use strict; # check for bad value support use PDL::Config; my $bvalflag = $PDL::Config{WITH_BADVAL} || 0; pp_addhdr(<<'EOD'); #ifndef RAND_MAX #error "You must have a working RAND_MAX! Something's wrong with your include files" #endif EOD pp_addpm({At=>'Top'},<<'EOD'); use PDL::Slices; use Carp; =head1 NAME PDL::Primitive - primitive operations for pdl =head1 DESCRIPTION This module provides some primitive and useful functions defined using PDL::PP and able to use the new indexing tricks. See L for how to use indices creatively. For explanation of the signature format, see L. =head1 SYNOPSIS use PDL::Primitive; =cut EOD pp_addpm({At=>'Bot'},<<'EOD'); =head1 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. =cut EOD ################################################################ # a whole bunch of quite basic functions for inner, outer # and matrix products (operations that are not normally # available via operator overloading) ################################################################ pp_def( 'inner', HandleBad => 1, Pars => 'a(n); b(n); [o]c();', Code => 'double tmp = 0; loop(n) %{ tmp += $a() * $b(); %} $c() = tmp;', BadCode => 'double tmp = 0; int flag = 0; loop(n) %{ if ( $ISGOOD(a()) && $ISGOOD(b()) ) { tmp += $a() * $b(); flag = 1; } %} if ( flag ) { $c() = tmp; } else { $SETBAD(c()); $PDLSTATESETBAD(c); }', CopyBadStatusCode => '', Doc => ' =for ref Inner product over one dimension c = sum_i a_i * b_i ', BadDoc => 'If C 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 "C<*>" operator but this function is provided for convenience. '); # pp_def( outer ) pp_addpm(<<'EOD'); =head2 matmult =for sig Signature: (a(x,y),b(y,z),[o]c(x,z)) =for ref Matrix multiplication We peruse the inner product to define matrix multiplication via a threaded inner product =cut sub PDL::matmult { barf "Invalid number of arguments for matmult" if $#_ < 1; my ($a,$b,$c) = @_; while ($a->getndims < 2) {$a = $a->dummy(-1)} # promote if necessary while ($b->getndims < 2) {$b = $b->dummy(-1)} if(!defined $c) {$c = PDL->nullcreate($a)} $a->dummy(1)->inner($b->xchg(0,1)->dummy(2),$c); return $c; } *matmult = \&PDL::matmult; EOD pp_add_exported('', 'matmult'); pp_def( 'innerwt', HandleBad => 1, Pars => 'a(n); b(n); c(n); [o]d();', Code => 'double tmp = 0; loop(n) %{ tmp += $a() * $b() * $c(); %} $d() = tmp;', BadCode => 'double tmp = 0; int flag = 0; loop(n) %{ if ( $ISGOOD(a()) && $ISGOOD(b()) && $ISGOOD(c()) ) { tmp += $a() * $b() * $c(); flag = 1; } %} if ( flag ) { $d() = tmp; } else { $SETBAD(d()); }', Doc => '=for ref Weighted (i.e. triple) inner product d = sum_i a(i) b(i) c(i) ' ); pp_def( 'inner2', HandleBad => 1, Pars => 'a(n); b(n,m); c(m); [o]d();', Code => 'double tmp=0; loop(n,m) %{ tmp += $a() * $b() * $c(); %} $d() = tmp;', BadCode => 'double tmp = 0; int flag = 0; loop(n,m) %{ if ( $ISGOOD(a()) && $ISGOOD(b()) && $ISGOOD(c()) ) { tmp += $a() * $b() * $c(); flag = 1; } %} if ( flag ) { $d() = tmp; } else { $SETBAD(d()); }', Doc => '=for ref Inner product of two vectors and a matrix d = sum_ij a(i) b(i,j) c(j) Note that you should probably not thread over C and C since that would be very wasteful. Instead, you should use a temporary for C. ' ); pp_def( 'inner2d', HandleBad => 1, Pars => 'a(n,m); b(n,m); [o]c();', Code => 'double tmp=0; loop(n,m) %{ tmp += $a() * $b(); %} $c() = tmp;', BadCode => 'double tmp = 0; int flag = 0; loop(n,m) %{ if ( $ISGOOD(a()) && $ISGOOD(b()) ) { tmp += $a() * $b(); flag = 1; } %} if ( flag ) { $c() = tmp; } else { $SETBAD(c()); }', Doc => '=for ref Inner product over 2 dimensions. Equivalent to $c = inner($a->clump(2), $b->clump(2)) ' ); pp_def( 'inner2t', HandleBad => 1, Pars => 'a(j,n); b(n,m); c(m,k); [t]tmp(n,k); [o]d(j,k));', Code => 'loop(n,k) %{ double tmp0 = 0; loop(m) %{ tmp0 += $b() * $c(); %} $tmp() = tmp0; %} loop(j,k) %{ double tmp1 = 0; loop(n) %{ tmp1 += $a() * $tmp(); %} $d() = tmp1; %}', BadCode => 'loop(n,k) %{ double tmp0 = 0; int flag = 0; loop(m) %{ if ( $ISGOOD(b()) && $ISGOOD(c()) ) { tmp0 += $b() * $c(); flag = 1; } %} if ( flag ) { $tmp() = tmp0; } else { $SETBAD(tmp()); } %} loop(j,k) %{ double tmp1 = 0; int flag = 0; loop(n) %{ if ( $ISGOOD(a()) && $ISGOOD(tmp()) ) { tmp1 += $a() * $tmp(); flag = 1; } %} if ( flag ) { $d() = tmp1; } else { $SETBAD(d()); } %}', Doc => '=for ref Efficient Triple matrix product C Efficiency comes from by using the temporary C. This operation only scales as C whereas threading using L would scale as C. The reason for having this routine is that you do not need to have the same thread-dimensions for C as for the other arguments, which in case of large numbers of matrices makes this much more memory-efficient. It is hoped that things like this could be taken care of as a kind of closures at some point. ' ); # pp_def inner2t() # a helper function for the cross product definition sub crassgn { "\$c(tri => $_[0]) = \$a(tri => $_[1])*\$b(tri => $_[2]) - \$a(tri => $_[2])*\$b(tri => $_[1]);" } pp_def('crossp', Doc => <<'EOD', =for ref Cross product of two 3D vectors After =for example $c = crossp $a, $b the inner product C<$c*$a> and C<$c*$b> will be zero, i.e. C<$c> is orthogonal to C<$a> and C<$b> =cut EOD Pars => 'a(tri=3); b(tri); [o] c(tri)', Code => crassgn(0,1,2)."\n". crassgn(1,2,0)."\n". crassgn(2,0,1), ); pp_def('norm', HandleBad => 1, Pars => 'vec(n); [o] norm(n)', Doc => 'Normalises a vector to unit Euclidean length', Code => 'double sum=0; loop(n) %{ sum += $vec()*$vec(); %} if (sum > 0) { sum = sqrt(sum); loop(n) %{ $norm() = $vec()/sum; %} } else { loop(n) %{ $norm() = $vec(); %} }', BadCode => 'double sum=0; int flag = 0; loop(n) %{ sum += $vec()*$vec(); flag = 1; %} if ( flag ) { if (sum > 0) { sum = sqrt(sum); loop(n) %{ if ( $ISBAD(vec()) ) { $SETBAD(norm()); } else { $norm() = $vec()/sum; } %} } else { loop(n) %{ if ( $ISBAD(vec()) ) { $SETBAD(norm()); } else { $norm() = $vec(); } %} } } else { loop(n) %{ $SETBAD(norm()); %} }', ); # this one was motivated by the need to compute # the circular mean efficiently # without it could not be done efficiently or without # creating large intermediates (check pdl-porters for # discussion) # see PDL::ImageND for info about the circ_mean function pp_def( 'indadd', HandleBad => 1, Pars => 'a(); int ind(); [o] sum(m)', Code => 'register int foo = $ind(); if( foo<0 || foo>=$SIZE(m) ) { barf("PDL::indadd: invalid index"); } $sum(m => foo) += $a();', BadCode => 'register int foo = $ind(); if( $ISBADVAR(foo,ind) || foo<0 || foo>=$SIZE(m) ) { barf("PDL::indadd: invalid index"); } if ( $ISBAD(a()) ) { $SETBAD(sum(m => foo)); } else { $sum(m => foo) += $a(); }', BadDoc => 'The routine barfs if any of the indices are bad.', Doc=>' =for ref Threaded Index Add: Add C to the C element of C, i.e: sum(ind) += a =for example 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] =cut '); # 1D convolution # useful for threaded 1D filters pp_addhdr(' /* Fast Modulus with proper negative behaviour */ #define REALMOD(a,b) while ((a)>=(b)) (a) -= (b); while ((a)<0) (a) += (b); '); pp_def('conv1d', Doc => << 'EOD', =for ref 1d convolution along first dimension =for example $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 C 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 L, L, L, L, L 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) 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 =for example $goodmsk = $labels->in($goodlabels); print pdl(4,3,1)->in(pdl(2,3,3)); [0 1 0] C is akin to the I of set theory. In priciple, PDL threading could be used to achieve its functionality by using a construct like $msk = ($labels->dummy(0) == $goodlabels)->orover; However, C doesn't create a (potentially large) intermediate and is generally faster. EOD ); pp_add_exported '', 'uniq'; pp_addpm << 'EOPM'; =head2 uniq =for ref return all unique elements of a piddle The unique elements are returned in ascending order. =for example print pdl(2,2,2,4,0,-1,6,6)->uniq; [-1 0 2 4 6] Note: The returned pdl is 1D; any structure of the input piddle is lost. =cut *uniq = \&PDL::uniq; # return unique elements of array # find as jumps in the sorted array # flattens in the process sub PDL::uniq { use PDL::Core 'barf'; my ($arr) = @_; return $arr if($arr->nelem == 0); # The null list is unique (CED) my $srt = $arr->clump(-1)->qsort; my $uniq = $srt->where($srt != $srt->rotate(-1)); # make sure we return something if there is only one value return $uniq->nelem == 0 ? $srt->index(0) : $uniq; } =head2 uniqvec =for ref return all unique vectors out of a collection The unique vectors are returned in lexicographically sorted ascending order. The 0th dimension of the input PDL is treated as a dimensional index within each vector, and the 1st and any higher dimensions are taken to run across vectors. The return value is always 2D; any structure of the input PDL (beyond using the 0th dimension for vector index) is lost. See also L for a uniqe list of scalars; and L for sorting a list of vectors lexicographcally. =cut sub PDL::uniqvec { my($pdl) = shift; return $pdl if($pdl->nelem == 0 || $pdl->ndims <2 ); my $srt = $pdl->mv(0,-1)-> clump($pdl->ndims - 1)-> mv(-1,0)->qsortvec-> mv(0,-1); my $uniq = ($srt != $srt->rotate(-1)) -> mv(0,-1) -> orover->which; return $uniq->nelem==0 ? $srt->slice(":,(0)") : $srt->dice($uniq)->mv(0,-1); } EOPM ##################################################################### # clipping routines ##################################################################### # clipping for my $opt ( ['hclip','>'], ['lclip','<'] ) { my $name = $opt->[0]; my $op = $opt->[1]; pp_def( $name, HandleBad => 1, Pars => 'a(); b(); [o] c()', Code => '$c() = ($a() '.$op.' $b()) ? $b() : $a();', BadCode => 'if ( $ISBAD(a()) || $ISBAD(b()) ) { $SETBAD(c()); } else { $c() = ($a() '.$op.' $b()) ? $b() : $a(); }', Doc => 'clip C<$a> by C<$b> (C<$b> is '. ($name eq 'hclip' ? 'upper' : 'lower').' bound)', PMCode=><<"EOD", sub PDL::$name { my (\$a,\$b) = \@_; my \$c; if (\$a->is_inplace) { \$a->set_inplace(0); \$c = \$a; } elsif (\$#_ > 1) {\$c=\$_[2]} else {\$c=PDL->nullcreate(\$a)} &PDL::_${name}_int(\$a,\$b,\$c); return \$c; } EOD ); # pp_def $name } # for: my $opt pp_add_exported('', 'clip'); pp_addpm(<<'EOD'); =head2 clip =for ref Clip a piddle by (optional) upper or lower bounds. =for usage $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 L and L. EOD } # if: $bvalflag pp_addpm(<<'EOD'); =cut *clip = \&PDL::clip; sub PDL::clip { my($a, $b, $c) = @_; my $d; if($a->is_inplace) {$a->set_inplace(0); $d = $a} elsif($#_ > 2) {$d=$_[3]} else {$d = PDL->nullcreate($a)} if(defined $b) { &PDL::_lclip_int($a,$b,$d); if(defined $c) { &PDL::_hclip_int($d,$c,$d); } } elsif(defined $c) { &PDL::_hclip_int($a,$c,$d); } return $d; } EOD ############################################################ # elementary statistics and histograms ############################################################ pp_def( 'wtstat', HandleBad => 1, Pars => 'a(n); wt(n); avg(); [o]b();', OtherPars => 'int deg', Code => 'double wtsum = 0; double statsum = 0; loop(n) %{ register double tmp; register int i; wtsum += $wt(); tmp=1; for(i=0; i<$COMP(deg); i++) tmp *= $a(); statsum += $wt() * (tmp - $avg()); %} $b() = statsum / wtsum;', BadCode => 'double wtsum = 0; double statsum = 0; int flag = 0; loop(n) %{ if ( $ISGOOD(wt()) && $ISGOOD(a()) && $ISGOOD(avg()) ) { register double tmp; register int i; wtsum += $wt(); tmp=1; for(i=0; i<$COMP(deg); i++) tmp *= $a(); statsum += $wt() * (tmp - $avg()); flag = 1; } %} if ( flag ) { $b() = statsum / wtsum; } else { $SETBAD(b()); $PDLSTATESETBAD(b); }', CopyBadStatusCode => '', Doc => '=for ref Weighted statistical moment of given degree This calculates a weighted statistic over the vector C. The formula is b() = (sum_i wt_i * (a_i ** degree - avg)) / (sum_i wt_i) ', BadDoc => 'Bad values are ignored in any calculation; C<$b> will only have its bad flag set if the output contains any bad data.', ); pp_def('statsover', HandleBad => 1, Pars => 'a(n); w(n); int+ [o]avg(); int+ [o]rms(); int+ [o]min(); int+ [o]max(); int+ [o]adev()', Code => '$GENERIC(avg) tmp = 0; $GENERIC(rms) tmp1 = 0; $GENERIC(adev) tmp2 = 0; $GENERIC(rms) diff = 0; $GENERIC(min) curmin, curmax; $GENERIC(w) norm = 0; loop(n) %{ tmp += $a()*$w(); norm += $w(); if (!n) { curmin = $a(); curmax = $a();} if ($a() < curmin) { curmin = $a(); } else if ($a() > curmax) { curmax = $a(); } %} $avg() = tmp / norm; $min() = curmin; $max() = curmax; /* Calculate the RMS using the corrected two-pass algorithm */ tmp = 0; loop(n) %{ diff = ($a()*$w() - $avg()); tmp += diff*diff; tmp1 += diff; tmp2 += abs(diff); %} $rms() = sqrt ( (tmp - tmp1*tmp1/norm)/((norm - ($GENERIC(rms)) 1)) ); $adev() = sqrt( tmp2/ norm );', BadCode => '$GENERIC(avg) tmp = 0; $GENERIC(rms) tmp1 = 0; $GENERIC(adev) tmp2 = 0; $GENERIC(rms) diff = 0; $GENERIC(min) curmin, curmax; $GENERIC(w) norm = 0; int flag = 0; loop(n) %{ /* perhaps should check w() for bad values too ? */ if ( $ISGOOD(a()) ) { tmp += $a()*$w(); norm += $w(); if (!flag) { curmin = $a(); curmax = $a(); flag=1; } if ($a() < curmin) { curmin = $a(); } else if ($a() > curmax) { curmax = $a(); } } %} /* have at least one valid point if flag == 1 */ if ( flag ) { $avg() = tmp / norm; $min() = curmin; $max() = curmax; tmp = 0; loop(n) %{ if ($ISGOOD(a())) { diff = ($a()*$w() - $avg()); tmp += diff*diff; tmp1 += diff; tmp2 += abs(diff); } %} $rms() = sqrt ( (tmp - tmp1*tmp1/norm)/( (norm - ($GENERIC(rms)) 1))); $adev() = sqrt ( tmp2 / norm); } else { $SETBAD(avg()); $SETBAD(rms()); $SETBAD(adev()); $SETBAD(min()); $SETBAD(max()); }', PMCode => ' sub PDL::statsover { barf(\'Usage: ($mean,[$rms, $median, $min, $max, $adev]) = statsover($data,[$weights])\') if $#_>1; my ($data, $weights) = @_; $weights = $data->ones() if !defined($weights); my $median = $data->medover(); my $mean = PDL->nullcreate($data); my $rms = PDL->nullcreate($data); my $min = PDL->nullcreate($data); my $max = PDL->nullcreate($data); my $adev = PDL->nullcreate($data); &PDL::_statsover_int($data, $weights, $mean, $rms, $min, $max, $adev); return $mean unless wantarray; return ($mean, $rms, $median, $min, $max, $adev); } ', Doc => ' =for ref Calculate useful statistics over a dimension of a piddle =for usage ($mean, $rms, $median, $min, $max, $adev) = statover($piddle, $weights); This utility function calculates various useful quantities of a piddle. These are the mean: MEAN = sum (x)/ N with C being the number of elements in x, the root mean square deviation from the mean, RMS, given as, RMS = sqrt(sum( (x-mean(x))^2 )/(N-1)); Note the use of C which for almost all cases should be the right normalisation factor. The routine also returns the median, minimum and maximum of the piddle as well as the mean absolute deviation, defined as: ADEV = sqrt(sum( abs(x-mean(x)) )/N) note here that we use the mean and not the median. This could possibly be changed in future versions of the code. This operator is a projection operator so the calculation will take place over the final dimension. Thus if the input is N-dimensional each returned value will be N-1 dimensional, to calculate the statistics for the entire piddle either use C directly on the piddle or call C. ', BadDoc => ' Bad values are simply ignored in the calculation and if all data are bad the results will also be bad. ', ); pp_add_exported('','stats'); pp_addpm(<<'EOD'); =head2 stats =for ref Calculates useful statistics on a piddle =for usage ($mean,$rms,$median,$min,$max) = stats($piddle,[$weights]); This utility calculates all the most useful quantities in one call. B 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 ( $bvalflag ) { pp_addpm(<<'EOD'); =for bad The return values if all elements are bad is currently poorly defined. EOD } # if: bvalflag pp_addpm(<<'EOD'); =cut *stats = \&PDL::stats; sub PDL::stats { barf('Usage: ($mean,[$rms]) = stats($data,[$weights])') if $#_>1; my ($data,$weights) = @_; my ($mean,$rms); if ($#_==0) { EOD if ( $bvalflag ) { pp_addpm(<<'!NO!SUBS!'); my $npts = $data->ngood; !NO!SUBS! } else { pp_addpm(<<'!NO!SUBS!'); my $npts = $data->nelem; !NO!SUBS! } # if: $bvalflag pp_addpm(<<'EOD'); if ( $npts == 0 ) { $mean = 0.0; $rms = 0.0; } else { $mean = $data->dsum / $npts; $rms = sqrt( ((($data-$mean)**2 )->dsum) / ($npts-1) ); } } else { my $wtsum = $weights->dsum; if ( $wtsum == 0.0 ) { $mean = 0.0; $rms = 0.0; } else { $mean = (($weights*$data)->dsum) / $wtsum; $rms = sqrt( ( ( $weights*(($data-$mean)**2) )->dsum ) / $wtsum ); } } my ($median,$min,$max) = ($data->median,$data->min,$data->max); print "Mean = $mean, RMS = $rms, Median = $median\n". "Min = $min, Max = $max\n" if $PDL::verbose; return $mean unless wantarray; return ($mean,$rms,$median,$min,$max); } EOD for( {Name => 'histogram', WeightPar => '', HistType => 'int+', HistOp => '++', Doc1 => "", Doc2 => "", Doc3 => "number of\n", Doc4 => "\nUse L instead for a high-level interface.\n", Doc5 => "histogram(pdl(1,1,2),1,0,3)\n [0 2 1]" }, {Name => 'whistogram', WeightPar => 'float+ wt(n);', HistType => 'float+', HistOp => '+= $wt()', Doc1 => " from weighted data", Doc2 => "\$weights, ", Doc3 => "sum of the values in C<\$weights>\nthat correspond to ", Doc4 => "", Doc5 => "whistogram(pdl(1,1,2), pdl(0.1,0.1,0.5), 1, 0, 4)\n [0 0.2 0.5 0]" } ) { pp_def($_->{Name}, Pars => 'in(n); '.$_->{WeightPar}.$_->{HistType}. '[o] hist(m)', # set outdim by Par! OtherPars => 'double step; double min; int msize => m', HandleBad => 1, Code => 'register int j; register int maxj = $SIZE(m)-1; register double min = $COMP(min); register double step = $COMP(step); threadloop %{ loop(m) %{ $hist() = 0; %} %} threadloop %{ loop(n) %{ j = (int) (($in()-min)/step); if (j<0) j=0; if (j > maxj) j = maxj; ($hist(m => j))'.$_->{HistOp}.'; %} %}', BadCode => 'register int j; register int maxj = $SIZE(m)-1; register double min = $COMP(min); register double step = $COMP(step); threadloop %{ loop(m) %{ $hist() = 0; %} %} threadloop %{ loop(n) %{ if ( $ISGOOD(in()) ) { j = (int) (($in()-min)/step); if (j<0) j=0; if (j > maxj) j = maxj; ($hist(m => j))'.$_->{HistOp}.'; } %} %}', Doc=><<"EOD"); =for ref Calculates a histogram$_->{Doc1} for given stepsize and minimum. =for usage \$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 C<\$numbins> bins starting from C<\$min>, each C<\$step> wide. The value in each bin is the $_->{Doc3}values in C<\$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 C<\$a(10,12)> into C<\$b(15)> and get the result you want. $_->{Doc4} =for example 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 => '+= $wt()', Doc1 => " from weighted data", Doc2 => " \$weights,", Doc3 => "sum of the values in\nC<\$weights> that correspond to ", Doc5 => "whistogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),pdl(0.1,0.2,0.3,0.4,0.5),1,0,3,1,0,3) [ [ 0 0 0] [ 0 0.5 0.9] [ 0 0.1 0] ] "} ) { pp_def($_->{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))'.$_->{HistOp}.'; } %} %} ', Doc=><<"EOD"); =for ref Calculates a 2d histogram$_->{Doc1}. =for usage \$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 C<\$nbinx> x C<\$nbiny> bins, with the lower limits of the first one at C<(\$minx, \$miny)>, and with bin size C<(\$stepx, \$stepy)>. The value in each bin is the $_->{Doc3}values in C<\$datax> and C<\$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. =for example 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 =for example $a = ones(2,4,7); $b = sequence 5; $c = $a->append($b); # size of $c is now (7,4,7) (a jumbo-piddle ;) C 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 C. ' ); pp_addpm(<<'EOD') =head2 glue =for usage $c = $a->glue(,$b,...) =for ref Glue two or more PDLs together along an arbitrary dimension (N-D L). Sticks $a, $b, and all following arguments together using a combination of xchg() and append(). All other dimensions must be compatible in the threading sense. C is implemented in pdl, and should probably be updated (one day) to a pure PP function. =cut sub PDL::glue{ my($a) = shift; my($dim) = shift; if($dim - $a->dim(0) > 100) { print STDERR "warning:: PDL::glue allocating >100 dimensions!\n"; } while($dim > $a->ndims) { $a = $a->dummy(-1,1); } $a = $a->xchg(0,$dim); while(scalar(@_)){ my $b = shift; while($dim > $b->ndims) { $b = $b->dummy(-1,1); } $b = $b->xchg(0,$dim); $a = $a->append($b); } $a->xchg(0,$dim); } EOD ; pp_def( 'axisvalues', Pars => '[o,nc]a(n)', Code => 'loop(n) %{ $a() = n; %}', Doc => ' =for ref Internal routine C is the internal primitive that implements L and alters its argument. ' ); # pp_def: axisvalues pp_addpm(<<'EOD'); =head2 random =for ref Constructor which returns piddle of random numbers =for usage $a = random([type], $nx, $ny, $nz,...); $a = random $b; etc (see L). This is the uniform distribution between 0 and 1 (assumedly excluding 1 itself). The arguments are the same as C (q.v.) - i.e. one can specify dimensions, types or give a template. You can use the perl function L to seed the random generator. For further details consult Perl's L documentation. =head2 randsym =for ref Constructor which returns piddle of random numbers =for usage $a = randsym([type], $nx, $ny, $nz,...); $a = randsym $b; etc (see L). This is the uniform distribution between 0 and 1 (excluding both 0 and 1, cf L). The arguments are the same as C (q.v.) - i.e. one can specify dimensions, types or give a template. You can use the perl function L to seed the random generator. For further details consult Perl's L documentation. =cut EOD pp_addhdr(<<'EOH'); #ifndef Drand01 #define Drand01() (((double)rand()) / (RAND_MAX+1.0)) #endif EOH pp_def( 'random', Pars=>'a();', PMFunc => '', Code => '$a() = Drand01();', Doc=>undef, PMCode=><<'EOD', sub random { ref($_[0]) && ref($_[0]) ne 'PDL::Type' ? $_[0]->random : PDL->random(@_) } sub PDL::random { my $class = shift; my $x = scalar(@_)? $class->new_from_specification(@_) : $class->new_or_inplace; &PDL::_random_int($x); return $x; } EOD ); pp_def( 'randsym', Pars=>'a();', PMFunc => '', Code => 'double tmp; do tmp = Drand01(); while (tmp == 0.0); /* 0 < tmp < 1 */ $a() = tmp;', Doc=>undef, PMCode=><<'EOD', sub randsym { ref($_[0]) && ref($_[0]) ne 'PDL::Type' ? $_[0]->randsym : PDL->randsym(@_) } sub PDL::randsym { my $class = shift; my $x = scalar(@_)? $class->new_from_specification(@_) : $class->new_or_inplace; &PDL::_randsym_int($x); return $x; } EOD ); pp_addpm(<<'EOD'); =head2 grandom =for ref Constructor which returns piddle of Gaussian random numbers =for usage $a = grandom([type], $nx, $ny, $nz,...); $a = grandom $b; etc (see L). This is generated using the math library routine C. Mean = 0, Stddev = 1 You can use the perl function L to seed the random generator. For further details consult Perl's L documentation. =cut sub grandom { ref($_[0]) && ref($_[0]) ne 'PDL::Type' ? $_[0]->grandom : PDL->grandom(@_) } sub PDL::grandom { my $class = shift; my $x = scalar(@_)? $class->new_from_specification(@_) : $class->new_or_inplace; use PDL::Math 'ndtri'; $x .= ndtri(randsym($x)); return $x; } EOD pp_add_exported('','grandom'); ############################################################### # routines somehow related to interpolation ############################################################### # The last x is ignored... pp_def('vsearch', HandleBad => 0, BadDoc => 'needs major (?) work to handles bad values', Pars => 'i(); x(n); int [o]ip()', GenericTypes => ['F','D'], # too restrictive ? Code => 'int carp=0; threadloop %{ long n1 = $SIZE(n)-1; long jl=-1, jh=n1, m; int up = ($x(n => n1) > $x(n => 0)); $GENERIC() d; while (jh-jl > 1) /* binary search */ { m = (jh+jl) >> 1; if ($i() > $x(n => m) == up) jl = m; else jh = m; } if (jl == -1) { jh = 0; } else if (jl == n1) { if ($i() != $x(n => n1)) carp = 1; jh = n1; } else { jh = jl+1; } $ip() = jh; %} if (carp) warn("some values had to be extrapolated"); ', Doc=><<'EOD'); =for ref routine for searching 1D values i.e. step-function interpolation. =for usage $inds = vsearch($vals, $xs); Returns for each value of C<$vals> the index of the least larger member of C<$xs> (which need to be in increasing order). If the value is larger than any member of C<$xs>, the index to the last element of C<$xs> is returned. =for example 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 L 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'); =for ref routine for 1D linear interpolation =for usage ( $yi, $err ) = interpolate($xi, $x, $y) Given a set of points C<($x,$y)>, use linear interpolation to find the values C<$yi> at a set of points C<$xi>. C uses a binary search to find the suspects, er..., interpolation indices and therefore abscissas (ie C<$x>) have to be I 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 C 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 C<$err> to 1, which is otherwise 0. See also L, which uses the same routine, differing only in the handling of extrapolation - an error message is printed rather than returning an error piddle. =cut EOD pp_add_exported('', 'interpol'); pp_addpm(<<'EOD'); =head2 interpol =for sig Signature: (xi(); x(n); y(n); [o] yi()) =for ref routine for 1D linear interpolation =for usage $yi = interpol($xi, $x, $y) C uses the same search method as L, hence C<$x> must be I ordered (either increasing or decreasing). The difference occurs in the handling of out-of-bounds values; here an error message is printed. =cut # kept in for backwards compatability sub interpol ($$$;$) { my $xi = shift; my $x = shift; my $y = shift; my $yi; if ( $#_ == 0 ) { $yi = $_[0]; } else { $yi = PDL->null; } interpolate( $xi, $x, $y, $yi, my $err = PDL->null ); print "some values had to be extrapolated\n" if any $err; return $yi if $#_ == -1; } # sub: interpol() *PDL::interpol = \&interpol; EOD pp_add_exported('','interpND'); pp_addpm(<<'EOD'); =head2 interpND =for ref Interpolate values from an N-D piddle, with switchable method =for example $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( $index ); InterpND acts like L, collapsing C<$index> by lookup into C<$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 C 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: =over 3 =item method Values can be: =over 3 =item * 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). =item * 1, l, linear, Linear (default for floating point source types) The values are N-linearly interpolated from an N-dimensional cube of size 2. =item * 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). =item * 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. =back =item b, bound, boundary, Boundary This option is passed unmodified into L, which is used as the indexing engine for the interpolation. Some current allowed values are 'extend', 'periodic', 'truncate', and 'mirror' (default is 'truncate'). =item bad contains the fill value used for 'truncate' boundary. (default 0) =item fft An array ref whose associated list is used to stash the FFT of the source data, for the FFT method. =back =cut *interpND = *PDL::interpND; sub PDL::interpND { my $source = shift; my $index = shift; my $options = shift; barf 'Usage: interp_nd($source,$index,[{%options}])\n' if(defined $options and ref $options ne 'HASH'); my($opt) = (defined $options) ? $options : {}; my($method) = $opt->{m} || $opt->{meth} || $opt->{method} || $opt->{Method}; if(!defined $method) { $method = ($source->type <= zeroes(long,1)->type) ? 'sample' : 'linear'; } my($boundary) = $opt->{b} || $opt->{boundary} || $opt->{Boundary} || $opt->{bound} || $opt->{Bound} || 'extend'; my($bad) = $opt->{bad} || $opt->{Bad} || 0.0; if($method =~ m/^s(am(p(le)?)?)?/i) { return $source->range(PDL::Math::floor($index+0.5),0,$boundary); } elsif (($method eq 1) || $method =~ m/^l(in(ear)?)?/i) { ## key: (ith = index thread; cth = cube thread; sth = source thread) my $d = $index->dim(0); my $di = $index->ndims - 1; # Grab a 2-on-a-side n-cube around each desired pixel my $samp = $source->range($index->floor,2,$boundary); # (ith, cth, sth) # Reorder to put the cube dimensions in front and convert to a list $samp = $samp->reorder( $di .. $di+$d-1, 0 .. $di-1, $di+$d .. $samp->ndims-1) # (cth, ith, sth) ->clump($d); # (clst, ith, sth) # Enumerate the corners of an n-cube and convert to a list # (the 'x' is the normal perl repeat operator) my $crnr = PDL::Basic::ndcoords( (2) x $index->dim(0) ) # (index,cth) ->mv(0,-1)->clump($index->dim(0))->mv(-1,0); # (index, clst) # a & b are the weighting coefficients. my($a,$b); { my $bb = PDL::Math::floor($index); $a = ($index - $bb) -> dummy(1,$crnr->dim(1)); # index, clst, ith $b = ($bb + 1 - $index) -> dummy(1,$crnr->dim(1)); # index, clst, ith } # Use 1/0 corners to select which multiplier happens, multiply # 'em all together to get sample weights, and sum to get the answer. my $out = ( ($a * ($crnr==1) + $b * ($crnr==0)) #index, clst, ith -> prodover #clst, ith ); $out = ($out * $samp)->sumover; # ith, sth return $out; } elsif(($method eq 3) || $method =~ m/^c(u(b(e|ic)?)?)?/i) { my ($d,@di) = $index->dims; my $di = $index->ndims - 1; # Grab a 4-on-a-side n-cube around each desired pixel my $samp = $source->range($index->floor - 1,4,$boundary) #ith, cth, sth ->reorder( $di .. $di+$d-1, 0..$di-1, $di+$d .. $source->ndims-1 ); # (cth, ith, sth) # Make a cube of the subpixel offsets, and expand its dims to # a 4-on-a-side N-1 cube, to match the slices of $samp (used below). my $b = $index - $index->floor; for my $i(1..$d-1) { $b = $b->dummy($i,4); } # Collapse by interpolation, one dimension at a time... for my $i(0..$d-1) { my $a0 = $samp->slice("(1)"); # Just-under-sample my $a1 = $samp->slice("(2)"); # Just-over-sample my $a1a0 = $a1 - $a0; my $gradient = 0.5 * ($samp->slice("2:3")-$samp->slice("0:1")); my $s0 = $gradient->slice("(0)"); # Just-under-gradient my $s1 = $gradient->slice("(1)"); # Just-over-gradient $bb = $b->slice("($i)"); # Collapse the sample... $samp = ( $a0 + $bb * ( $s0 + $bb * ( (3 * $a1a0 - 2*$s0 - $s1) + $bb * ( $s1 + $s0 - 2*$a1a0 ) ) ) ); # "Collapse" the subpixel offset... $b = $b->slice(":,($i)"); } return $samp; } elsif($method =~ m/^f(ft|ourier)?/i) { eval "use PDL::FFT;"; my $fftref = $opt->{fft}; $fftref = [] unless(ref $fftref eq 'ARRAY'); if(@$fftref != 2) { my $a = $source->copy; my $b = zeroes($source); fftnd($a,$b); $fftref->[0] = sqrt($a*$a+$b*$b) / $a->nelem; $fftref->[1] = - atan2($b,$a); } my $i; my $c = PDL::Basic::ndcoords($source); # (dim, source-dims) for $i(1..$index->ndims-1) { $c = $c->dummy($i,$index->dim($i)) } my $id = $index->ndims-1; my $phase = (($c * $index * 3.14159 * 2 / pdl($source->dims)) ->sumover) # (index-dims, source-dims) ->reorder($id..$id+$source->ndims-1,0..$id-1); # (src, index) my $phref = $fftref->[1]->copy; # (source-dims) my $mag = $fftref->[0]->copy; # (source-dims) for $i(1..$index->ndims-1) { $phref = $phref->dummy(-1,$index->dim($i)); $mag = $mag->dummy(-1,$index->dim($i)); } my $out = cos($phase + $phref ) * $mag; $out = $out->clump($source->ndims)->sumover; return $out; } else { barf("interpND: unknown method '$method'; valid ones are 'linear' and 'sample'.\n"); } } EOD ############################################################## # things related to indexing: one2nd, which, where ############################################################## pp_add_exported("", 'one2nd'); pp_addpm(<<'EOD'); =head2 one2nd =for ref Converts a one dimensional index piddle to a set of ND coordinates =for usage @coords=one2nd($a, $indices) returns an array of piddles containing the ND indexes corresponding to the one dimensional list indices. The indices are assumed to correspond to array C<$a> clumped using C. This routine is used in L, but is useful on its own occasionally. =for example 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 =cut *one2nd = \&PDL::one2nd; sub PDL::one2nd { barf "Usage: one2nd \$array \$indices\n" if $#_ != 1; my ($a, $ind)=@_; my @dimension=$a->dims; my(@index); my $count=0; foreach (@dimension) { $index[$count++]=$ind % $_; $ind=long($ind/$_); } return @index; } EOD my $doc_which = <<'EOD'; =for ref Returns piddle of indices of non-zero values. =for usage $i = which($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 L for similar functionality. If you want to return both the indices of non-zero values and the complement, use the function L. =for example 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 $doc_which_both = <<'EOD'; =for ref Returns piddle of indices of non-zero values and their complement =for usage ($i, $c_i) = which_both($mask); This works just as L, but the complement of C<$i> will be in C<$c_i>. =for example 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; idims[0]; i++) { if ( *(m_datap+inc*i+offs)) sum++; } '.$_->{Autosize} . ' /* printf("RedoDimsCode: setting dim m to %ld\n",sum); */' ); } pp_addpm(<<'EOD' =head2 where =for ref Return the values from a piddle for whose indices a condition piddle is nonzero. =for usage $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, $x+5>0); Note: C<$i> is always 1-D, even if C<$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. =cut sub PDL::where { barf "Usage: where( \$pdl1, ..., \$pdlN, \$mask )\n" if $#_ == 0; if($#_ == 1) { my($data,$mask) = @_; $data = $_[0]->clump(-1) if $_[0]->getndims>1; $mask = $_[1]->clump(-1) if $_[0]->getndims>1; return $data->index($mask->which()); } else { if($_[-1]->getndims > 1) { my $mask = $_[-1]->clump(-1)->which; return map {$_->clump(-1)->index($mask)} @_[0..$#_-1]; } else { my $mask = $_[-1]->which; return map {$_->index($mask)} @_[0..$#_-1]; } } } *where = \&PDL::where; EOD ); pp_add_exported("", 'where'); pp_addpm(<<'EOD' =head2 whichND =for ref Returns the coordinates for non-zero values. =for usage 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 L or L; 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 C<$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 C<$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. =for example 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 =cut *whichND = \&PDL::whichND; sub PDL::whichND { my $mask = shift; # List context: generate a perl list by dimension if(wantarray) { my $ind=($mask->clump(-1))->which; return $mask->one2nd($ind); } # Scalar context: generate an N-D index piddle return null() unless ($mask->getndims); $ind = $mask->flat->which->dummy(0,$mask->getndims)->long->make_physical; my $mult = ones($mask->getndims)->long; my @mdims = $mask->dims; my $i; for $i(0..$#mdims-1) { # use $tmp for 5.005_03 compatibility (my $tmp = $mult->index($i+1)) .= $mult->index($i)*$mdims[$i]; } for $i(0..$#mdims) { my($s) = $ind->index($i); $s /= $mult->index($i); $s %= $mdims[$i]; } return $ind; } EOD ); pp_add_exported("", 'whichND'); pp_done();