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primitive.pd
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primitive.pd
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use strict;
use warnings;
use PDL::Types qw(ppdefs_all types);
my $F = [map $_->ppsym, grep $_->real && !$_->integer, types()];
my $AF = [map $_->ppsym, grep !$_->integer, types];
pp_addpm({At=>'Top'},<<'EOD');
use strict;
use warnings;
use PDL::Slices;
use Carp;
{ package PDL;
use overload (
'x' => sub {
PDL::Primitive::matmult(@_[0,1], my $foo=$_[0]->null());
$foo;
},
);
}
=head1 NAME
PDL::Primitive - primitive operations for pdl
=head1 DESCRIPTION
This module provides some primitive and useful functions defined
using PDL::PP and able to use the new indexing tricks.
See L<PDL::Indexing> for how to use indices creatively.
For explanation of the signature format, see L<PDL::PP>.
=head1 SYNOPSIS
# Pulls in PDL::Primitive, among other modules.
use PDL;
# Only pull in PDL::Primitive:
use PDL::Primitive;
=cut
EOD
################################################################
# a whole bunch of quite basic functions for inner, outer
# and matrix products (operations that are not normally
# available via operator overloading)
################################################################
pp_def('inner',
HandleBad => 1,
Pars => 'a(n); b(n); [o]c();',
GenericTypes => [ppdefs_all],
Code =>
'complex long double tmp = 0;
PDL_IF_BAD(int badflag = 0;,)
loop(n) %{
PDL_IF_BAD(if (!($ISGOOD(a()) && $ISGOOD(b()))) { badflag = 1; break; }
else,) { tmp += $a() * $b(); }
%}
PDL_IF_BAD(if (badflag) { $SETBAD(c()); $PDLSTATESETBAD(c); }
else,) { $c() = tmp; }',
Doc => '
=for ref
Inner product over one dimension
c = sum_i a_i * b_i
',
BadDoc => '
=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.
',
); # pp_def( inner )
pp_def('outer',
HandleBad => 1,
Pars => 'a(n); b(m); [o]c(n,m);',
GenericTypes => [ppdefs_all],
Code =>
'loop(n,m) %{
PDL_IF_BAD(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 broadcasting over the "C<*>"
operator but this function is provided for convenience.
'); # pp_def( outer )
pp_addpm(<<'EOD');
=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.
Broadcasting 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 broadcast over either of those dims.
Of note, due to how Perl v5.14.0 and above implement operator overloading of
the C<x> operator, the use of parentheses for the left operand creates a list
context, that is
pdl> ( $x * $y ) x $z
ERROR: Argument "..." isn't numeric in repeat (x) ...
treats C<$z> as a numeric count for the list repeat operation and does not call
the scalar form of the overloaded operator. To use the operator in this case,
use a scalar context:
pdl> scalar( $x * $y ) x $z
or by calling L</matmult> directly:
pdl> ( $x * $y )->matmult( $z )
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 $r # column x row = matrix
[
[3 6]
[4 8]
]
INTERNALS
The mechanics of the multiplication are carried out by the
L</matmult> method.
=cut
EOD
pp_def('matmult',
HandleBad=>0,
Pars => 'a(t,h); b(w,t); [o]c(w,h);',
GenericTypes => [ppdefs_all],
PMCode => pp_line_numbers(__LINE__, <<'EOPM'),
sub PDL::matmult {
my ($x,$y,$c) = @_;
$y = PDL->topdl($y);
$c = PDL->null unless do { local $@; 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 && $y->dim(1)==1) );
barf sprintf 'Dim mismatch in matmult of [%1$dx%2$d] x [%3$dx%4$d]: %1$d != %4$d',$x->dim(0),$x->dim(1),$y->dim(0),$y->dim(1)
if $y->dim(1) != $x->dim(0);
PDL::_matmult_int($x,$y,$c);
$c;
}
EOPM
Code => <<'EOC',
PDL_Indx tsiz = 8 * sizeof(double) / sizeof($GENERIC());
// Cache the dimincs to avoid constant lookups
PDL_Indx atdi = PDL_REPRINCS($PDL(a))[0];
PDL_Indx btdi = PDL_REPRINCS($PDL(b))[1];
broadcastloop %{
// Loop over tiles
loop (h=::tsiz,w=::tsiz) %{
PDL_Indx h_outer = h, w_outer = w;
// Zero the output for this tile
loop (h=h_outer:h_outer+tsiz,w=w_outer:w_outer+tsiz) %{ $c() = 0; %}
loop (t=::tsiz,h=h_outer:h_outer+tsiz,w=w_outer:w_outer+tsiz) %{
// Cache the accumulated value for the output
$GENERIC() cc = $c();
// Cache data pointers before 't' run through tile
$GENERIC() *ad = &($a());
$GENERIC() *bd = &($b());
// Hotspot - run the 't' summation
PDL_Indx t_outer = t;
loop (t=t_outer:t_outer+tsiz) %{
cc += *ad * *bd;
ad += atdi;
bd += btdi;
%}
// put the output back to be further accumulated later
$c() = cc;
%}
%}
%}
EOC
Doc => <<'EOD'
=for ref
Matrix multiplication
Notionally, matrix multiplication $x x $y is equivalent to the
broadcasting 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>, a description of the overloaded 'x' operator
EOD
);
pp_def('innerwt',
HandleBad => 1,
Pars => 'a(n); b(n); c(n); [o]d();',
GenericTypes => [ppdefs_all],
Code =>
'complex long double tmp = 0;
PDL_IF_BAD(int flag = 0;,)
loop(n) %{
PDL_IF_BAD(if (!( $ISGOOD(a()) && $ISGOOD(b()) && $ISGOOD(c()) )) continue;,)
tmp += $a() * $b() * $c();
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if (!flag) { $SETBAD(d()); }
else,) { $d() = tmp; }',
Doc => '
=for ref
Weighted (i.e. triple) inner product
d = sum_i a(i) b(i) c(i)
=cut
'
);
pp_def('inner2',
HandleBad => 1,
Pars => 'a(n); b(n,m); c(m); [o]d();',
GenericTypes => [ppdefs_all],
Code =>
'complex long double tmp = 0;
PDL_IF_BAD(int flag = 0;,)
loop(n,m) %{
PDL_IF_BAD(if (!( $ISGOOD(a()) && $ISGOOD(b()) && $ISGOOD(c()) )) continue;,)
tmp += $a() * $b() * $c();
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if (!flag) { $SETBAD(d()); }
else,) { $d() = tmp; }',
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 broadcast 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();',
GenericTypes => [ppdefs_all],
Code =>
'complex long double tmp = 0;
PDL_IF_BAD(int flag = 0;,)
loop(n,m) %{
PDL_IF_BAD(if (!( $ISGOOD(a()) && $ISGOOD(b()) )) continue;,)
tmp += $a() * $b();
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if (!flag) { $SETBAD(c()); }
else,) { $c() = tmp; }',
Doc => '
=for ref
Inner product over 2 dimensions.
Equivalent to
$c = inner($x->clump(2), $y->clump(2))
=cut
'
);
pp_def('inner2t',
HandleBad => 1,
Pars => 'a(j,n); b(n,m); c(m,k); [t]tmp(n,k); [o]d(j,k);',
GenericTypes => [ppdefs_all],
Code =>
'loop(n,k) %{
complex long double tmp0 = 0;
PDL_IF_BAD(int flag = 0;,)
loop(m) %{
PDL_IF_BAD(if (!( $ISGOOD(b()) && $ISGOOD(c()) )) continue;,)
tmp0 += $b() * $c();
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if (!flag) { $SETBAD(tmp()); }
else,) { $tmp() = tmp0; }
%}
loop(j,k) %{
complex long double tmp1 = 0;
PDL_IF_BAD(int flag = 0;,)
loop(n) %{
PDL_IF_BAD(if (!( $ISGOOD(a()) && $ISGOOD(tmp()) )) continue;,)
tmp1 += $a() * $tmp();
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if (!flag) { $SETBAD(d()); }
else,) { $d() = tmp1; }
%}',
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 broadcasting using L</inner2> would scale
as C<N**4>.
The reason for having this routine is that you do not need to
have the same broadcast-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.
=cut
'
); # 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 $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>
=cut
EOD
Pars => 'a(tri=3); b(tri); [o] c(tri)',
GenericTypes => [ppdefs_all],
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)',
GenericTypes => [ppdefs_all],
Doc => 'Normalises a vector to unit Euclidean length',
Code =>
'long double sum=0;
PDL_IF_BAD(int flag = 0;,)
loop(n) %{
PDL_IF_BAD(if (!( $ISGOOD(vec()) )) continue;,)
sum +=
PDL_IF_GENTYPE_REAL(
$vec()*$vec(),
creall($vec())*creall($vec()) + cimagl($vec())*cimagl($vec())
);
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if ( !flag ) {
loop(n) %{ $SETBAD(norm()); %}
continue;
},)
if (sum > 0) {
sum = sqrt(sum);
loop(n) %{
PDL_IF_BAD(if ( $ISBAD(vec()) ) { $SETBAD(norm()); }
else ,) {
$norm() = $vec()/sum;
}
%}
} else {
loop(n) %{
PDL_IF_BAD(if ( $ISBAD(vec()) ) { $SETBAD(norm()); }
else ,) { $norm() = $vec(); }
%}
}
',
);
# 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 => 'input(n); indx ind(n); [io] sum(m)',
GenericTypes => [ppdefs_all],
Code =>
'loop(n) %{
register PDL_Indx this_ind = $ind();
if ( PDL_IF_BAD($ISBADVAR(this_ind,ind) ||,) this_ind<0 || this_ind>=$SIZE(m) )
$CROAK("invalid index %"IND_FLAG"; range 0..%"IND_FLAG, this_ind, $SIZE(m));
PDL_IF_BAD(
if ( $ISBAD(input()) ) { $SETBAD(sum(m => this_ind)); }
else,) { $sum(m => this_ind) += $input(); }
%}',
BadDoc => '
=for bad
The routine barfs on bad indices, and bad inputs set target outputs bad.
=cut
',
Doc=>'
=for ref
Broadcasting index add: add C<input> to the C<ind> element of C<sum>, i.e:
sum(ind) += input
=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]
Broadcasting 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 $sum)
# [0 1 0 0 2 0 3 0 0 0]
=cut
');
# 1D convolution
# useful for broadcasted 1D filters
pp_def('conv1d',
Doc => << 'EOD',
=for ref
1D convolution along first dimension
The m-th element of the discrete convolution of an input ndarray
C<$a> of size C<$M>, and a kernel ndarray C<$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 broadcasted filtering of 1D signals.
Compare also L<conv2d|PDL::Image2D/conv2d>, L<convolve|PDL::ImageND/convolve>,
L<fftconvolve|PDL::FFT/fftconvolve()>
=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.
=cut
EOD
Pars => 'a(m); kern(p); [o]b(m);',
GenericTypes => [ppdefs_all],
OtherPars => 'int reflect;',
HandleBad => 0,
PMCode => pp_line_numbers(__LINE__, <<'EOPM'),
sub PDL::conv1d {
my $opt = pop @_ if ref($_[-1]) eq 'HASH';
die 'Usage: conv1d( a(m), kern(p), [o]b(m), {Options} )'
if @_<2 || @_>3;
my($x,$kern) = @_;
my $c = @_ == 3 ? $_[2] : PDL->null;
PDL::_conv1d_int($x,$kern,$c,
!(defined $opt && exists $$opt{Boundary}) ? 0 :
lc $$opt{Boundary} eq "reflect");
return $c;
}
EOPM
CHeader => '
/* Fast Modulus with proper negative behaviour */
#define REALMOD(a,b) while ((a)>=(b)) (a) -= (b); while ((a)<0) (a) += (b);
',
Code => '
int reflect = $COMP(reflect);
PDL_Indx m_size = $SIZE(m), p_size = $SIZE(p);
PDL_Indx poff = (p_size-1)/2;
loop(m) %{
complex long double tmp = 0;
loop(p) %{
PDL_Indx pflip = p_size - 1 - p, i2 = m+p - 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=>pflip);
%}
$b() = tmp;
%}
');
# this can be achieved by
# ($x->dummy(0) == $y)->orover
# but this one avoids a larger intermediate and potentially shortcuts
pp_def('in',
Pars => 'a(); b(n); [o] c()',
GenericTypes => [ppdefs_all],
Code => '$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(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 broadcasting 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.
=cut
EOD
);
pp_add_exported ('', 'uniq');
pp_addpm (<< 'EOPM');
=head2 uniq
=for ref
return all unique elements of an ndarray
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
ndarray 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 ndarray. This follows the Matlab usage.
See L</uniqind> if you need the indices of the unique
elements rather than the values.
=for bad
Bad values are not considered unique by uniq and are ignored.
$x=sequence(10);
$x=$x->setbadif($x%3);
print $x->uniq;
[0 3 6 9]
=cut
*uniq = \&PDL::uniq;
# return unique elements of array
# find as jumps in the sorted array
# flattens in the process
sub PDL::uniq {
my ($arr) = @_;
return $arr if($arr->nelem == 0); # The null list is unique (CED)
return $arr->flat if($arr->nelem == 1); # singleton list is unique
my $aflat = $arr->flat;
my $srt = $aflat->where($aflat==$aflat)->qsort; # no NaNs or BADs for qsort
my $nans = $aflat->where($aflat!=$aflat);
my $uniq = ($srt->nelem > 1) ? $srt->where($srt != $srt->rotate(-1)) : $srt;
# make sure we return something if there is only one value
(
$uniq->nelem > 0 ? $uniq :
$srt->nelem == 0 ? $srt :
PDL::pdl( ref($srt), [$srt->index(0)] )
)->append($nans);
}
EOPM
pp_add_exported ('', 'uniqind');
pp_addpm (<< 'EOPM');
=head2 uniqind
=for ref
Return the indices of all unique elements of an ndarray
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
ndarray is lost.
See L</uniq> if you want the unique values instead of the
indices.
=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 = PDL->sequence(indx, $aflat->dims)->where($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 $ansind;
}
EOPM
pp_add_exported ('', 'uniqvec');
pp_addpm (<< 'EOPM');
=head2 uniqvec
=for ref
Return all unique vectors out of a collection
NOTE: If any vectors in the input ndarray have NaN values
they are returned at the end of the non-NaN ones. This is
because, by definition, NaN values never compare equal with
any other value.
NOTE: The current implementation does not sort the vectors
containing NaN values.
The unique vectors are returned in lexicographically sorted
ascending order. The 0th dimension of the input PDL is treated
as a dimensional index within each vector, and the 1st and any
higher dimensions are taken to run across vectors. The return
value is always 2D; any structure of the input PDL (beyond using
the 0th dimension for vector index) is lost.
See also L</uniq> for a unique list of scalars; and
L<qsortvec|PDL::Ufunc/qsortvec> for sorting a list of vectors
lexicographcally.
=for bad
If a vector contains all bad values, it is ignored as in L</uniq>.
If some of the values are good, it is treated as a normal vector. For
example, [1 2 BAD] and [BAD 2 3] could be returned, but [BAD BAD BAD]
could not. Vectors containing BAD values will be returned after any
non-NaN and non-BAD containing vectors, followed by the NaN vectors.
=cut
sub PDL::uniqvec {
my($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 = $pdl->clump(1..$pdl->ndims-1);
my $ngood = $pdl2d->ngoodover;
$pdl2d = $pdl2d->mv(0,-1)->dice($ngood->which)->mv(-1,0); # remove all-BAD vectors
my $numnan = ($pdl2d!=$pdl2d)->sumover; # works since no all-BADs to confuse
my $presrt = $pdl2d->mv(0,-1)->dice($numnan->not->which)->mv(0,-1); # remove vectors with any NaN values
my $nanvec = $pdl2d->mv(0,-1)->dice($numnan->which)->mv(0,-1); # the vectors with any NaN values
my $srt = $presrt->qsortvec->mv(0,-1); # BADs are sorted by qsortvec
my $srtdice = $srt;
my $somebad = null;
if ($srt->badflag) {
$srtdice = $srt->dice($srt->mv(0,-1)->nbadover->not->which);
$somebad = $srt->dice($srt->mv(0,-1)->nbadover->which);
}
my $uniq = $srtdice->nelem > 0
? ($srtdice != $srtdice->rotate(-1))->mv(0,-1)->orover->which
: $srtdice->orover->which;
my $ans = $uniq->nelem > 0 ? $srtdice->dice($uniq) :
($srtdice->nelem > 0) ? $srtdice->slice("0,:") :
$srtdice;
return $ans->append($somebad)->append($nanvec->mv(0,-1))->mv(0,-1);
}
EOPM
#####################################################################
# clipping routines
#####################################################################
# clipping
for my $opt (
['hclip','PDLMIN'],
['lclip','PDLMAX']
) {
my $name = $opt->[0];
my $op = $opt->[1];
my $code = '$c() = '.$op.'($b(), $a());';
pp_def(
$name,
HandleBad => 1,
Pars => 'a(); b(); [o] c()',
Code =>
'PDL_IF_BAD(if ( $ISBAD(a()) || $ISBAD(b()) ) {
$SETBAD(c());
} else,) { '.$code.' }',
Doc => 'clip (threshold) C<$a> by C<$b> (C<$b> is '.
($name eq 'hclip' ? 'upper' : 'lower').' bound)',
PMCode=>pp_line_numbers(__LINE__, <<"EOD"),
sub PDL::$name {
my (\$x,\$y) = \@_;
my \$c;
if (\$x->is_inplace) {
\$x->set_inplace(0); \$c = \$x;
} elsif (\@_ > 2) {\$c=\$_[2]} else {\$c=PDL->nullcreate(\$x)}
PDL::_${name}_int(\$x,\$y,\$c);
return \$c;
}
EOD
); # pp_def $name
} # for: my $opt
pp_add_exported('', 'clip');
pp_addpm(<<'EOD');
=head2 clip
=for ref
Clip (threshold) an ndarray by (optional) upper or lower bounds.
=for usage
$y = $x->clip(0,3);
$c = $x->clip(undef, $x);
=for bad
clip handles bad values since it is just a
wrapper around L</hclip> and
L</lclip>.
=cut
EOD
pp_def(
'clip',
HandleBad => 1,
Pars => 'a(); l(); h(); [o] c()',
Code => <<'EOBC',
PDL_IF_BAD(
if( $ISBAD(a()) || $ISBAD(l()) || $ISBAD(h()) ) {
$SETBAD(c());
} else,) {
$c() = PDLMIN($h(), PDLMAX($l(), $a()));
}
EOBC
PMCode=>pp_line_numbers(__LINE__, <<'EOPM'),
*clip = \&PDL::clip;
sub PDL::clip {
my($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 (@_ > 3) {
$d=$_[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 $d;
}
EOPM
); # end of clip pp_def call
############################################################
# elementary statistics and histograms
############################################################
pp_def('wtstat',
HandleBad => 1,
Pars => 'a(n); wt(n); avg(); [o]b();',
GenericTypes => [ppdefs_all],
OtherPars => 'int deg',
Code =>
'complex long double wtsum = 0;
complex long double statsum = 0;
PDL_IF_BAD(int flag = 0;,)
loop(n) %{
PDL_IF_BAD(if (!($ISGOOD(wt()) && $ISGOOD(a()) && $ISGOOD(avg()))) continue;,)
PDL_Indx i;
wtsum += $wt();
complex long double tmp=1;
for(i=0; i<$COMP(deg); i++)
tmp *= $a();
statsum += $wt() * (tmp - $avg());
PDL_IF_BAD(flag = 1;,)
%}
PDL_IF_BAD(if (!flag) { $SETBAD(b()); $PDLSTATESETBAD(b); }
else,) { $b() = statsum / wtsum; }',
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)
',