# # GENERATED WITH PDL::PP! Don't modify! # package PDL::Primitive; @EXPORT_OK = qw( PDL::PP inner PDL::PP outer matmult PDL::PP matmult PDL::PP innerwt PDL::PP inner2 PDL::PP inner2d PDL::PP inner2t PDL::PP crossp PDL::PP norm PDL::PP indadd PDL::PP conv1d PDL::PP in uniq uniqind uniqvec PDL::PP hclip PDL::PP lclip clip PDL::PP clip PDL::PP wtstat PDL::PP statsover stats PDL::PP histogram PDL::PP whistogram PDL::PP histogram2d PDL::PP whistogram2d PDL::PP fibonacci PDL::PP append PDL::PP axisvalues PDL::PP random PDL::PP randsym grandom vsearch PDL::PP vsearch_sample PDL::PP vsearch_insert_leftmost PDL::PP vsearch_insert_rightmost PDL::PP vsearch_match PDL::PP vsearch_bin_inclusive PDL::PP vsearch_bin_exclusive PDL::PP interpolate interpol interpND one2nd PDL::PP which PDL::PP which_both where whereND whichND setops intersect ); %EXPORT_TAGS = (Func=>[@EXPORT_OK]); use PDL::Core; use PDL::Exporter; use DynaLoader; @ISA = ( 'PDL::Exporter','DynaLoader' ); push @PDL::Core::PP, __PACKAGE__; bootstrap PDL::Primitive ; 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<PDL::Indexing|PDL::Indexing> for how to use indices creatively. For explanation of the signature format, see L<PDL::PP|PDL::PP>. =head1 SYNOPSIS # Pulls in PDL::Primitive, among other modules. use PDL; # Only pull in PDL::Primitive: use PDL::Primitive; =cut =head1 FUNCTIONS =cut =head2 inner =for sig Signature: (a(n); b(n); [o]c()) =for ref Inner product over one dimension c = sum_i a_i * b_i =for bad =for bad If C<a() * b()> contains only bad data, C<c()> is set bad. Otherwise C<c()> will have its bad flag cleared, as it will not contain any bad values. =cut *inner = \&PDL::inner; =head2 outer =for sig Signature: (a(n); b(m); [o]c(n,m)) =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. =for bad outer processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *outer = \&PDL::outer; =head2 x =for sig Signature: (a(i,z), b(x,i),[o]c(x,z)) =for ref Matrix multiplication PDL overloads the C<x> operator (normally the repeat operator) for matrix multiplication. The number of columns (size of the 0 dimension) in the left-hand argument must normally equal the number of rows (size of the 1 dimension) in the right-hand argument. Row vectors are represented as (N x 1) two-dimensional PDLs, or you may be sloppy and use a one-dimensional PDL. Column vectors are represented as (1 x N) two-dimensional PDLs. Threading occurs in the usual way, but as both the 0 and 1 dimension (if present) are included in the operation, you must be sure that you don't try to thread over either of those dims. EXAMPLES Here are some simple ways to define vectors and matrices: pdl> $r = pdl(1,2); # A row vector pdl> $c = pdl([[3],[4]]); # A column vector pdl> $c = pdl(3,4)->(*1); # A column vector, using NiceSlice pdl> $m = pdl([[1,2],[3,4]]); # A 2x2 matrix Now that we have a few objects prepared, here is how to matrix-multiply them: pdl> print $r x $m # row x matrix = row [ [ 7 10] ] pdl> print $m x $r # matrix x row = ERROR PDL: Dim mismatch in matmult of [2x2] x [2x1]: 2 != 1 pdl> print $m x $c # matrix x column = column [ [ 5] [11] ] pdl> print $m x 2 # Trivial case: scalar mult. [ [2 4] [6 8] ] pdl> print $r x $c # row x column = scalar [ [11] ] pdl> print $c x $r # column x row = matrix [ [3 6] [4 8] ] INTERNALS The mechanics of the multiplication are carried out by the L<matmult|/matmult> method. =cut =head2 matmult =for sig Signature: (a(t,h); b(w,t); [o]c(w,h)) =for ref Matrix multiplication Notionally, matrix multiplication $x x $y is equivalent to the threading expression $x->dummy(1)->inner($y->xchg(0,1)->dummy(2),$c); but for large matrices that breaks CPU cache and is slow. Instead, matmult calculates its result in 32x32x32 tiles, to keep the memory footprint within cache as long as possible on most modern CPUs. For usage, see L<x|/x>, a description of the overloaded 'x' operator =for bad matmult ignores the bad-value flag of the input piddles. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut sub PDL::matmult { my ($x,$y,$c) = @_; $y = pdl($y) unless eval { $y->isa('PDL') }; $c = PDL->null unless eval { $c->isa('PDL') }; while($x->getndims < 2) {$x = $x->dummy(-1)} while($y->getndims < 2) {$y = $y->dummy(-1)} return ($c .= $x * $y) if( ($x->dim(0)==1 && $x->dim(1)==1) || ($y->dim(0)==1 && $y->dim(1)==1) ); if($y->dim(1) != $x->dim(0)) { barf(sprintf("Dim mismatch in matmult of [%dx%d] x [%dx%d]: %d != %d",$x->dim(0),$x->dim(1),$y->dim(0),$y->dim(1),$x->dim(0),$y->dim(1))); } PDL::_matmult_int($x,$y,$c); $c; } *matmult = \&PDL::matmult; =head2 innerwt =for sig Signature: (a(n); b(n); c(n); [o]d()) =for ref Weighted (i.e. triple) inner product d = sum_i a(i) b(i) c(i) =for bad innerwt processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *innerwt = \&PDL::innerwt; =head2 inner2 =for sig Signature: (a(n); b(n,m); c(m); [o]d()) =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<a> and C<c> since that would be very wasteful. Instead, you should use a temporary for C<b*c>. =for bad inner2 processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *inner2 = \&PDL::inner2; =head2 inner2d =for sig Signature: (a(n,m); b(n,m); [o]c()) =for ref Inner product over 2 dimensions. Equivalent to $c = inner($x->clump(2), $y->clump(2)) =for bad inner2d processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *inner2d = \&PDL::inner2d; =head2 inner2t =for sig Signature: (a(j,n); b(n,m); c(m,k); [t]tmp(n,k); [o]d(j,k))) =for ref Efficient Triple matrix product C<a*b*c> Efficiency comes from by using the temporary C<tmp>. This operation only scales as C<N**3> whereas threading using L<inner2|/inner2> would scale as C<N**4>. The reason for having this routine is that you do not need to have the same thread-dimensions for C<tmp> 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. =for bad inner2t processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *inner2t = \&PDL::inner2t; =head2 crossp =for sig Signature: (a(tri=3); b(tri); [o] c(tri)) =for ref Cross product of two 3D vectors After =for example $c = crossp $x, $y the inner product C<$c*$x> and C<$c*$y> will be zero, i.e. C<$c> is orthogonal to C<$x> and C<$y> =for bad crossp 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. =cut *crossp = \&PDL::crossp; =head2 norm =for sig Signature: (vec(n); [o] norm(n)) =for ref Normalises a vector to unit Euclidean length =for bad norm processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *norm = \&PDL::norm; =head2 indadd =for sig Signature: (a(); indx ind(); [o] sum(m)) =for ref Threaded Index Add: Add C<a> to the C<ind> element of C<sum>, i.e: sum(ind) += a =for example Simple Example: $x = 2; $ind = 3; $sum = zeroes(10); indadd($x,$ind, $sum); print $sum #Result: ( 2 added to element 3 of $sum) # [0 0 0 2 0 0 0 0 0 0] Threaded Example: $x = pdl( 1,2,3); $ind = pdl( 1,4,6); $sum = zeroes(10); indadd($x,$ind, $sum); print $sum."\n"; #Result: ( 1, 2, and 3 added to elements 1,4,6 $sum) # [0 1 0 0 2 0 3 0 0 0] =for bad =for bad The routine barfs if any of the indices are bad. =cut *indadd = \&PDL::indadd; =head2 conv1d =for sig Signature: (a(m); kern(p); [o]b(m); int reflect) =for ref 1D convolution along first dimension The m-th element of the discrete convolution of an input piddle C<$a> of size C<$M>, and a kernel piddle C<$kern> of size C<$P>, is calculated as n = ($P-1)/2 ==== \ ($a conv1d $kern)[m] = > $a_ext[m - n] * $kern[n] / ==== n = -($P-1)/2 where C<$a_ext> is either the periodic (or reflected) extension of C<$a> so it is equal to C<$a> on C< 0..$M-1 > and equal to the corresponding periodic/reflected image of C<$a> outside that range. =for example $con = conv1d sequence(10), pdl(-1,0,1); $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<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. $y = $x->mv(2,0)->conv1d($kernel)->mv(0,2); # along third dim This function is useful for threaded filtering of 1D signals. Compare also L<conv2d|PDL::Image2D/conv2d>, L<convolve|PDL::ImageND/convolve>, L<fftconvolve|PDL::FFT/fftconvolve()>, L<fftwconv|PDL::FFTW/fftwconv>, L<rfftwconv|PDL::FFTW/rfftwconv> =for bad WARNING: C<conv1d> processes bad values in its inputs as the numeric value of C<< $pdl->badvalue >> so it is not recommended for processing pdls with bad values in them unless special care is taken. =for bad conv1d ignores the bad-value flag of the input piddles. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut sub PDL::conv1d { my $opt = pop @_ if ref($_[$#_]) eq 'HASH'; die 'Usage: conv1d( a(m), kern(p), [o]b(m), {Options} )' if $#_<1 || $#_>2; my($x,$kern) = @_; my $c = $#_ == 2 ? $_[2] : PDL->null; &PDL::_conv1d_int($x,$kern,$c, !(defined $opt && exists $$opt{Boundary}) ? 0 : lc $$opt{Boundary} eq "reflect"); return $c; } *conv1d = \&PDL::conv1d; =head2 in =for sig Signature: (a(); b(n); [o] c()) =for ref test if a is in the set of values b =for example $goodmsk = $labels->in($goodlabels); print pdl(3,1,4,6,2)->in(pdl(2,3,3)); [1 0 0 0 1] C<in> is akin to the I<is an element of> of set theory. In principle, PDL threading could be used to achieve its functionality by using a construct like $msk = ($labels->dummy(0) == $goodlabels)->orover; However, C<in> doesn't create a (potentially large) intermediate and is generally faster. =for bad in 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. =cut *in = \&PDL::in; =head2 uniq =for ref return all unique elements of a piddle The unique elements are returned in ascending order. =for example PDL> p pdl(2,2,2,4,0,-1,6,6)->uniq [-1 0 2 4 6] # 0 is returned 2nd (sorted order) PDL> p pdl(2,2,2,4,nan,-1,6,6)->uniq [-1 2 4 6 nan] # NaN value is returned at end Note: The returned pdl is 1D; any structure of the input piddle is lost. C<NaN> values are never compare equal to any other values, even themselves. As a result, they are always unique. C<uniq> returns the NaN values at the end of the result piddle. This follows the Matlab usage. See L<uniqind|uniqind> if you need the indices of the unique elements rather than the values. =cut =for bad Bad values are not considered unique by uniq and are ignored. $x=sequence(10); $x=$x->setbadif($x%3); print $x->uniq; [0 3 6 9] =cut *uniq = \&PDL::uniq; # return unique elements of array # find as jumps in the sorted array # flattens in the process sub PDL::uniq { use PDL::Core 'barf'; my ($arr) = @_; return $arr if($arr->nelem == 0); # The null list is unique (CED) my $srt = $arr->clump(-1)->where($arr==$arr)->qsort; # no NaNs or BADs for qsort my $nans = $arr->clump(-1)->where($arr!=$arr); my $uniq = ($srt->nelem > 0) ? $srt->where($srt != $srt->rotate(-1)) : $srt; # make sure we return something if there is only one value my $answ = $nans; # NaN values always uniq if ( $uniq->nelem > 0 ) { $answ = $uniq->append($answ); } else { $answ = ( ($srt->nelem == 0) ? $srt : PDL::pdl( ref($srt), [$srt->index(0)] ) )->append($answ); } return $answ; } =head2 uniqind =for ref Return the indices of all unique elements of a piddle The order is in the order of the values to be consistent with uniq. C<NaN> values never compare equal with any other value and so are always unique. This follows the Matlab usage. =for example PDL> p pdl(2,2,2,4,0,-1,6,6)->uniqind [5 4 1 3 6] # the 0 at index 4 is returned 2nd, but... PDL> p pdl(2,2,2,4,nan,-1,6,6)->uniqind [5 1 3 6 4] # ...the NaN at index 4 is returned at end Note: The returned pdl is 1D; any structure of the input piddle is lost. See L<uniq|uniq> if you want the unique values instead of the indices. =cut =for bad Bad values are not considered unique by uniqind and are ignored. =cut *uniqind = \&PDL::uniqind; # return unique elements of array # find as jumps in the sorted array # flattens in the process sub PDL::uniqind { use PDL::Core 'barf'; my ($arr) = @_; return $arr if($arr->nelem == 0); # The null list is unique (CED) # Different from uniq we sort and store the result in an intermediary my $aflat = $arr->flat; my $nanind = which($aflat!=$aflat); # NaN indexes my $good = $aflat->sequence->long->where($aflat==$aflat); # good indexes my $i_srt = $aflat->where($aflat==$aflat)->qsorti; # no BAD or NaN values for qsorti my $srt = $aflat->where($aflat==$aflat)->index($i_srt); my $uniqind; if ($srt->nelem > 0) { $uniqind = which($srt != $srt->rotate(-1)); $uniqind = $i_srt->slice('0') if $uniqind->isempty; } else { $uniqind = which($srt); } # Now map back to the original space my $ansind = $nanind; if ( $uniqind->nelem > 0 ) { $ansind = ($good->index($i_srt->index($uniqind)))->append($ansind); } else { $ansind = $uniqind->append($ansind); } return $ansind; } =head2 uniqvec =for ref Return all unique vectors out of a collection NOTE: If any vectors in the input piddle have NaN values they are returned at the end of the non-NaN ones. This is because, by definition, NaN values never compare equal with any other value. NOTE: The current implementation does not sort the vectors containing NaN values. The unique vectors are returned in lexicographically sorted ascending order. The 0th dimension of the input PDL is treated as a dimensional index within each vector, and the 1st and any higher dimensions are taken to run across vectors. The return value is always 2D; any structure of the input PDL (beyond using the 0th dimension for vector index) is lost. See also L<uniq|uniq> for a unique list of scalars; and L<qsortvec|PDL::Ufunc/qsortvec> for sorting a list of vectors lexicographcally. =cut =for bad If a vector contains all bad values, it is ignored as in L<uniq|uniq>. If some of the values are good, it is treated as a normal vector. For example, [1 2 BAD] and [BAD 2 3] could be returned, but [BAD BAD BAD] could not. Vectors containing BAD values will be returned after any non-NaN and non-BAD containing vectors, followed by the NaN vectors. =cut sub PDL::uniqvec { my($pdl) = shift; return $pdl if ( $pdl->nelem == 0 || $pdl->ndims < 2 ); return $pdl if ( $pdl->slice("(0)")->nelem < 2 ); # slice isn't cheap but uniqvec isn't either my $pdl2d = null; $pdl2d = $pdl->mv(0,-1)->clump($pdl->ndims-1)->mv(-1,0); # clump all but dim(0) my $ngood = null; $ngood = $pdl2d->ones->sumover; $ngood = $pdl2d->ngoodover if ($PDL::Bad::Status && $pdl->badflag); # number of good values each vector my $ngood2 = null; $ngood2 = $ngood->where($ngood); # number of good values with no all-BADs $pdl2d = $pdl2d->mv(0,-1)->dice($ngood->which)->mv(-1,0); # remove all-BAD vectors my $numnan = null; $numnan = ($pdl2d!=$pdl2d)->sumover; # works since no all-BADs to confuse my $presrt = null; $presrt = $pdl2d->mv(0,-1)->dice($numnan->not->which)->mv(0,-1); # remove vectors with any NaN values my $nanvec = null; $nanvec = $pdl2d->mv(0,-1)->dice($numnan->which)->mv(0,-1); # the vectors with any NaN values # use dice instead of nslice since qsortvec might be packing # the badvals to the front of the array instead of the end like # the docs say. If that is the case and it gets fixed, it won't # bust uniqvec. DAL 14-March 2006 my $srt = null; $srt = $presrt->qsortvec->mv(0,-1); # BADs are sorted by qsortvec my $srtdice = $srt; my $somebad = null; if ($PDL::Bad::Status && $srt->badflag) { $srtdice = $srt->dice($srt->mv(0,-1)->nbadover->not->which); $somebad = $srt->dice($srt->mv(0,-1)->nbadover->which); } my $uniq = null; if ($srtdice->nelem > 0) { $uniq = ($srtdice != $srtdice->rotate(-1))->mv(0,-1)->orover->which; } else { $uniq = $srtdice->orover->which; } my $ans = null; if ( $uniq->nelem > 0 ) { $ans = $srtdice->dice($uniq); } else { $ans = ($srtdice->nelem > 0) ? $srtdice->slice("0,:") : $srtdice; } return $ans->append($somebad)->append($nanvec->mv(0,-1))->mv(0,-1); } =head2 hclip =for sig Signature: (a(); b(); [o] c()) =for ref clip (threshold) C<$a> by C<$b> (C<$b> is upper bound) =for bad hclip processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut sub PDL::hclip { my ($x,$y) = @_; my $c; if ($x->is_inplace) { $x->set_inplace(0); $c = $x; } elsif ($#_ > 1) {$c=$_[2]} else {$c=PDL->nullcreate($x)} &PDL::_hclip_int($x,$y,$c); return $c; } *hclip = \&PDL::hclip; =head2 lclip =for sig Signature: (a(); b(); [o] c()) =for ref clip (threshold) C<$a> by C<$b> (C<$b> is lower bound) =for bad lclip processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut sub PDL::lclip { my ($x,$y) = @_; my $c; if ($x->is_inplace) { $x->set_inplace(0); $c = $x; } elsif ($#_ > 1) {$c=$_[2]} else {$c=PDL->nullcreate($x)} &PDL::_lclip_int($x,$y,$c); return $c; } *lclip = \&PDL::lclip; =head2 clip =for ref Clip (threshold) a piddle by (optional) upper or lower bounds. =for usage $y = $x->clip(0,3); $c = $x->clip(undef, $x); =cut =for bad clip handles bad values since it is just a wrapper around L<hclip|/hclip> and L<lclip|/lclip>. =cut =head2 clip =for sig Signature: (a(); l(); h(); [o] c()) =for ref info not available =for bad clip processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *clip = \&PDL::clip; sub PDL::clip { my($x, $l, $h) = @_; my $d; unless(defined($l) || defined($h)) { # Deal with pathological case if($x->is_inplace) { $x->set_inplace(0); return $x; } else { return $x->copy; } } if($x->is_inplace) { $x->set_inplace(0); $d = $x } elsif ($#_ > 2) { $d=$_[3] } else { $d = PDL->nullcreate($x); } if(defined($l) && defined($h)) { &PDL::_clip_int($x,$l,$h,$d); } elsif( defined($l) ) { &PDL::_lclip_int($x,$l,$d); } elsif( defined($h) ) { &PDL::_hclip_int($x,$h,$d); } else { die "This can't happen (clip contingency) - file a bug"; } return $d; } *clip = \&PDL::clip; =head2 wtstat =for sig Signature: (a(n); wt(n); avg(); [o]b(); int deg) =for ref Weighted statistical moment of given degree This calculates a weighted statistic over the vector C<a>. The formula is b() = (sum_i wt_i * (a_i ** degree - avg)) / (sum_i wt_i) =for bad =for bad Bad values are ignored in any calculation; C<$b> will only have its bad flag set if the output contains any bad data. =cut *wtstat = \&PDL::wtstat; =head2 statsover =for sig Signature: (a(n); w(n); float+ [o]avg(); float+ [o]prms(); int+ [o]median(); int+ [o]min(); int+ [o]max(); float+ [o]adev(); float+ [o]rms()) =for ref Calculate useful statistics over a dimension of a piddle =for usage ($mean,$prms,$median,$min,$max,$adev,$rms) = statsover($piddle, $weights); This utility function calculates various useful quantities of a piddle. These are: =over 3 =item * the mean: MEAN = sum (x)/ N with C<N> being the number of elements in x =item * the population RMS deviation from the mean: PRMS = sqrt( sum( (x-mean(x))^2 )/(N-1) The population deviation is the best-estimate of the deviation of the population from which a sample is drawn. =item * the median The median is the 50th percentile data value. Median is found by L<medover|PDL::Ufunc/medover>, so WEIGHTING IS IGNORED FOR THE MEDIAN CALCULATION. =item * the minimum =item * the maximum =item * the average absolute deviation: AADEV = sum( abs(x-mean(x)) )/N =item * RMS deviation from the mean: RMS = sqrt(sum( (x-mean(x))^2 )/N) (also known as the root-mean-square deviation, or the square root of the variance) =back This operator is a projection operator so the calculation will take place over the final dimension. Thus if the input is N-dimensional each returned value will be N-1 dimensional, to calculate the statistics for the entire piddle either use C<clump(-1)> directly on the piddle or call C<stats>. =for bad =for bad Bad values are simply ignored in the calculation, effectively reducing the sample size. If all data are bad then the output data are marked bad. =cut sub PDL::statsover { barf('Usage: ($mean,[$prms, $median, $min, $max, $adev, $rms]) = statsover($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); my $prms = PDL->nullcreate($data); &PDL::_statsover_int($data, $weights, $mean, $prms, $median, $min, $max, $adev, $rms); return $mean unless wantarray; return ($mean, $prms, $median, $min, $max, $adev, $rms); } *statsover = \&PDL::statsover; =head2 stats =for ref Calculates useful statistics on a piddle =for usage ($mean,$prms,$median,$min,$max,$adev,$rms) = stats($piddle,[$weights]); This utility calculates all the most useful quantities in one call. It works the same way as L</statsover>, except that the quantities are calculated considering the entire input PDL as a single sample, rather than as a collection of rows. See L</statsover> for definitions of the returned quantities. =cut =for bad Bad values are handled; if all input values are bad, then all of the output values are flagged bad. =cut *stats = \&PDL::stats; sub PDL::stats { barf('Usage: ($mean,[$rms]) = stats($data,[$weights])') if $#_>1; my ($data,$weights) = @_; # Ensure that $weights is properly threaded over; this could be # done rather more efficiently... if(defined $weights) { $weights = pdl($weights) unless UNIVERSAL::isa($weights,'PDL'); if( ($weights->ndims != $data->ndims) or (pdl($weights->dims) != pdl($data->dims))->or ) { $weights = $weights + zeroes($data) } $weights = $weights->flat; } return PDL::statsover($data->flat,$weights); } =head2 histogram =for sig Signature: (in(n); int+[o] hist(m); double step; double min; int msize => m) =for ref Calculates a histogram for given stepsize and minimum. =for usage $h = histogram($data, $step, $min, $numbins); $hist = zeroes $numbins; # Put histogram in existing piddle. histogram($data, $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 number of 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. For a higher-level interface, see L<hist|PDL::Basic/hist>. =for example pdl> p histogram(pdl(1,1,2),1,0,3) [0 2 1] =for bad histogram processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *histogram = \&PDL::histogram; =head2 whistogram =for sig Signature: (in(n); float+ wt(n);float+[o] hist(m); double step; double min; int msize => m) =for ref Calculates a histogram from weighted data for given stepsize and minimum. =for usage $h = whistogram($data, $weights, $step, $min, $numbins); $hist = zeroes $numbins; # Put histogram in existing piddle. whistogram($data, $weights, $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 sum of the values in C<$weights> that correspond to values in C<$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. =for example pdl> p whistogram(pdl(1,1,2), pdl(0.1,0.1,0.5), 1, 0, 4) [0 0.2 0.5 0] =for bad whistogram processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *whistogram = \&PDL::whistogram; =head2 histogram2d =for sig Signature: (ina(n); inb(n); int+[o] hist(ma,mb); double stepa; double mina; int masize => ma; double stepb; double minb; int mbsize => mb;) =for ref Calculates a 2d histogram. =for usage $h = histogram2d($datax, $datay, $stepx, $minx, $nbinx, $stepy, $miny, $nbiny); $hist = zeroes $nbinx, $nbiny; # Put histogram in existing piddle. histogram2d($datax, $datay, $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, $stepy)>. The value in each bin is the number of values in C<$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 pdl> p 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] ] =for bad histogram2d processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *histogram2d = \&PDL::histogram2d; =head2 whistogram2d =for sig Signature: (ina(n); inb(n); float+ wt(n);float+[o] hist(ma,mb); double stepa; double mina; int masize => ma; double stepb; double minb; int mbsize => mb;) =for ref Calculates a 2d histogram from weighted data. =for usage $h = whistogram2d($datax, $datay, $weights, $stepx, $minx, $nbinx, $stepy, $miny, $nbiny); $hist = zeroes $nbinx, $nbiny; # Put histogram in existing piddle. whistogram2d($datax, $datay, $weights, $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, $stepy)>. The value in each bin is the sum of the values in C<$weights> that correspond to 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 pdl> p 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] ] =for bad whistogram2d processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut *whistogram2d = \&PDL::whistogram2d; =head2 fibonacci =for sig Signature: ([o]x(n)) =for ref Constructor - a vector with Fibonacci's sequence =for bad fibonacci 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. =cut 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; } =head2 append =for sig Signature: (a(n); b(m); [o] c(mn)) =for ref append two piddles by concatenating along their first dimensions =for example $x = ones(2,4,7); $y = sequence 5; $c = $x->append($y); # size of $c is now (7,4,7) (a jumbo-piddle ;) C<append> appends two piddles along their first dimensions. The rest of the dimensions must be compatible in the threading sense. The resulting size of the first dimension is the sum of the sizes of the first dimensions of the two argument piddles - i.e. C<n + m>. Similar functions include L<glue|/glue> (below), which can append more than two piddles along an arbitrary dimension, and L<cat|PDL::Core/cat>, which can append more than two piddles that all have the same sized dimensions. =for bad append 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. =cut *append = \&PDL::append; =head2 glue =for usage $c = $x->glue(<dim>,$y,...) =for ref Glue two or more PDLs together along an arbitrary dimension (N-D L<append|append>). Sticks $x, $y, and all following arguments together along the specified dimension. All other dimensions must be compatible in the threading sense. Glue is permissive, in the sense that every PDL is treated as having an infinite number of trivial dimensions of order 1 -- so C<< $x->glue(3,$y) >> works, even if $x and $y are only one dimensional. If one of the PDLs has no elements, it is ignored. Likewise, if one of them is actually the undefined value, it is treated as if it had no elements. If the first parameter is a defined perl scalar rather than a pdl, then it is taken as a dimension along which to glue everything else, so you can say C<$cube = PDL::glue(3,@image_list);> if you like. C<glue> is implemented in pdl, using a combination of L<xchg|PDL::Slices/xchg> and L<append|append>. It should probably be updated (one day) to a pure PP function. Similar functions include L<append|/append> (above), which appends only two piddles along their first dimension, and L<cat|PDL::Core/cat>, which can append more than two piddles that all have the same sized dimensions. =cut sub PDL::glue{ my($x) = shift; my($dim) = shift; if(defined $x && !(ref $x)) { my $y = $dim; $dim = $x; $x = $y; } if(!defined $x || $x->nelem==0) { return $x unless(@_); return shift() if(@_<=1); $x=shift; return PDL::glue($x,$dim,@_); } if($dim - $x->dim(0) > 100) { print STDERR "warning:: PDL::glue allocating >100 dimensions!\n"; } while($dim >= $x->ndims) { $x = $x->dummy(-1,1); } $x = $x->xchg(0,$dim); while(scalar(@_)){ my $y = shift; next unless(defined $y && $y->nelem); while($dim >= $y->ndims) { $y = $y->dummy(-1,1); } $y = $y->xchg(0,$dim); $x = $x->append($y); } $x->xchg(0,$dim); } =head2 axisvalues =for sig Signature: ([o,nc]a(n)) =for ref Internal routine C<axisvalues> is the internal primitive that implements L<axisvals|PDL::Basic/axisvals> and alters its argument. =for bad axisvalues 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. =cut *axisvalues = \&PDL::axisvalues; =head2 random =for ref Constructor which returns piddle of random numbers =for usage $x = random([type], $nx, $ny, $nz,...); $x = random $y; etc (see L<zeroes|PDL::Core/zeroes>). This is the uniform distribution between 0 and 1 (assumedly excluding 1 itself). The arguments are the same as C<zeroes> (q.v.) - i.e. one can specify dimensions, types or give a template. You can use the perl function L<srand|perlfunc/srand> to seed the random generator. For further details consult Perl's L<srand|perlfunc/srand> documentation. =head2 randsym =for ref Constructor which returns piddle of random numbers =for usage $x = randsym([type], $nx, $ny, $nz,...); $x = randsym $y; etc (see L<zeroes|PDL::Core/zeroes>). This is the uniform distribution between 0 and 1 (excluding both 0 and 1, cf L<random|/random>). The arguments are the same as C<zeroes> (q.v.) - i.e. one can specify dimensions, types or give a template. You can use the perl function L<srand|perlfunc/srand> to seed the random generator. For further details consult Perl's L<srand|perlfunc/srand> documentation. =cut sub random { ref($_[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 $x; } sub randsym { ref($_[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; } =head2 grandom =for ref Constructor which returns piddle of Gaussian random numbers =for usage $x = grandom([type], $nx, $ny, $nz,...); $x = grandom $y; etc (see L<zeroes|PDL::Core/zeroes>). This is generated using the math library routine C<ndtri>. Mean = 0, Stddev = 1 You can use the perl function L<srand|perlfunc/srand> to seed the random generator. For further details consult Perl's L<srand|perlfunc/srand> documentation. =cut sub grandom { ref($_[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; } =head2 vsearch =for sig Signature: ( vals(); xs(n); [o] indx(); [\%options] ) =for ref Efficiently search for values in a sorted piddle, returning indices. =for usage $idx = vsearch( $vals, $x, [\%options] ); vsearch( $vals, $x, $idx, [\%options ] ); B<vsearch> performs a binary search in the ordered piddle C<$x>, for the values from C<$vals> piddle, returning indices into C<$x>. What is a "match", and the meaning of the returned indices, are determined by the options. The C<mode> option indicates which method of searching to use, and may be one of: =over =item C<sample> invoke L<B<vsearch_sample>|/vsearch_sample>, returning indices appropriate for sampling within a distribution. =item C<insert_leftmost> invoke L<B<vsearch_insert_leftmost>|/vsearch_insert_leftmost>, returning the left-most possible insertion point which still leaves the piddle sorted. =item C<insert_rightmost> invoke L<B<vsearch_insert_rightmost>|/vsearch_insert_rightmost>, returning the right-most possible insertion point which still leaves the piddle sorted. =item C<match> invoke L<B<vsearch_match>|/vsearch_match>, returning the index of a matching element, else -(insertion point + 1) =item C<bin_inclusive> invoke L<B<vsearch_bin_inclusive>|/vsearch_bin_inclusive>, returning an index appropriate for binning on a grid where the left bin edges are I<inclusive> of the bin. See below for further explanation of the bin. =item C<bin_exclusive> invoke L<B<vsearch_bin_exclusive>|/vsearch_bin_exclusive>, returning an index appropriate for binning on a grid where the left bin edges are I<exclusive> of the bin. See below for further explanation of the bin. =back The default value of C<mode> is C<sample>. =for example use PDL; my @modes = qw( sample insert_leftmost insert_rightmost match bin_inclusive bin_exclusive ); # Generate a sequence of 3 zeros, 3 ones, ..., 3 fours. my $x = zeroes(3,5)->yvals->flat; for my $mode ( @modes ) { # if the value is in $x my $contained = 2; my $idx_contained = vsearch( $contained, $x, { mode => $mode } ); my $x_contained = $x->copy; $x_contained->slice( $idx_contained ) .= 9; # if the value is not in $x my $not_contained = 1.5; my $idx_not_contained = vsearch( $not_contained, $x, { mode => $mode } ); my $x_not_contained = $x->copy; $x_not_contained->slice( $idx_not_contained ) .= 9; print sprintf("%-23s%30s\n", '$x', $x); print sprintf("%-23s%30s\n", "$mode ($contained)", $x_contained); print sprintf("%-23s%30s\n\n", "$mode ($not_contained)", $x_not_contained); } # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4] # sample (2) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4] # sample (1.5) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4] # # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4] # insert_leftmost (2) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4] # insert_leftmost (1.5) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4] # # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4] # insert_rightmost (2) [0 0 0 1 1 1 2 2 2 9 3 3 4 4 4] # insert_rightmost (1.5) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4] # # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4] # match (2) [0 0 0 1 1 1 2 9 2 3 3 3 4 4 4] # match (1.5) [0 0 0 1 1 1 2 2 9 3 3 3 4 4 4] # # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4] # bin_inclusive (2) [0 0 0 1 1 1 2 2 9 3 3 3 4 4 4] # bin_inclusive (1.5) [0 0 0 1 1 9 2 2 2 3 3 3 4 4 4] # # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4] # bin_exclusive (2) [0 0 0 1 1 9 2 2 2 3 3 3 4 4 4] # bin_exclusive (1.5) [0 0 0 1 1 9 2 2 2 3 3 3 4 4 4] Also see L<B<vsearch_sample>|/vsearch_sample>, L<B<vsearch_insert_leftmost>|/vsearch_insert_leftmost>, L<B<vsearch_insert_rightmost>|/vsearch_insert_rightmost>, L<B<vsearch_match>|/vsearch_match>, L<B<vsearch_bin_inclusive>|/vsearch_bin_inclusive>, and L<B<vsearch_bin_exclusive>|/vsearch_bin_exclusive> =cut sub vsearch { my $opt = 'HASH' eq ref $_[-1] ? pop : { mode => 'sample' }; croak( "unknown options to vsearch\n" ) if ( ! defined $opt->{mode} && keys %$opt ) || keys %$opt > 1; my $mode = $opt->{mode}; goto $mode eq 'sample' ? \&vsearch_sample : $mode eq 'insert_leftmost' ? \&vsearch_insert_leftmost : $mode eq 'insert_rightmost' ? \&vsearch_insert_rightmost : $mode eq 'match' ? \&vsearch_match : $mode eq 'bin_inclusive' ? \&vsearch_bin_inclusive : $mode eq 'bin_exclusive' ? \&vsearch_bin_exclusive : croak( "unknown vsearch mode: $mode\n" ); } *PDL::vsearch = \&vsearch; =head2 vsearch_sample =for sig Signature: (vals(); x(n); indx [o]idx()) =for ref Search for values in a sorted array, return index appropriate for sampling from a distribution =for usage $idx = vsearch_sample($vals, $x); C<$x> must be sorted, but may be in decreasing or increasing order. B<vsearch_sample> returns an index I<I> for each value I<V> of C<$vals> appropriate for sampling C<$vals> I<I> has the following properties: =over =item * if C<$x> is sorted in increasing order V <= x[0] : I = 0 x[0] < V <= x[-1] : I s.t. x[I-1] < V <= x[I] x[-1] < V : I = $x->nelem -1 =item * if C<$x> is sorted in decreasing order V > x[0] : I = 0 x[0] >= V > x[-1] : I s.t. x[I] >= V > x[I+1] x[-1] >= V : I = $x->nelem - 1 =back If all elements of C<$x> are equal, I<< I = $x->nelem - 1 >>. If C<$x> contains duplicated elements, I<I> is the index of the leftmost (by position in array) duplicate if I<V> matches. =for example This function is useful e.g. when you have a list of probabilities for events and want to generate indices to events: $x = pdl(.01,.86,.93,1); # Barnsley IFS probabilities cumulatively $y = random 20; $c = vsearch_sample($y, $x); # Now, $c will have the appropriate distr. It is possible to use the L<cumusumover|PDL::Ufunc/cumusumover> function to obtain cumulative probabilities from absolute probabilities. =for bad needs major (?) work to handles bad values =cut *vsearch_sample = \&PDL::vsearch_sample; =head2 vsearch_insert_leftmost =for sig Signature: (vals(); x(n); indx [o]idx()) =for ref Determine the insertion point for values in a sorted array, inserting before duplicates. =for usage $idx = vsearch_insert_leftmost($vals, $x); C<$x> must be sorted, but may be in decreasing or increasing order. B<vsearch_insert_leftmost> returns an index I<I> for each value I<V> of C<$vals> equal to the leftmost position (by index in array) within C<$x> that I<V> may be inserted and still maintain the order in C<$x>. Insertion at index I<I> involves shifting elements I<I> and higher of C<$x> to the right by one and setting the now empty element at index I<I> to I<V>. I<I> has the following properties: =over =item * if C<$x> is sorted in increasing order V <= x[0] : I = 0 x[0] < V <= x[-1] : I s.t. x[I-1] < V <= x[I] x[-1] < V : I = $x->nelem =item * if C<$x> is sorted in decreasing order V > x[0] : I = -1 x[0] >= V >= x[-1] : I s.t. x[I] >= V > x[I+1] x[-1] >= V : I = $x->nelem -1 =back If all elements of C<$x> are equal, i = 0 If C<$x> contains duplicated elements, I<I> is the index of the leftmost (by index in array) duplicate if I<V> matches. =for bad needs major (?) work to handles bad values =cut *vsearch_insert_leftmost = \&PDL::vsearch_insert_leftmost; =head2 vsearch_insert_rightmost =for sig Signature: (vals(); x(n); indx [o]idx()) =for ref Determine the insertion point for values in a sorted array, inserting after duplicates. =for usage $idx = vsearch_insert_rightmost($vals, $x); C<$x> must be sorted, but may be in decreasing or increasing order. B<vsearch_insert_rightmost> returns an index I<I> for each value I<V> of C<$vals> equal to the rightmost position (by index in array) within C<$x> that I<V> may be inserted and still maintain the order in C<$x>. Insertion at index I<I> involves shifting elements I<I> and higher of C<$x> to the right by one and setting the now empty element at index I<I> to I<V>. I<I> has the following properties: =over =item * if C<$x> is sorted in increasing order V < x[0] : I = 0 x[0] <= V < x[-1] : I s.t. x[I-1] <= V < x[I] x[-1] <= V : I = $x->nelem =item * if C<$x> is sorted in decreasing order V >= x[0] : I = -1 x[0] > V >= x[-1] : I s.t. x[I] >= V > x[I+1] x[-1] > V : I = $x->nelem -1 =back If all elements of C<$x> are equal, i = $x->nelem - 1 If C<$x> contains duplicated elements, I<I> is the index of the leftmost (by index in array) duplicate if I<V> matches. =for bad needs major (?) work to handles bad values =cut *vsearch_insert_rightmost = \&PDL::vsearch_insert_rightmost; =head2 vsearch_match =for sig Signature: (vals(); x(n); indx [o]idx()) =for ref Match values against a sorted array. =for usage $idx = vsearch_match($vals, $x); C<$x> must be sorted, but may be in decreasing or increasing order. B<vsearch_match> returns an index I<I> for each value I<V> of C<$vals>. If I<V> matches an element in C<$x>, I<I> is the index of that element, otherwise it is I<-( insertion_point + 1 )>, where I<insertion_point> is an index in C<$x> where I<V> may be inserted while maintaining the order in C<$x>. If C<$x> has duplicated values, I<I> may refer to any of them. =for bad needs major (?) work to handles bad values =cut *vsearch_match = \&PDL::vsearch_match; =head2 vsearch_bin_inclusive =for sig Signature: (vals(); x(n); indx [o]idx()) =for ref Determine the index for values in a sorted array of bins, lower bound inclusive. =for usage $idx = vsearch_bin_inclusive($vals, $x); C<$x> must be sorted, but may be in decreasing or increasing order. C<$x> represents the edges of contiguous bins, with the first and last elements representing the outer edges of the outer bins, and the inner elements the shared bin edges. The lower bound of a bin is inclusive to the bin, its outer bound is exclusive to it. B<vsearch_bin_inclusive> returns an index I<I> for each value I<V> of C<$vals> I<I> has the following properties: =over =item * if C<$x> is sorted in increasing order V < x[0] : I = -1 x[0] <= V < x[-1] : I s.t. x[I] <= V < x[I+1] x[-1] <= V : I = $x->nelem - 1 =item * if C<$x> is sorted in decreasing order V >= x[0] : I = 0 x[0] > V >= x[-1] : I s.t. x[I+1] > V >= x[I] x[-1] > V : I = $x->nelem =back If all elements of C<$x> are equal, i = $x->nelem - 1 If C<$x> contains duplicated elements, I<I> is the index of the righmost (by index in array) duplicate if I<V> matches. =for bad needs major (?) work to handles bad values =cut *vsearch_bin_inclusive = \&PDL::vsearch_bin_inclusive; =head2 vsearch_bin_exclusive =for sig Signature: (vals(); x(n); indx [o]idx()) =for ref Determine the index for values in a sorted array of bins, lower bound exclusive. =for usage $idx = vsearch_bin_exclusive($vals, $x); C<$x> must be sorted, but may be in decreasing or increasing order. C<$x> represents the edges of contiguous bins, with the first and last elements representing the outer edges of the outer bins, and the inner elements the shared bin edges. The lower bound of a bin is exclusive to the bin, its upper bound is inclusive to it. B<vsearch_bin_exclusive> returns an index I<I> for each value I<V> of C<$vals>. I<I> has the following properties: =over =item * if C<$x> is sorted in increasing order V <= x[0] : I = -1 x[0] < V <= x[-1] : I s.t. x[I] < V <= x[I+1] x[-1] < V : I = $x->nelem - 1 =item * if C<$x> is sorted in decreasing order V > x[0] : I = 0 x[0] >= V > x[-1] : I s.t. x[I-1] >= V > x[I] x[-1] >= V : I = $x->nelem =back If all elements of C<$x> are equal, i = $x->nelem - 1 If C<$x> contains duplicated elements, I<I> is the index of the righmost (by index in array) duplicate if I<V> matches. =for bad needs major (?) work to handles bad values =cut *vsearch_bin_exclusive = \&PDL::vsearch_bin_exclusive; =head2 interpolate =for sig Signature: (xi(); x(n); y(n); [o] yi(); int [o] err()) =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<$xi>. C<interpolate> uses a binary search to find the suspects, er..., interpolation indices and therefore abscissas (ie C<$x>) have to be I<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 C<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 C<$err> to 1, which is otherwise 0. See also L<interpol|/interpol>, which uses the same routine, differing only in the handling of extrapolation - an error message is printed rather than returning an error piddle. =for bad needs major (?) work to handles bad values =cut *interpolate = \&PDL::interpolate; =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, $y) C<interpol> uses the same search method as L<interpolate|/interpolate>, hence C<$x> must be I<strictly> 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; =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( $index ); InterpND acts like L<indexND|PDL::Slices/indexND>, collapsing C<$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<sample> method will return C<< $a->(0) >> for coordinate values on the set [-0.5,0.5), and all methods will return C<< $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<indexND|PDL::Slices/indexND>, 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($x,$y); my($indexwhere); ($indexwhere = $index->where( 0 * $index )) .= -10; # Change NaN to invalid { my $bb = PDL::Math::floor($index); $x = ($index - $bb) -> dummy(1,$crnr->dim(1)); # index, clst, ith $y = ($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 $out0 = ( ($x * ($crnr==1) + $y * ($crnr==0)) #index, clst, ith -> prodover #clst, ith ); my $out = ($out0 * $samp)->sumover; # ith, sth # Work around BAD-not-being-contagious bug in PDL <= 2.6 bad handling code --CED 3-April-2013 if($PDL::Bad::Status and $source->badflag) { my $baddies = $samp->isbad->orover; $out = $out->setbadif($baddies); } 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 $y = $index - $index->floor; for my $i(1..$d-1) { $y = $y->dummy($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 = $y->slice("($i)"); # Collapse the sample... $samp = ( $a0 + $bb * ( $s0 + $bb * ( (3 * $a1a0 - 2*$s0 - $s1) + $bb * ( $s1 + $s0 - 2*$a1a0 ) ) ) ); # "Collapse" the subpixel offset... $y = $y->slice(":,($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 $x = $source->copy; my $y = zeroes($source); fftnd($x,$y); $fftref->[0] = sqrt($x*$x+$y*$y) / $x->nelem; $fftref->[1] = - atan2($y,$x); } 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"); } } =head2 one2nd =for ref Converts a one dimensional index piddle to a set of ND coordinates =for usage @coords=one2nd($x, $indices) returns an array of piddles containing the ND indexes corresponding to the one dimensional list indices. The indices are assumed to correspond to array C<$x> clumped using C<clump(-1)>. This routine is used in the old vector form of L<whichND|/whichND>, but is useful on its own occasionally. Returned piddles have the L<indx|PDL::Core/indx> datatype. C<$indices> can have values larger than C<< $x->nelem >> but negative values in C<$indices> will not give the answer you expect. =for example pdl> $x=pdl [[[1,2],[-1,1]], [[0,-3],[3,2]]]; $c=$x->clump(-1) pdl> $maxind=maximum_ind($c); p $maxind; 6 pdl> print one2nd($x, maximum_ind($c)) 0 1 1 pdl> p $x->at(0,1,1) 3 =cut *one2nd = \&PDL::one2nd; sub PDL::one2nd { barf "Usage: one2nd \$array \$indices\n" if $#_ != 1; my ($x, $ind)=@_; my @dimension=$x->dims; $ind = indx($ind); my(@index); my $count=0; foreach (@dimension) { $index[$count++]=$ind % $_; $ind /= $_; } return @index; } =head2 which =for sig Signature: (mask(n); indx [o] inds(m)) =for ref Returns indices of non-zero values from a 1-D PDL =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 feed in a multidimensional mask, it will be flattened before the indices are calculated. See also L<whichND|/whichND> for multidimensional masks. If you want to index into the original mask or a similar piddle with output from C<which>, 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<where|/where> for similar functionality. SEE ALSO: L<which_both|/which_both> returns separately the indices of both zero and nonzero values in the mask. L<where|/where> returns associated values from a data PDL, rather than indices into the mask PDL. L<whichND|/whichND> returns N-D indices into a multidimensional PDL. =for example pdl> $x = sequence(10); p $x [0 1 2 3 4 5 6 7 8 9] pdl> $indx = which($x>6); p $indx [7 8 9] =for bad which processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut sub which { my ($this,$out) = @_; $this = $this->flat; $out = $this->nullcreate unless defined $out; PDL::_which_int($this,$out); return $out; } *PDL::which = \&which; *which = \&PDL::which; =head2 which_both =for sig Signature: (mask(n); indx [o] inds(m); indx [o]notinds(q)) =for ref Returns indices of zero and nonzero values in a mask PDL =for usage ($i, $c_i) = which_both($mask); This works just as L<which|/which>, but the complement of C<$i> will be in C<$c_i>. =for example pdl> $x = sequence(10); p $x [0 1 2 3 4 5 6 7 8 9] pdl> ($small, $big) = which_both ($x >= 5); p "$small\n $big" [5 6 7 8 9] [0 1 2 3 4] =for bad which_both processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles. =cut sub which_both { my ($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; *which_both = \&PDL::which_both; =head2 where =for ref Use a mask to select values from one or more data PDLs C<where> accepts one or more data piddles and a mask piddle. It returns a list of output piddles, corresponding to the input data piddles. Each output piddle is a 1-dimensional list of values in its corresponding data piddle. The values are drawn from locations where the mask is nonzero. The output PDLs are still connected to the original data PDLs, for the purpose of dataflow. C<where> combines the functionality of L<which|/which> and L<index|PDL::Slices/index> into a single operation. BUGS: While C<where> works OK for most N-dimensional cases, it does not thread properly over (for example) the (N+1)th dimension in data that is compared to an N-dimensional mask. Use C<whereND> for that. =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 E<gt>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; =head2 whereND =for ref C<where> with support for ND masks and threading C<whereND> accepts one or more data piddles and a mask piddle. It returns a list of output piddles, corresponding to the input data piddles. The values are drawn from locations where the mask is nonzero. C<whereND> differs from C<where> in that the mask dimensionality is preserved which allows for proper threading of the selection operation over higher dimensions. As with C<where> the output PDLs are still connected to the original data PDLs, for the purpose of dataflow. =for usage $sdata = whereND $data, $mask ($s1, $s2, ..., $sn) = whereND $d1, $d2, ..., $dn, $mask where $data is M dimensional $mask is N < M dimensional dims($data) 1..N == dims($mask) 1..N with threading over N+1 to M dimensions =for example $data = sequence(4,3,2); # example data array $mask4 = (random(4)>0.5); # example 1-D mask array, has $n4 true values $mask43 = (random(4,3)>0.5); # example 2-D mask array, has $n43 true values $sdat4 = whereND $data, $mask4; # $sdat4 is a [$n4,3,2] pdl $sdat43 = whereND $data, $mask43; # $sdat43 is a [$n43,2] pdl Just as with C<where>, you can use the returned value in an assignment. That means that both of these examples are valid: # Used to create a new slice stored in $sdat4: $sdat4 = $data->whereND($mask4); $sdat4 .= 0; # Used in lvalue context: $data->whereND($mask4) .= 0; =cut sub PDL::whereND :lvalue { barf "Usage: whereND( \$pdl1, ..., \$pdlN, \$mask )\n" if $#_ == 0; my $mask = pop @_; # $mask has 0==false, 1==true my @to_return; my $n = PDL::sum($mask); foreach my $arr (@_) { my $sub_i = $mask * ones($arr); my $where_sub_i = PDL::where($arr, $sub_i); # count the number of dims in $mask and $arr # $mask = a b c d e f..... my @idims = dims($arr); # ...and pop off the number of dims in $mask foreach ( dims($mask) ) { shift(@idims) }; my $ndim = 0; foreach my $id ($n, @idims[0..($#idims-1)]) { $where_sub_i = $where_sub_i->splitdim($ndim++,$id) if $n>0; } push @to_return, $where_sub_i; } return (@to_return == 1) ? $to_return[0] : @to_return; } *whereND = \&PDL::whereND; =head2 whichND =for ref Return the coordinates of non-zero values in a mask. =for usage WhichND returns the N-dimensional coordinates of each nonzero value in a mask PDL with any number of dimensions. The returned values arrive as an array-of-vectors suitable for use in L<indexND|PDL::Slices/indexND> or L<range|PDL::Slices/range>. $coords = whichND($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 $coords has dimension 4x100. If no such elements exist, then whichND returns a structured empty PDL: an Nx0 PDL that contains no values (but matches, threading-wise, with the vectors that would be produced if such elements existed). DEPRECATED BEHAVIOR IN LIST CONTEXT: whichND once delivered different values in list context than in scalar context, for historical reasons. In list context, it returned the coordinates transposed, as a collection of 1-PDLs (one per dimension) in a list. This usage is deprecated in PDL 2.4.10, and will cause a warning to be issued every time it is encountered. To avoid the warning, you can set the global variable "$PDL::whichND" to 's' to get scalar behavior in all contexts, or to 'l' to get list behavior in list context. In later versions of PDL, the deprecated behavior will disappear. Deprecated list context whichND expressions can be replaced with: @list = $x->whichND->mv(0,-1)->dog; SEE ALSO: L<which|/which> finds coordinates of nonzero values in a 1-D mask. L<where|/where> extracts values from a data PDL that are associated with nonzero values in a mask PDL. =for example pdl> $s=sequence(10,10,3,4) pdl> ($x, $y, $z, $w)=whichND($s == 203); p $x, $y, $z, $w [3] [0] [2] [0] pdl> print $s->at(list(cat($x,$y,$z,$w))) 203 =cut *whichND = \&PDL::whichND; sub PDL::whichND { my $mask = shift; $mask = PDL::pdl('PDL',$mask) unless(UNIVERSAL::isa($mask,'PDL')); # List context: generate a perl list by dimension if(wantarray) { if(!defined($PDL::whichND)) { printf STDERR "whichND: WARNING - list context deprecated. Set \$PDL::whichND. Details in pod."; } elsif($PDL::whichND =~ m/l/i) { # old list context enabled by setting $PDL::whichND to 'l' my $ind=($mask->clump(-1))->which; return $mask->one2nd($ind); } # if $PDL::whichND does not contain 'l' or 'L', fall through to scalar context } # Scalar context: generate an N-D index piddle unless($mask->nelem) { return PDL::new_from_specification('PDL',indx,$mask->ndims,0); } unless($mask->getndims) { return $mask ? pdl(indx,0) : PDL::new_from_specification('PDL',indx,0); } $ind = $mask->flat->which->dummy(0,$mask->getndims)->make_physical; if($ind->nelem==0) { # In the empty case, explicitly return the correct type of structured empty return PDL::new_from_specification('PDL',indx,$mask->ndims, 0); } 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; } =head2 setops =for ref Implements simple set operations like union and intersection =for usage Usage: $set = setops($x, <OPERATOR>, $y); The operator can be C<OR>, C<XOR> or C<AND>. This is then applied to C<$x> viewed as a set and C<$y> viewed as a set. Set theory says that a set may not have two or more identical elements, but setops takes care of this for you, so C<$x=pdl(1,1,2)> is OK. The functioning is as follows: =over =item C<OR> The resulting vector will contain the elements that are either in C<$x> I<or> in C<$y> or both. This is the union in set operation terms =item C<XOR> The resulting vector will contain the elements that are either in C<$x> or C<$y>, but not in both. This is Union($x, $y) - Intersection($x, $y) in set operation terms. =item C<AND> The resulting vector will contain the intersection of C<$x> and C<$y>, so the elements that are in both C<$x> and C<$y>. Note that for convenience this operation is also aliased to L<intersect|intersect>. =back It should be emphasized that these routines are used when one or both of the sets C<$x>, C<$y> are hard to calculate or that you get from a separate subroutine. Finally IDL users might be familiar with Craig Markwardt's C<cmset_op.pro> routine which has inspired this routine although it was written independently However the present routine has a few less options (but see the examples) =for example You will very often use these functions on an index vector, so that is what we will show here. We will in fact something slightly silly. First we will find all squares that are also cubes below 10000. Create a sequence vector: pdl> $x = sequence(10000) Find all odd and even elements: pdl> ($even, $odd) = which_both( ($x % 2) == 0) Find all squares pdl> $squares= which(ceil(sqrt($x)) == floor(sqrt($x))) Find all cubes (being careful with roundoff error!) pdl> $cubes= which(ceil($x**(1.0/3.0)) == floor($x**(1.0/3.0)+1e-6)) Then find all squares that are cubes: pdl> $both = setops($squares, 'AND', $cubes) And print these (assumes that C<PDL::NiceSlice> is loaded!) pdl> p $x($both) [0 1 64 729 4096] Then find all numbers that are either cubes or squares, but not both: pdl> $cube_xor_square = setops($squares, 'XOR', $cubes) pdl> p $cube_xor_square->nelem() 112 So there are a total of 112 of these! Finally find all odd squares: pdl> $odd_squares = setops($squares, 'AND', $odd) Another common occurrence is to want to get all objects that are in C<$x> and in the complement of C<$y>. But it is almost always best to create the complement explicitly since the universe that both are taken from is not known. Thus use L<which_both|which_both> if possible to keep track of complements. If this is impossible the best approach is to make a temporary: This creates an index vector the size of the universe of the sets and set all elements in C<$y> to 0 pdl> $tmp = ones($n_universe); $tmp($y) .= 0; This then finds the complement of C<$y> pdl> $C_b = which($tmp == 1); and this does the final selection: pdl> $set = setops($x, 'AND', $C_b) =cut *setops = \&PDL::setops; sub PDL::setops { my ($x, $op, $y)=@_; # Check that $x and $y are 1D. if ($x->ndims() > 1 || $y->ndims() > 1) { warn 'setops: $x and $y must be 1D - flattening them!'."\n"; $x = $x->flat; $y = $y->flat; } #Make sure there are no duplicate elements. $x=$x->uniq; $y=$y->uniq; my $result; if ($op eq 'OR') { # Easy... $result = uniq(append($x, $y)); } elsif ($op eq 'XOR') { # Make ordered list of set union. my $union = append($x, $y)->qsort; # Index lists. my $s1=zeroes(byte, $union->nelem()); my $s2=zeroes(byte, $union->nelem()); # Find indices which are duplicated - these are to be excluded # # We do this by comparing x with x shifted each way. my $i1 = which($union != rotate($union, 1)); my $i2 = which($union != rotate($union, -1)); # # We then mark/mask these in the s1 and s2 arrays to indicate which ones # are not equal to their neighbours. # my $ts; ($ts = $s1->index($i1)) .= 1 if $i1->nelem() > 0; ($ts = $s2->index($i2)) .= 1 if $i2->nelem() > 0; my $inds=which($s1 == $s2); if ($inds->nelem() > 0) { return $union->index($inds); } else { return $inds; } } elsif ($op eq 'AND') { # The intersection of the arrays. # Make ordered list of set union. my $union = append($x, $y)->qsort; return $union->where($union == rotate($union, -1)); } else { print "The operation $op is not known!"; return -1; } } =head2 intersect =for ref Calculate the intersection of two piddles =for usage Usage: $set = intersect($x, $y); This routine is merely a simple interface to L<setops|setops>. See that for more information =for example Find all numbers less that 100 that are of the form 2*y and 3*x pdl> $x=sequence(100) pdl> $factor2 = which( ($x % 2) == 0) pdl> $factor3 = which( ($x % 3) == 0) pdl> $ii=intersect($factor2, $factor3) pdl> p $x($ii) [0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96] =cut *intersect = \&PDL::intersect; sub PDL::intersect { return setops($_[0], 'AND', $_[1]); } ; =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), Craig DeForest (deforest@boulder.swri.edu) and Jarle Brinchmann (jarle@astro.up.pt) 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. Updated for CPAN viewing compatibility by David Mertens. =cut # Exit with OK status 1;