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<PDL::Indexing|PDL::Indexing> for how to use indices creatively.
For explanation of the signature format, see L<PDL::PP|PDL::PP>.
=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<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.',
); # 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<a> and C<c> since that would be
very wasteful. Instead, you should use a temporary for C<b*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<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.
'
); # 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<a> to the C<ind> element of C<sum>, 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<Boundary> option:
{Boundary => 'reflect'} # case in 'reflect' doesn't matter
The convolution is performed along the first dimension. To apply it across
another dimension use the slicing routines, e.g.
$b = $a->mv(2,0)->conv1d($kernel)->mv(0,2); # along third dim
This function is useful for threaded filtering of 1D signals.
Compare also 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>
EOD
Pars => 'a(m); kern(p); [o]b(m);',
OtherPars => 'int reflect;',
PMCode => '
sub PDL::conv1d {
my $opt = pop @_ if ref($_[$#_]) eq \'HASH\';
die \'Usage: conv1d( a(m), kern(p), [o]b(m), {Options} )\'
if $#_<1 || $#_>2;
my($a,$kern) = @_;
my $c = $#_ == 2 ? $_[2] : PDL->null;
&PDL::_conv1d_int($a,$kern,$c,
!(defined $opt && exists $$opt{Boundary}) ? 0 :
lc $$opt{Boundary} eq "reflect");
return $c;
}
',
Code => '
int i,i1,i2,poff;
double tmp;
int reflect = $COMP(reflect);
int m_size = $COMP(__m_size);
int p_size = $COMP(__p_size);
poff = (p_size-1)/2;
for(i=0; i<m_size; i++) {
tmp = 0;
for(i1=0; i1<p_size; i1++) {
i2 = i+i1 - poff;
if (reflect && i2<0)
i2 = -i2;
if (reflect && i2>=m_size)
i2 = m_size-(i2-m_size+1);
REALMOD(i2,m_size);
tmp += $a(m=>i2) * $kern(p=>i1);
}
$b(m=>i) = tmp;
}
');
# this can be achieved by
# ($a->dummy(0) == $b)->orover
# but this one avoids a larger intermediate and potentially shortcuts
pp_def('in',
Pars => 'a(); b(n); [o] c()',
Code => '$c() = 0;
loop(n) %{ if ($a() == $b()) {$c() = 1; break;} %}',
Doc => <<'EOD',
=for ref
test if a is in the set of values b
=for example
$goodmsk = $labels->in($goodlabels);
print pdl(4,3,1)->in(pdl(2,3,3));
[0 1 0]
C<in> is akin to the I<is an element of> of set theory. In priciple,
PDL threading could be used to achieve its functionality by using a
construct like
$msk = ($labels->dummy(0) == $goodlabels)->orover;
However, C<in> doesn't create a (potentially large) intermediate
and is generally faster.
EOD
);
pp_add_exported '', 'uniq';
pp_addpm << 'EOPM';
=head2 uniq
=for ref
return all unique elements of a piddle
The unique elements are returned in ascending order.
=for example
print pdl(2,2,2,4,0,-1,6,6)->uniq;
[-1 0 2 4 6]
Note: The returned pdl is 1D; any structure of the input
piddle is lost.
=cut
*uniq = \&PDL::uniq;
# return unique elements of array
# find as jumps in the sorted array
# flattens in the process
sub PDL::uniq {
use PDL::Core 'barf';
my ($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) : $uniq;
}
=head2 uniqvec
=for ref
return all unique vectors out of a collection
The unique vectors are returned in lexicographically sorted
ascending order. The 0th dimension of the input PDL is treated
as a dimensional index within each vector, and the 1st and any higher
dimensions are taken to run across vectors. The return value is always
2D; any structure of the input PDL (beyond using the 0th dimension
for vector index) is lost.
See also L<uniq|uniq> for a uniqe list of scalars; and
L<qsortvec|PDL::Ufunc/qsortvec> for sorting a list of vectors
lexicographcally.
=cut
sub PDL::uniqvec {
my($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<hclip|/hclip> and
L<lclip|/lclip>.
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()); $PDLSTATESETBAD(b); }',
CopyBadStatusCode => '',
Doc =>
'=for ref
Weighted statistical moment of given degree
This calculates a weighted statistic over the vector C<a>.
The formula is
b() = (sum_i wt_i * (a_i ** degree - avg)) / (sum_i wt_i)
',
BadDoc =>
'Bad values are ignored in any calculation; C<$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, $weights);
This utility function calculates various useful
quantities of a piddle. These are the mean:
MEAN = sum (x)/ N
with C<N> being the number of elements in x, the root mean
square deviation from the mean, RMS, given as,
RMS = sqrt(sum( (x-mean(x))^2 )/(N-1));
Note the use of C<N-1> which for almost all cases should be
the right normalisation factor. The routine also returns
the median, minimum and maximum of the piddle as well as
the mean absolute deviation, defined as:
ADEV = sqrt(sum( abs(x-mean(x)) )/N)
note here that we use the mean and not the median. This could
possibly be changed in future versions of the code.
This operator is a projection operator so the calculation
will take place over the final dimension. Thus if the input
is N-dimensional each returned value will be N-1 dimensional,
to calculate the statistics for the entire piddle either
use C<clump(-1)> directly on the piddle or call C<stats>.
',
BadDoc =>
'
Bad values are simply ignored in the calculation and if all data are
bad the results will also be bad.
',
);
pp_add_exported('','stats');
pp_addpm(<<'EOD');
=head2 stats
=for ref
Calculates useful statistics on a piddle
=for usage
($mean,$rms,$median,$min,$max) = stats($piddle,[$weights]);
This utility calculates all the most useful
quantities in one call.
B<Note:> The RMS value that this function returns in the RMS
deviation from the mean, also known as the population standard-
deviation: $rms = sqrt(sum(($val-$mean)**2)) / ($n-1)
EOD
if ( $bvalflag ) {
pp_addpm(<<'EOD');
=for bad
The return values if all elements are bad is currently poorly
defined.
EOD
} # if: bvalflag
pp_addpm(<<'EOD');
=cut
*stats = \&PDL::stats;
sub PDL::stats {
barf('Usage: ($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<hist|PDL::Basic/hist> 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<append> appends two piddles along their first dims. Rest of the dimensions
must be compatible in the threading sense. Resulting size of first dim is
the sum of the sizes of the first dims of the two argument piddles -
ie C<n + m>.
'
);
pp_addpm(<<'EOD')
=head2 glue
=for usage
$c = $a->glue(<dim>,$b,...)
=for ref
Glue two or more PDLs together along an arbitrary dimension (N-D L<append|append>).
Sticks $a, $b, and all following arguments together using a combination
of xchg() and append(). All other dimensions must be compatible in the
threading sense.
C<glue> is implemented in pdl, and should probably be updated (one day) to a
pure PP function.
=cut
sub PDL::glue{
my($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<axisvalues> is the internal primitive that implements
L<axisvals|PDL::Basic/axisvals>
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<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
$a = randsym([type], $nx, $ny, $nz,...);
$a = randsym $b;
etc (see L<zeroes|PDL::Core/zeroes>).
This is the uniform distribution between 0 and 1 (excluding both 0 and
1, cf L<random|/random>). The arguments are the same as C<zeroes> (q.v.) -
i.e. one can specify dimensions, types or give a template.
You can use the perl function L<srand|perlfunc/srand> to seed the random
generator. For further details consult Perl's L<srand|perlfunc/srand>
documentation.
=cut
EOD
pp_addhdr(<<'EOH');
#ifndef Drand01
#define Drand01() (((double)rand()) / (RAND_MAX+1.0))
#endif
EOH
pp_def(
'random',
Pars=>'a();',
PMFunc => '',
Code =>
'$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 $b;
etc (see L<zeroes|PDL::Core/zeroes>).
This is generated using the math library routine C<ndtri>.
Mean = 0, Stddev = 1
You can use the perl function L<srand|perlfunc/srand> to seed the random
generator. For further details consult Perl's L<srand|perlfunc/srand>
documentation.
=cut
sub grandom { ref($_[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;
}
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<cumusumover|PDL::Ufunc/cumusumover>
function to obtain cumulative probabilities from absolute probabilities.
EOD
pp_def('interpolate',
HandleBad => 0,
BadDoc => 'needs major (?) work to handles bad values',
Pars => 'xi(); x(n); y(n); [o] yi(); int [o] err()',
GenericTypes => ['F','D'], # too restrictive ?
Code => '
$GENERIC() d;
long n = $SIZE(n);
long n1 = n-1;
int up = ($x(n => n1) > $x(n => 0));
long jl, jh, m;
int carp;
threadloop %{
jl = -1;
jh = n;
carp = 0;
while (jh-jl > 1) /* binary search */
{
m = (jh+jl) >> 1;
if ($xi() > $x(n => m) == up)
jl = m;
else
jh = m;
}
if (jl == -1) {
if ($xi() != $x(n => 0)) carp = 1;
jl = 0;
} else if (jh == n) {
if ($xi() != $x(n => n1)) carp = 1;
jl = n1-1;
}
jh = jl+1;
if ((d = $x(n => jh)-$x(n => jl)) == 0)
barf("identical abscissas");
d = ($x(n => jh)-$xi())/d;
$yi() = d*$y(n => jl) + (1-d)*$y(n => jh);
$err() = carp;
%}
', Doc=><<'EOD');
=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.
=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, $y)
C<interpol> uses the same search method as L<interpolate|/interpolate>,
hence C<$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;
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( $index );
InterpND acts like L<indexND|PDL::Slices/indexND>,
collapsing C<$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 $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<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($a,$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<clump(-1)>. This routine is used in
L<whichND|/whichND>,
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<where|/where> for similar functionality.
If you want to return both the indices of non-zero values and the
complement, use the function L<which_both|/which_both>.
=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<which|/which>, 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; i<dpdl->dims[0]; i++) {
if ( *(m_datap+inc*i+offs)) sum++;
}
'.$_->{Autosize} . '
/* printf("RedoDimsCode: setting dim m to %ld\n",sum); */'
);
}
pp_addpm(<<'EOD'
=head2 where
=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<indexND|PDL::Slices/indexND> or L<range|PDL::Slices/range>;
in list context, the coordinates are broken out into separate PDLs.
$coords = whichND($mask);
returns a PDL containing the coordinates of the elements that are non-zero
in 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();