Christian Soeller > PDL-2.4.1 > PDL::Primitive

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NAME ^

PDL::Primitive - primitive operations for pdl

DESCRIPTION ^

This module provides some primitive and useful functions defined using PDL::PP and able to use the new indexing tricks.

See PDL::Indexing for how to use indices creatively. For explanation of the signature format, see PDL::PP.

SYNOPSIS ^

 use PDL::Primitive;

AUTHOR ^

Copyright (C) Tuomas J. Lukka 1997 (lukka@husc.harvard.edu). Contributions by Christian Soeller (c.soeller@auckland.ac.nz), Karl Glazebrook (kgb@aaoepp.aao.gov.au), and Craig DeForest (deforest@boulder.swri.edu). All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.

Inner product over one dimension

 c = sum_i a_i * b_i

', BadDoc => 'If a() * b() contains only bad data, c() is set bad. Otherwise c() will have its bad flag cleared, as it will not contain any bad values.', ); # pp_def( inner )

pp_def( 'outer', HandleBad => 1, Pars => 'a(n); b(m); [o]c(n,m);', Code => 'loop(n,m) %{ $c() = $a() * $b(); %}', BadCode => 'loop(n,m) %{ if ( $ISBAD(a()) || $ISBAD(b()) ) { $SETBAD(c()); } else { $c() = $a() * $b(); } %}', Doc => ' =for ref

outer product over one dimension

Naturally, it is possible to achieve the effects of outer product simply by threading over the "*" operator but this function is provided for convenience.

'); # pp_def( outer )

pp_addpm(<<'EOD'); =head2 matmult

 Signature: (a(x,y),b(y,z),[o]c(x,z))

Matrix multiplication

We peruse the inner product to define matrix multiplication via a threaded inner product

Cross product of two 3D vectors

After

 $c = crossp $a, $b

the inner product $c*$a and $c*$b will be zero, i.e. $c is orthogonal to $a and $b

Threaded Index Add: Add a to the ind element of sum, i.e:

 sum(ind) += a

Simple Example:

  $a = 2;
  $ind = 3;
  $sum = zeroes(10);
  indadd($a,$ind, $sum);
  print $sum
  #Result: ( 2 added to element 3 of $sum)
  # [0 0 0 2 0 0 0 0 0 0]

Threaded Example:

  $a = pdl( 1,2,3);
  $ind = pdl( 1,4,6);
  $sum = zeroes(10);
  indadd($a,$ind, $sum);
  print $sum."\n";
  #Result: ( 1, 2, and 3 added to elements 1,4,6 $sum)
  # [0 1 0 0 2 0 3 0 0 0]

1d convolution along first dimension

  $con = conv1d sequence(10), pdl(-1,0,1), {Boundary => 'reflect'};

By default, periodic boundary conditions are assumed (i.e. wrap around). Alternatively, you can request reflective boundary conditions using the Boundary option:

  {Boundary => 'reflect'} # case in 'reflect' doesn't matter

The convolution is performed along the first dimension. To apply it across another dimension use the slicing routines, e.g.

  $b = $a->mv(2,0)->conv1d($kernel)->mv(0,2); # along third dim

This function is useful for threaded filtering of 1D signals.

Compare also conv2d, convolve, fftconvolve, fftwconv, rfftwconv

EOD Pars => 'a(m); kern(p); [o]b(m);', OtherPars => 'int reflect;', PMCode => '

sub PDL::conv1d { my $opt = pop @_ if ref($_[$#_]) eq \'HASH\'; die \'Usage: conv1d( a(m), kern(p), [o]b(m), {Options} )\' if $#_<1 || $#_>2; my($a,$kern) = @_; my $c = $#_ == 2 ? $_[2] : PDL->null; &PDL::_conv1d_int($a,$kern,$c, !(defined $opt && exists $$opt{Boundary}) ? 0 : lc $$opt{Boundary} eq "reflect"); return $c; }

', Code => ' int i,i1,i2,poff; double tmp; int reflect = $COMP(reflect); int m_size = $COMP(__m_size); int p_size = $COMP(__p_size);

           poff = (p_size-1)/2;
           for(i=0; i<m_size; i++) { 
              tmp = 0; 
                  for(i1=0; i1<p_size; i1++) { 
                     i2 = i+i1 - poff; 
                     if (reflect && i2<0)
                        i2 = -i2;
                     if (reflect && i2>=m_size)
                        i2 = m_size-(i2-m_size+1);

                     REALMOD(i2,m_size); 
                     tmp += $a(m=>i2) * $kern(p=>i1);
                  }
              $b(m=>i) = tmp;
           }
');

# this can be achieved by # ($a->dummy(0) == $b)->orover # but this one avoids a larger intermediate and potentially shortcuts pp_def('in', Pars => 'a(); b(n); [o] c()', Code => '$c() = 0; loop(n) %{ if ($a() == $b()) {$c() = 1; break;} %}', Doc => <<'EOD', =for ref

test if a is in the set of values b

   $goodmsk = $labels->in($goodlabels);
   print pdl(4,3,1)->in(pdl(2,3,3));
  [0 1 0]

in is akin to the is an element of of set theory. In priciple, PDL threading could be used to achieve its functionality by using a construct like

   $msk = ($labels->dummy(0) == $goodlabels)->orover;

However, in doesn't create a (potentially large) intermediate and is generally faster. EOD );

pp_add_exported '', 'uniq'; pp_addpm << 'EOPM';

uniq

return all unique elements of a piddle

The unique elements are returned in ascending order.

  print pdl(2,2,2,4,0,-1,6,6)->uniq;
 [-1 0 2 4 6]

Note: The returned pdl is 1D; any structure of the input piddle is lost.

uniqvec

return all unique vectors out of a collection

The unique vectors are returned in lexicographically sorted ascending order. The 0th dimension of the input PDL is treated as a dimensional index within each vector, and the 1st and any higher dimensions are taken to run across vectors. The return value is always 2D; any structure of the input PDL (beyond using the 0th dimension for vector index) is lost.

See also uniq for a uniqe list of scalars; and qsortvec for sorting a list of vectors lexicographcally.

clip

Clip a piddle by (optional) upper or lower bounds.

 $b = $a->clip(0,3);
 $c = $a->clip(undef, $x);

EOD

    if ( $bvalflag ) {
        pp_addpm(<<'EOD');
=for bad

clip handles bad values since it is just a wrapper around hclip and lclip.

EOD } # if: $bvalflag

pp_addpm(<<'EOD');

Calculate useful statistics over a dimension of a piddle

  ($mean, $rms, $median, $min, $max, $adev) = statover($piddle, $weights);

This utility function calculates various useful quantities of a piddle. These are the mean:

  MEAN = sum (x)/ N

with N being the number of elements in x, the root mean square deviation from the mean, RMS, given as,

  RMS = sqrt(sum( (x-mean(x))^2 )/(N-1));

Note the use of N-1 which for almost all cases should be the right normalisation factor. The routine also returns the median, minimum and maximum of the piddle as well as the mean absolute deviation, defined as:

  ADEV = sqrt(sum( abs(x-mean(x)) )/N)

note here that we use the mean and not the median. This could possibly be changed in future versions of the code.

This operator is a projection operator so the calculation will take place over the final dimension. Thus if the input is N-dimensional each returned value will be N-1 dimensional, to calculate the statistics for the entire piddle either use clump(-1) directly on the piddle or call stats.

', BadDoc => ' Bad values are simply ignored in the calculation and if all data are bad the results will also be bad. ', );

pp_add_exported('','stats'); pp_addpm(<<'EOD');

stats

Calculates useful statistics on a piddle

 ($mean,$rms,$median,$min,$max) = stats($piddle,[$weights]);

This utility calculates all the most useful quantities in one call.

Note: The RMS value that this function returns in the RMS deviation from the mean, also known as the population standard- deviation: $rms = sqrt(sum(($val-$mean)**2)) / ($n-1)

EOD

    if ( $bvalflag ) {
        pp_addpm(<<'EOD');
=for bad

The return values if all elements are bad is currently poorly defined.

EOD } # if: bvalflag pp_addpm(<<'EOD');

Calculates a histogram$_->{Doc1} for given stepsize and minimum.

 \$h = $_->{Name}(\$data, $_->{Doc2}\$step, \$min, \$numbins);
 \$hist = zeroes \$numbins;  # Put histogram in existing piddle.
 $_->{Name}(\$data, $_->{Doc2}\$hist, \$step, \$min, \$numbins);

The histogram will contain \$numbins bins starting from \$min, each \$step wide. The value in each bin is the $_->{Doc3}values in \$data that lie within the bin limits.

Data below the lower limit is put in the first bin, and data above the upper limit is put in the last bin.

The output is reset in a different threadloop so that you can take a histogram of \$a(10,12) into \$b(15) and get the result you want. $_->{Doc4}

 perldl> p $_->{Doc5}

EOD }

for( {Name => 'histogram2d', WeightPar => '', HistType => 'int+', HistOp => '++', Doc1 => "", Doc2 => "", Doc3 => "number of\n", Doc5 => "histogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),1,0,3,1,0,3) [ [0 0 0] [0 2 2] [0 1 0] ]

"}, {Name => 'whistogram2d', WeightPar => 'float+ wt(n);', HistType => 'float+', HistOp => '+= $wt()', Doc1 => " from weighted data", Doc2 => " \$weights,", Doc3 => "sum of the values in\n\$weights that correspond to ", Doc5 => "whistogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),pdl(0.1,0.2,0.3,0.4,0.5),1,0,3,1,0,3) [ [ 0 0 0] [ 0 0.5 0.9] [ 0 0.1 0] ]

"} ) { pp_def($_->{Name}, Pars => 'ina(n); inb(n); '.$_->{WeightPar}.$_->{HistType}. '[o] hist(ma,mb)', # set outdim by Par! OtherPars => 'double stepa; double mina; int masize => ma; double stepb; double minb; int mbsize => mb;', HandleBad => 1, Code => 'register int ja,jb; register int maxja = $SIZE(ma)-1; register int maxjb = $SIZE(mb)-1; register double mina = $COMP(mina); register double minb = $COMP(minb); register double stepa = $COMP(stepa); register double stepb = $COMP(stepb); threadloop %{ loop(ma,mb) %{ $hist() = 0; %} %} threadloop %{ loop(n) %{ ja = (int) (($ina()-mina)/stepa); jb = (int) (($inb()-minb)/stepb); if (ja<0) ja=0; if (ja > maxja) ja = maxja; if (jb<0) jb=0; if (jb > maxjb) jb = maxjb; ($hist(ma => ja,mb => jb))'.$_->{HistOp}.'; %} %} ', BadCode => 'register int ja,jb; register int maxja = $SIZE(ma)-1; register int maxjb = $SIZE(mb)-1; register double mina = $COMP(mina); register double minb = $COMP(minb); register double stepa = $COMP(stepa); register double stepb = $COMP(stepb); threadloop %{ loop(ma,mb) %{ $hist() = 0; %} %} threadloop %{ loop(n) %{ if ( $ISGOOD(ina()) && $ISGOOD(inb()) ) { ja = (int) (($ina()-mina)/stepa); jb = (int) (($inb()-minb)/stepb); if (ja<0) ja=0; if (ja > maxja) ja = maxja; if (jb<0) jb=0; if (jb > maxjb) jb = maxjb; ($hist(ma => ja,mb => jb))'.$_->{HistOp}.'; } %} %} ', Doc=><<"EOD");

Calculates a 2d histogram$_->{Doc1}.

 \$h = $_->{Name}(\$datax, \$datay,$_->{Doc2}
       \$stepx, \$minx, \$nbinx, \$stepy, \$miny, \$nbiny);
 \$hist = zeroes \$nbinx, \$nbiny;  # Put histogram in existing piddle.
 $_->{Name}(\$datax, \$datay,$_->{Doc2} \$hist,
       \$stepx, \$minx, \$nbinx, \$stepy, \$miny, \$nbiny);

The histogram will contain \$nbinx x \$nbiny bins, with the lower limits of the first one at (\$minx, \$miny), and with bin size (\$stepx, \$stepy). The value in each bin is the $_->{Doc3}values in \$datax and \$datay that lie within the bin limits.

Data below the lower limit is put in the first bin, and data above the upper limit is put in the last bin.

 perldl> p $_->{Doc5}

EOD }

########################################################### # a number of constructors: fibonacci, append, axisvalues & # random numbers ###########################################################

pp_def('fibonacci', Pars => '[o]x(n);', Doc=>'Constructor - a vector with Fibonacci\'s sequence', PMFunc=>'', PMCode=><<'EOD', sub fibonacci { ref($_[0]) && ref($_[0]) ne 'PDL::Type' ? $_[0]->fibonacci : PDL->fibonacci(@_) } sub PDL::fibonacci{ my $class = shift; my $x = scalar(@_)? $class->new_from_specification(@_) : $class->new_or_inplace; &PDL::_fibonacci_int($x->clump(-1)); return $x; } EOD Code => ' PDL_Long i=0; $GENERIC() x1, x2;

        x1 = 1; x2 = 0;

        loop(n) %{
           $x() = x1 + x2;
           if (i++>0) {
              x2 = x1;
              x1 = $x();
           }
        %}
');

pp_def('append', Pars => 'a(n); b(m); [o] c(mn)', # note that ideally we want to say '$SIZE(mn) = $SIZE(m)+$SIZE(n);' # but that requires placing RedoDimsParsedCode *after* assignment of # childdims to $SIZE(XXX)!!! XXXXXmake that workXXXXX RedoDimsCode => ' pdl * dpdla = $PDL(a); pdl * dpdlb = $PDL(b); $SIZE(mn) = (dpdla->ndims > 0 ? dpdla->dims[0] : 1) + (dpdlb->ndims > 0 ? dpdlb->dims[0] : 1); ', Code => 'register PDL_Long mnp; PDL_Long ns = $SIZE(n); threadloop %{ loop(n) %{ $c(mn => n) = $a(); %} loop(m) %{ mnp = m+ns; $c(mn => mnp) = $b(); %} %}', Doc => '=for ref

append two or more piddles by concatenating along their first dimensions

 $a = ones(2,4,7);
 $b = sequence 5;
 $c = $a->append($b);  # size of $c is now (7,4,7) (a jumbo-piddle ;)

append appends two piddles along their first dims. Rest of the dimensions must be compatible in the threading sense. Resulting size of first dim is the sum of the sizes of the first dims of the two argument piddles - ie n + m.

' );

pp_addpm(<<'EOD')

glue

  $c = $a->glue(<dim>,$b,...)

Glue two or more PDLs together along an arbitrary dimension (N-D append).

Sticks $a, $b, and all following arguments together using a combination of xchg() and append(). All other dimensions must be compatible in the threading sense.

glue is implemented in pdl, and should probably be updated (one day) to a pure PP function.

Internal routine

axisvalues is the internal primitive that implements axisvals and alters its argument.

' ); # pp_def: axisvalues

pp_addpm(<<'EOD');

random

Constructor which returns piddle of random numbers

 $a = random([type], $nx, $ny, $nz,...);
 $a = random $b;

etc (see zeroes).

This is the uniform distribution between 0 and 1 (assumedly excluding 1 itself). The arguments are the same as zeroes (q.v.) - i.e. one can specify dimensions, types or give a template.

You can use the perl function srand to seed the random generator. For further details consult Perl's srand documentation.

randsym

Constructor which returns piddle of random numbers

 $a = randsym([type], $nx, $ny, $nz,...);
 $a = randsym $b;

etc (see zeroes).

This is the uniform distribution between 0 and 1 (excluding both 0 and 1, cf random). The arguments are the same as zeroes (q.v.) - i.e. one can specify dimensions, types or give a template.

You can use the perl function srand to seed the random generator. For further details consult Perl's srand documentation.

grandom

Constructor which returns piddle of Gaussian random numbers

 $a = grandom([type], $nx, $ny, $nz,...);
 $a = grandom $b;

etc (see zeroes).

This is generated using the math library routine ndtri.

Mean = 0, Stddev = 1

You can use the perl function srand to seed the random generator. For further details consult Perl's srand documentation.

routine for searching 1D values i.e. step-function interpolation.

 $inds = vsearch($vals, $xs);

Returns for each value of $vals the index of the least larger member of $xs (which need to be in increasing order). If the value is larger than any member of $xs, the index to the last element of $xs is returned.

This function is useful e.g. when you have a list of probabilities for events and want to generate indices to events:

 $a = pdl(.01,.86,.93,1); # Barnsley IFS probabilities cumulatively
 $b = random 20;
 $c = vsearch($b, $a); # Now, $c will have the appropriate distr.

It is possible to use the cumusumover function to obtain cumulative probabilities from absolute probabilities.

EOD

pp_def('interpolate', HandleBad => 0, BadDoc => 'needs major (?) work to handles bad values', Pars => 'xi(); x(n); y(n); [o] yi(); int [o] err()', GenericTypes => ['F','D'], # too restrictive ? Code => ' $GENERIC() d; long n = $SIZE(n); long n1 = n-1; int up = ($x(n => n1) > $x(n => 0)); long jl, jh, m; int carp;

                 threadloop %{
                   jl = -1;
                   jh = n;
                   carp = 0;
                   while (jh-jl > 1)  /* binary search */
                        {
                                m = (jh+jl) >> 1;
                                if ($xi() > $x(n => m) == up)
                                        jl = m;
                                else
                                        jh = m;
                        }
                   if (jl == -1) {
                        if ($xi() != $x(n => 0)) carp = 1;
                        jl = 0;
                   } else if (jh == n) {
                        if ($xi() != $x(n => n1)) carp = 1;
                        jl = n1-1;
                   }
                   jh = jl+1;
                   if ((d = $x(n => jh)-$x(n => jl)) == 0)
                        barf("identical abscissas");
                   d = ($x(n => jh)-$xi())/d;
                   $yi() = d*$y(n => jl) + (1-d)*$y(n => jh);
                   $err() = carp;
                %}
', Doc=><<'EOD');

routine for 1D linear interpolation

 ( $yi, $err ) = interpolate($xi, $x, $y)

Given a set of points ($x,$y), use linear interpolation to find the values $yi at a set of points $xi.

interpolate uses a binary search to find the suspects, er..., interpolation indices and therefore abscissas (ie $x) have to be strictly ordered (increasing or decreasing). For interpolation at lots of closely spaced abscissas an approach that uses the last index found as a start for the next search can be faster (compare Numerical Recipes hunt routine). Feel free to implement that on top of the binary search if you like. For out of bounds values it just does a linear extrapolation and sets the corresponding element of $err to 1, which is otherwise 0.

See also interpol, which uses the same routine, differing only in the handling of extrapolation - an error message is printed rather than returning an error piddle.

interpol

 Signature: (xi(); x(n); y(n); [o] yi())

routine for 1D linear interpolation

 $yi = interpol($xi, $x, $y)

interpol uses the same search method as interpolate, hence $x must be strictly ordered (either increasing or decreasing). The difference occurs in the handling of out-of-bounds values; here an error message is printed.

interpND

Interpolate values from an N-D piddle, with switchable method

  $source = 10*xvals(10,10) + yvals(10,10);
  $index = pdl([[2.2,3.5],[4.1,5.0]],[[6.0,7.4],[8,9]]);
  print $source->interpND( $index );

InterpND acts like indexND, collapsing $index by lookup into $source; but it does interpolation rather than direct sampling. The interpolation method and boundary condition are switchable via an options hash.

By default, linear or sample interpolation is used, with constant value outside the boundaries of the source pdl. No dataflow occurs, because in general the output is computed rather than indexed.

All the interpolation methods treat the pixels as value-centered, so the sample method will return $a->(0) for coordinate values on the set [-0.5,0.5), and all methods will return $a->(1) for a coordinate value of exactly 1.

Recognized options:

method

Values can be:

  • 0, s, sample, Sample (default for integer source types)

    The nearest value is taken. Pixels are regarded as centered on their respective integer coordinates (no offset from the linear case).

  • 1, l, linear, Linear (default for floating point source types)

    The values are N-linearly interpolated from an N-dimensional cube of size 2.

  • 3, c, cube, cubic, Cubic

    The values are interpolated using a local cubic fit to the data. The fit is constrained to match the original data and its derivative at the data points. The second derivative of the fit is not continuous at the data points. Multidimensional datasets are interpolated by the successive-collapse method.

    (Note that the constraint on the first derivative causes a small amount of ringing around sudden features such as step functions).

  • f, fft, fourier, Fourier

    The source is Fourier transformed, and the interpolated values are explicitly calculated from the coefficients. The boundary condition option is ignored -- periodic boundaries are imposed.

    If you pass in the option "fft", and it is a list (ARRAY) ref, then it is a stash for the magnitude and phase of the source FFT. If the list has two elements then they are taken as already computed; otherwise they are calculated and put in the stash.

b, bound, boundary, Boundary

This option is passed unmodified into indexND, which is used as the indexing engine for the interpolation. Some current allowed values are 'extend', 'periodic', 'truncate', and 'mirror' (default is 'truncate').

bad

contains the fill value used for 'truncate' boundary. (default 0)

fft

An array ref whose associated list is used to stash the FFT of the source data, for the FFT method.

one2nd

Converts a one dimensional index piddle to a set of ND coordinates

 @coords=one2nd($a, $indices)

returns an array of piddles containing the ND indexes corresponding to the one dimensional list indices. The indices are assumed to correspond to array $a clumped using clump(-1). This routine is used in whichND, but is useful on its own occasionally.

 perldl> $a=pdl [[[1,2],[-1,1]], [[0,-3],[3,2]]]; $c=$a->clump(-1)
 perldl> $maxind=maximum_ind($c); p $maxind;
 6
 perldl> print one2nd($a, maximum_ind($c))
 0 1 1
 perldl> p $a->at(0,1,1)
 3

Returns piddle of indices of non-zero values.

 $i = which($mask);

returns a pdl with indices for all those elements that are nonzero in the mask. Note that the returned indices will be 1D. If you want to index into the original mask or a similar piddle remember to flatten it before calling index:

  $data = random 5, 5;
  $idx = which $data > 0.5; # $idx is now 1D
  $bigsum = $data->flat->index($idx)->sum;  # flatten before indexing

Compare also where for similar functionality.

If you want to return both the indices of non-zero values and the complement, use the function which_both.

 perldl> $x = sequence(10); p $x
 [0 1 2 3 4 5 6 7 8 9]
 perldl> $indx = which($x>6); p $indx
 [7 8 9]

EOD

my $doc_which_both = <<'EOD';

Returns piddle of indices of non-zero values and their complement

 ($i, $c_i) = which_both($mask);

This works just as which, but the complement of $i will be in $c_i.

 perldl> $x = sequence(10); p $x
 [0 1 2 3 4 5 6 7 8 9]
 perldl> ($small, $big) = which_both ($x >= 5); p "$small\n $big"
 [5 6 7 8 9]
 [0 1 2 3 4]

EOD

    for (
         {Name=>'which',
          Pars => 'mask(n); int [o] inds(m);',
          Variables => 'int dm=0;',
          Elseclause => "",
          Autosize => '$SIZE(m) = sum;',
          Doc => $doc_which,
          PMCode=><<'EOD',
   sub which { my ($this,$out) = @_;
                $this = $this->flat;
                $out = $this->nullcreate unless defined $out;
                PDL::_which_int($this,$out);
                return $out;
   }
   *PDL::which = \&which;
EOD
          },
         {Name => 'which_both',
          Pars => 'mask(n); int [o] inds(m); int [o]notinds(q)',
          Variables => 'int dm=0; int dm2=0;',
          Elseclause => "else { \n          \$notinds(q => dm2)=n; \n           dm2++;\n     }",
          Autosize => '$SIZE(m) = sum;'."\n".'            $SIZE(q) = dpdl->dims[0]-sum;',
          Doc => $doc_which_both,
          PMCode=><<'EOD',
   sub which_both { my ($this,$outi,$outni) = @_;
                $this = $this->flat;
                $outi = $this->nullcreate unless defined $outi; 
                $outni = $this->nullcreate unless defined $outni;
                PDL::_which_both_int($this,$outi,$outni);
                return wantarray ? ($outi,$outni) : $outi;
   }
   *PDL::which_both = \&which_both;
EOD
          }
         )
{
    pp_def($_->{Name},
           Doc => $_->{Doc},
           Pars => $_->{Pars},
           PMCode => $_->{PMCode},
           Code => $_->{Variables} .
                 'loop(n) %{
                        if ($mask()) {
                                $inds(m => dm) = n;
                                dm++;
                        }'.$_->{Elseclause} . "\n".
                ' %}',
#               the next one is currently a dirty hack
#               this will probably break once dataflow is enabled again
#               *unless* we have made sure that mask is physical by now!!!
           RedoDimsCode => '
                PDL_Long sum = 0;
                /* not sure if this is necessary */
                pdl * dpdl = $PDL(mask);
                $GENERIC() *m_datap = (($GENERIC() *)(PDL_REPRP(dpdl)));
                PDL_Long inc = PDL_REPRINC(dpdl,0);
                PDL_Long offs = PDL_REPROFFS(dpdl);
                int i;

                if (dpdl->ndims != 1)
                  barf("dimflag currently works only with 1D pdls");

                for (i=0; i<dpdl->dims[0]; i++) {
                       if ( *(m_datap+inc*i+offs)) sum++;
                }

                '.$_->{Autosize} . '
                /* printf("RedoDimsCode: setting dim m to %ld\n",sum); */'
           );
}

pp_addpm(<<'EOD' =head2 where

Return the values from a piddle for whose indices a condition piddle is nonzero.

 $i = $x->where($x+5 > 0); # $i contains those elements of $x
                           # where mask ($x+5 > 0) is 1
 $i .= -5;  # Set those elements (of $x) to -5. Together, these
            # commands clamp $x to a maximum of -5. 

It is also possible to use the same mask for several piddles with the same call:

 ($i,$j,$k) = where($x,$y,$z, $x+5>0);

Note: $i is always 1-D, even if $x is >1-D.

WARNING: The first argument (the values) and the second argument (the mask) currently have to have the exact same dimensions (or horrible things happen). You *cannot* thread over a smaller mask, for example.

whichND

Returns the coordinates for non-zero values.

For historical reasons the return value is different in list and scalar context. In scalar context, you get back a PDL containing coordinates suitable for use in indexND or range; in list context, the coordinates are broken out into separate PDLs.

 $coords = whichND($mask);

returns a PDL containing the coordinates of the elements that are non-zero in $mask, suitable for use in indexND. The 0th dimension contains the full coordinate listing of each point; the 1st dimension lists all the points. For example, if $mask has rank 4 and 100 matching elements, then $coords has dimension 4x100.

 @coords=whichND($mask);

returns a perl list of piddles containing the coordinates of the elements that are non-zero in $mask. Each element corresponds to a particular index dimension. For example, if $mask has rank 4 and 100 matching elements, then @coords has 4 elements, each of which is a pdl of size 100.

 perldl> $a=sequence(10,10,3,4)
 perldl> ($x, $y, $z, $w)=whichND($a == 203); p $x, $y, $z, $w
 [3] [0] [2] [0]
 perldl> print $a->at(list(cat($x,$y,$z,$w)))
 203
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