzvals) = ccsencode($a);
 $ptr->reshape($ptr->nelem+1);
 $ptr->set(-1, $rowids->nelem);

 svdlas2($ptr, $rowids, $nzvals, $m, $maxiters, $end, $kappa, $ut, $s, $vt);

 ##---------------------------------------------------------------------
 ## SVD decoding (lookup)
 ##---------------------------------------------------------------------
 $vals = svdindexND ($u, $s, $v, $which);
 $vals = svdindexNDt($ut,$s,$vt, $which);
 $vals = svdindexccs($u, $s, $v, $ptr,$rowids);
 $err  = svderror   ($u, $s, $v, $ptr,$rowids,$nzvals);

DESCRIPTION

PDL::SVDLIBC provides a PDL interface to the SVDLIBC routines for singular value decomposition of large sparse matrices. SVDLIBC is available from http://tedlab.mit.edu/~dr/SVDLIBC/

FUNCTIONS

SVDLIBC Globals

There are several global data structures still lurking in the SVDLIBC code, so expect problems if you are trying to run more than one 'las2' procedure at once (even in different processes).

PDL::SVDLIBC provides access to (some of) the SVDLIBC globals through the following functions, which are not exported.

PDL::SVDLIBC::verbosity()

PDL::SVDLIBC::verbosity($level)

Get/set the current SVDLIBC verbosity level. Valid values for $level are between 0 (no messages) and 2 (many messages).

PDL::SVDLIBC::svdVersion()

Returns a string representing the SVDLIBC version this module was compiled with.

SVD Utilities

_svdccsencode

  Signature: (double a(n,m); indx      [o]ptr(n1); indx      [o]rowids(nnz); double [o]nzvals(nnz))

info not available

_svdccsencode 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.

svdlas2a

    indx    ptr(nplus1);
    indx    rowids(nnz);
    double  nzvals(nnz);
    indx    m();          ##-- default: max($rowids)+1
    int     d();          ##-- default: max(nplus1-1,m)
    int     iterations(); ##-- default: 2*$d
    double  end(2);       ##-- default: [-1e-30,1e-30]
    double  kappa();      ##-- default: 1e-6
    double  [o]ut(m,d);   ##-- default: new
    double  [o] s(d);     ##-- default: new
    double  [o]vt(n,d);   ##-- default: new

Uses a variant of the single-vector Lanczos method (Lanczos, 1950) to compute the singular value decomposition of a sparse matrix with $m() rows and data encoded in Harwell-Boeing sparse format in the input parameters $ptr(), $rowids(), and $nzvals(). See "PDL::CCS" for a way to acquire these parameters from a dense input matrix, but note that for svdlas2(), the column pointer $ptr() is of size ($n+1) for a dense matrix $a with $n columns, where $ptr($n)==$nnz is the total number of nonzero values in $a.

$iterations() is the maximum number of Lanczos iterations to perform.

$end() specifies two endpoints of an interval within which all unwanted eigenvalues lie.

$kappa() is a double containing the relative accuracy of Ritz values acceptable as eigenvalues.

The left singular components are returned in the matrix $ut(), the singular values themselved in the vector $s(), and the right singular components in the matrix $vt(). Note that $ut() and $vt() are transposed, and must be specified explicitly in the call, so that the degree of reduction (the size parameter $d) can be determined. If $d==$n, then a full decomposition will be computed, and on return, $ut() and $vt() should be transposed instances of the matrices $u() and $v() as returned by PDL::MatrixOps::svd().

The Lanczos method as used here seems to be consistently the fastest. This algorithm has the drawback that the low order singular values may be relatively imprecise, but that is not a problem for most users who only want the higher-order values or who can tolerate some imprecision.

See also: svdlas2aw(), svdlas2d()

svdlas2

  Signature: (
    indx   ptr(nplus1);
    indx   rowids(nnz);
    double  nzvals(nnz);
    indx   m();
    int     iterations();
    double  end(2);
    double  kappa();
    double  [o]ut(m,d);
    double  [o] s(d);
    double  [o]vt(n,d);
    )

Guts for svdlas2a(). No default instantiation, and slightly different calling conventions.

svdlas2 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.

svdlas2aw

    indx    which(nnz,2); ##-- sorted indices of non-zero values
    double  nzvals(nnz);  ##-- non-zero values
    indx    n();          ##-- default: max($indx(0,:))+1
    indx    m();          ##-- default: max($indx(1,:))+1
    int     d();          ##-- default: max(n,m)
    int     iterations(); ##-- default: 2*$d
    double  end(2);       ##-- default: [-1e-30,1e-30]
    double  kappa();      ##-- default: 1e-6
    double  [o]ut(m,d);   ##-- default: new
    double  [o] s(d);     ##-- default: new
    double  [o]vt(n,d);   ##-- default: new

As for svdlas2a(), but implicitly converts the index-encoded matrix ($which(),$nzvals()) to an internal CCS-like sparse format before computing the decomposition. Should be slightly more efficient than using PDL::CCS::ccsencode() or similar if you already have $which() and $nzvals() available. These can be attained for a dense matric $a() e.g. by:

 $which  = $a->whichND->qsortvec->xchg(0,1);
 $nzvals = $a->indexND($which->xchg(0,1));

For convenience, $which() will be implicitly transposed if it is passed as a list-of-vectors $whichND(2,nnz) such as returned by whichND(), but it must still be lexicographically sorted.

See also: svdlas2a(), svdlas2d()

svdlas2w

  Signature: (
    indx   whichi(nnz,Two);
    double  nzvals(nnz);
    indx   n();
    indx   m();
    int     iterations();
    double  end(2);
    double  kappa();
    double  [o]ut(m,d);
    double  [o] s(d);
    double  [o]vt(n,d);
    )

Guts for svdlas2a(). No default instantiation, and slightly different calling conventions.

svdlas2w 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.

svdlas2ad

    double  a(n,m);
    int     d();          ##-- default: max($n,$m)
    int     iterations(); ##-- default: 2*$d
    double  end(2);       ##-- default: [-1e-30,1e-30]
    double  kappa();      ##-- default: 1e-6
    double  [o]ut(m,d);   ##-- default: new
    double  [o] s(d);     ##-- default: new
    double  [o]vt(n,d);   ##-- default: new

As for svdlas2(), but implicitly converts the dense input matrix $a() to sparse format before computing the decomposition.

svdlas2d

  Signature: (
    double  a(n,m);
    int     iterations();
    double  end(2);
    double  kappa();
    double  [o]ut(m,d);
    double  [o] s(d);
    double  [o]vt(n,d);
    )

Guts for _svdlas2d().

svdlas2d 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.

svdindexND

  Signature: (
     u(d,m);
     s(d);
     v(d,n);
    indx which(Two,nnz);
    [o] vals(nnz);
    )

Lookup selected values in an SVD-encoded matrix, indexND()-style. Should be equivalent to:

 ($u x stretcher($s) x $v->xchg(0,1))->indexND($which)

or its PDL-friendlier variant:

 ($u * $s)->matmult($v->xchg(0,1))->indexND($which)

... but only computes the specified values $which(), avoiding memory bottlenecks for large sparse matrices. This is a pure PDL::PP method, so you can use e.g. float for the SVD-encoded matrix if you wish.

svdindexND 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.

svdindexNDt

    ut(m,d); s(d); vt(n,d); indx which(Two,nnz); [o] vals(nnz);

Wrapper for svdindexND() accepting transposed singular components $ut() and $vt() as returned by e.g. svdlas2().

svdindexccs

  Signature: (
     u(d,m);
     s(d);
     v(d,n);
    indx ptr(nplus1);
    indx rowids(nnz);
    [o] vals(nnz);
    )

Lookup selected values in an SVD-encoded matrix using PDL::CCS-style indexing as for svdlas2a().

svdindexccs 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.

svderror

  Signature: (
    u(d,m);
    s(d);
    v(d,n);
    indx ptr(nplus1);
    indx rowids(nnz);
    nzvals(nnz);
    [o]err();
    )

Compute sum of squared errors for a sparse SVD-encoded matrix. Should be equivalent to:

 sum( ($a - ($u x stretcher($s) x $v->xchg(0,1)))**2 )

... but computes all values on-the-fly, avoiding memory bottlenecks for large sparse matrices. This is a pure PDL::PP method, so you can use e.g. float for the SVD-encoded matrix if you wish.

Error contributions are computed even for "missing" (zero) values, so running time is O(n*m). Consider using svdindexND() or svdindexccs() to compute error rates only for non-missing values if you have a large sparse matrix, e.g.:

 $svdvals = svdindexccs($u,$s,$v, $ptr,$rowids);
 $err_nz  = ($nzvals-$svdvals)->pow(2)->sumover;

svderror 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.

ACKNOWLEDGEMENTS

Perl by Larry Wall.

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

SVDLIBC by Dough Rohde.

SVDPACKC by Michael Berry, Theresa Do, Gavin O'Brien, Vijay Krishna and Sowmini Varadhan.

KNOWN BUGS

Globals still lurk in the depths of SVDLIBC.

AUTHOR

Bryan Jurish <moocow@cpan.org>

COPYRIGHT AND LICENSE

Copyright (c) 2005-2015, 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, either version 5.20.2 or any newer version of Perl 5 you have available.

The SVDLIBC sources included in this distribution are themselves released under a BSD-like license. See the file SVDLIBC/Manual/license.html in the PDL-SVDLIBC source distribution for details.

SEE ALSO

perl(1), PDL(3perl), PDL::CCS(3perl), SVDLIBC documentation.