sub defpdl {
my %hash = (Pars => $_[1],
OtherPars => $_[2],
Code => $_[3]);
$hash{Doc} = $_[4] if $#_>3;
pp_def($_[0],%hash);
}
pp_addhdr(<<'EOD');
#define IsNaN(x) (x != x)
#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> for how to use indices creatively.
For explanation of the signature format, see L<PDL::PP>.
=head1 SYNOPSIS
use PDL::Primitive;
=cut
EOD
sub projectdocs {
my $name = shift;
my $op = shift;
my $extras = shift;
return <<EOD;
=for ref
Project via $name to N-1 dimensions
This function reduces the dimensionality of a piddle
by one by taking the $name along the 1st dimension.
By using C<xchg> etc. (see L<PDL::Slices>) it is possible to use
I<any> dimension.
=for usage
\$a = $op(\$b);
=for example
\$spectrum = $op \$image->xchg(0,1)
$extras
=cut
EOD
}
sub cumuprojectdocs {
my $name = shift;
my $op = shift;
my $extras = shift;
return <<EOD;
=for ref
Cumulative $name
This function calculates the cumulative $name
along the 1st dimension.
By using C<xchg> etc. (see L<PDL::Slices>) it is possible to use
I<any> dimension.
The sum is started so that the first element in the cumulative $name
is the first element of the parameter.
=for usage
\$a = $op(\$b);
=for example
\$spectrum = $op \$image->xchg(0,1)
$extras
=cut
EOD
}
defpdl(
'sumover',
'a(n); int+ [o]b();',
'',
'$GENERIC(b) tmp = 0;
loop(n) %{ tmp += $a(); %}
$b() = tmp;',
projectdocs('sum','sumover','')
);
defpdl(
'zcover',
'a(n); int+ [o]b();',
'',
'$GENERIC(b) tmp = 1;
loop(n) %{ tmp = tmp && $a() == 0; if (!tmp) break; %}
$b() = tmp;',
projectdocs('!= 0','zcover','')
);
pp_def(
'andover',
Pars => 'a(n); int+ [o]b();',
GenericTypes => [B,S,U,L],
Code => '$GENERIC(b) tmp = 1;
loop(n) %{ tmp = tmp && $a(); if (!tmp) break; %}
$b() = tmp;',
Doc => projectdocs('and','andover','')
);
pp_def(
'bandover',
Pars => 'a(n); int+ [o]b();',
GenericTypes => [B,S,U,L],
Code => '$GENERIC(b) tmp = ~ 0 ;
loop(n) %{ tmp &= $a(); if (!tmp) break; %}
$b() = tmp;',
Doc => projectdocs('bitwise and','bandover','')
);
pp_def(
'orover',
Pars => 'a(n); int+ [o]b();',
GenericTypes => [B,S,U,L],
Code => '$GENERIC(b) tmp = 0;
loop(n) %{ tmp = tmp || $a(); if (tmp) break; %}
$b() = tmp;',
Doc => projectdocs('or','orover','')
);
pp_def(
'borover',
Pars => 'a(n); int+ [o]b();',
GenericTypes => [B,S,U,L],
Code => '$GENERIC(b) tmp = 0;
loop(n) %{ tmp |= $a(); if (!~tmp) break; %}
$b() = tmp;',
Doc => projectdocs('bitwise or','borover','')
);
defpdl(
'intover',
'a(n); int+ [o]b();',
'',
'$GENERIC(b) tmp = 0;
int ns = $SIZE(n), nn;
/* Integration formulae from Press et al 2nd Ed S 4.1 */
switch (ns) {
case 1:
threadloop %{
$b() = 0.; /* not a(n=>0); as interval has zero width */
%}
break;
case 2:
threadloop %{
$b() = 0.5*($a(n=>0)+$a(n=>1));
%}
break;
case 3:
threadloop %{
$b() = ($a(n=>0)+4*$a(n=>1)+$a(n=>2))/3.;
%}
break;
case 4:
threadloop %{
$b() = ($a(n=>0)+$a(n=>3)+3.*($a(n=>1)+$a(n=>2)))*0.375;
%}
break;
case 5:
threadloop %{
$b() = (14.*($a(n=>0)+$a(n=>4))
+64.*($a(n=>1)+$a(n=>3))
+24.*$a(n=>2))/45.;
%}
break;
default:
threadloop %{
for (nn=3;nn<ns-3;nn++) { tmp += $a(n=>nn); }
tmp += (23./24.)*($a(n=>2)+$a(n=>nn));nn++;
tmp += (7./6.) *($a(n=>1)+$a(n=>nn));nn++;
tmp += 0.375 *($a(n=>0)+$a(n=>nn));
$b() = tmp;
%}
}
',
projectdocs('integral','intover',
q~Notes:
For n > 3, these are all O(h^4) (like Simpson's rule), but are
integrals between the end points assuming the pdl gives values just at
these centres: for such `functions', sumover is correct to O(h), but
is the natural (and correct) choice for binned data, of course.
~)
);
defpdl(
'cumusumover',
'a(n); int+ [o]b(n);',
'',
'$GENERIC(b) tmp = 0;
loop(n) %{ tmp += $a();
$b() = tmp;
%}
',
cumuprojectdocs('sum','cumusumover','')
);
defpdl(
'prodover',
'a(n); int+ [o]b();',
'',
'$GENERIC(b) tmp = 1;
loop(n) %{ tmp *= $a(); %}
$b() = tmp;',
projectdocs('product','prodover','')
);
defpdl(
'cumuprodover',
'a(n); int+ [o]b(n);',
'',
'$GENERIC(b) tmp = 1;
loop(n) %{ tmp *= $a();
$b() = tmp;
%}
',
cumuprojectdocs('product','cumuprodover','')
);
# XXX why cnt? Why not size(n)? Why not threadloop for efficiency
defpdl(
'average',
'a(n); int+ [o]b();',
'',
'$GENERIC(b) tmp = 0, cnt;
cnt = 0;
loop(n) %{ tmp += $a(); cnt++; %}
$b() = tmp/cnt;',
projectdocs('average','average','')
);
# Internal utility sorting routine for median/qsort routines.
for (keys %PDL::Types::typehash) {
$ctype = $PDL::Types::typehash{$_}{ctype};
$ppsym = $PDL::Types::typehash{$_}{ppsym};
pp_addhdr("
void pdl_qsort_$ppsym($ctype* xx, int a, int b) {
int i,j;
$ctype t, median;
i = a; j = b;
median = xx[(i+j) / 2];
do {
while (xx[i] < median)
i++;
while (median < xx[j])
j--;
if (i <= j) {
t = xx[i]; xx[i] = xx[j]; xx[j] = t;
i++; j--;
}
} while (i <= j);
if (a < j)
pdl_qsort_$ppsym(xx,a,j);
if (i < b)
pdl_qsort_$ppsym(xx,i,b);
}
void pdl_qsort_ind_$ppsym($ctype* xx, int* ix, int a, int b) {
int i,j;
int t;
$ctype median;
i = a; j = b;
median = xx[ix[(i+j) / 2]];
do {
while (xx[ix[i]] < median)
i++;
while (median < xx[ix[j]])
j--;
if (i <= j) {
t = ix[i]; ix[i] = ix[j]; ix[j] = t;
i++; j--;
}
} while (i <= j);
if (a < j)
pdl_qsort_ind_$ppsym(xx,ix,a,j);
if (i < b)
pdl_qsort_ind_$ppsym(xx,ix,i,b);
}
");
}
pp_def('medover',
Pars => 'a(n); [o]b(); [t]tmp(n);',
Doc => projectdocs('median','medover',''),
Code => '
int nn, nn1, nn2;
loop(n) %{ $tmp() = $a(); %}
nn = $COMP(__n_size)-1;
$TBSULFD(pdl_qsort_B,pdl_qsort_S,pdl_qsort_U,
pdl_qsort_L,pdl_qsort_F,pdl_qsort_D) ($P(tmp), 0, nn);
nn1 = nn/2; nn2 = nn1+1;
if (nn%2==0) {
$b() = $tmp(n => nn1);
}
else {
$b() = 0.5*( $tmp(n => nn1) + $tmp(n => nn2) );
}
');
pp_def('oddmedover',
Pars => 'a(n); [o]b(); [t]tmp(n);',
Doc => projectdocs('oddmedian','oddmedover','
The median is sometimes not a good choice as if the array has
an even number of elements it lies half-way between the two
middle values - thus it does not always correspond to a data
value. The lower-odd median is just the lower of these two values
and so it ALWAYS sits on an actual data value which is useful in
some circumstances.
'),
Code => '
int nn, nn1;
loop(n) %{ $tmp() = $a(); %}
nn = $COMP(__n_size)-1;
$TBSULFD(pdl_qsort_B,pdl_qsort_S,pdl_qsort_U,
pdl_qsort_L,pdl_qsort_F,pdl_qsort_D) ($P(tmp), 0, nn);
nn1 = nn/2;
$b() = $tmp(n => nn1);
');
# Generate small ops functions to do entire array
for $op ( ['avg','average','average'],
['sum','sumover','sum'],
['zcheck','zcover','check for zero'],
['and','andover','logical and'],
['band','bandover','bitwise and'],
['or','orover','logical or'],
['bor','borover','bitwise or'],
['min','minimum','minimum'],
['max','maximum','maximum'],
['median', 'medover', 'median'],
['oddmedian','oddmedover','oddmedian']) {
pp_add_exported('', $op->[0]);
pp_addpm(<<"EOD");
=head2 $op->[0]
=for ref
Return the $op->[2] of all elements in a piddle
=for usage
\$x = $op->[0](\$data);
=cut
*$op->[0] = \\&PDL::$op->[0];
sub PDL::$op->[0] {
my(\$x) = \@_; my \$tmp;
\$x->clump(-1)->$op->[1](\$tmp=PDL->nullcreate(\$x) );
return \$tmp->at();
}
EOD
} # for $op
pp_add_exported('','any all');
pp_addpm(<<'EOPM');
=head2 any
=for ref
Return true if any element in piddle set
Useful in conditional expressions:
=for example
if (any $a>15) { print "some values are greater than 15\n" }
=cut
*any = \∨
*PDL::any = \&PDL::or;
=head2 all
=for ref
Return true if all elements in piddle set
Useful in conditional expressions:
=for example
if (all $a>15) { print "all values are greater than 15\n" }
=cut
*all = \∧
*PDL::all = \&PDL::and;
EOPM
pp_addpm(<<'EOD'
=head2 minmax
=for ref
Returns an array with minimum, maximum of a piddle.
=for usage
($mn, $mx) = minmax($pdl);
Return $mn as minimum, $mx as maximum, $mn_ind as the index of minimum and
$mx_ind as the index of the maximum.
=for example
perldl> $x = pdl [1,-2,3,5,0]
perldl> ($min, $max) = minmax($x);
perldl> p "$min $max\n";
=cut
*minmax = \&PDL::minmax;
sub PDL::minmax {
my ($x)=@_; my $tmp;
my @arr = $x->clump(-1)->minmaximum;
return @arr[0,1];
}
EOD
);
pp_add_exported('', 'minmax');
#pp_add_exported('', 'minmax_ind');
pp_def('qsort',
Pars => 'a(n); [o]b(n);',
Code => '
int nn;
loop(n) %{ $b() = $a(); %}
nn = $COMP(__n_size)-1;
$TBSULFD(pdl_qsort_B,pdl_qsort_S,pdl_qsort_U,
pdl_qsort_L,pdl_qsort_F,pdl_qsort_D) ($P(b), 0, nn);
', Doc=>'
=for ref
Quicksort a vector into ascending order.
=for example
print qsort random(10);
=cut
');
pp_def('qsorti',
Pars => 'a(n); int [o]indx(n);',
Code => '
int nn;
int i=0;
nn = $COMP(__n_size)-1;
loop(n) %{ $indx() = i++; %}
$TBSULFD(pdl_qsort_ind_B,pdl_qsort_ind_S,pdl_qsort_ind_U,
pdl_qsort_ind_L,pdl_qsort_ind_F,pdl_qsort_ind_D) ($P(a), $P(indx),
0, nn);
', Doc=>'
=for ref
Quicksort a vector and return index of elements in ascending order.
=for example
$ix = qsorti $a;
print $a->index($ix); # Sorted list
=cut
');
defpdl(
'axisvalues',
'[o,nc]a(n)',
'',
'loop(n) %{ $a() = n; %}',
'
=for ref
Internal routine
C<axisvalues> is the internal primitive that implements C<axisvals> and
alters its argument.
=cut
'
);
defpdl(
'inner',
'a(n); b(n); [o]c(); ', '',
'double tmp = 0;
loop(n) %{ tmp += $a() * $b(); %}
$c() = tmp;','
=for ref
Inner product over one dimension
c = sum_i a_i * b_i
');
defpdl(
'outer',
'a(n); b(m); [o]c(n,m); ', '',
'loop(n,m) %{ $c() = $a() * $b(); %}',
<<'EOD'
=for ref
outer product over one dimension
Naturally, it is possiblet to achieve the effects of outer
product simply by threading over the "C<*>"
operator but this function is provided for convenience.
=cut
EOD
);
pp_addpm(<<'EOD');
=head2 matmult
=for sig
Signature: matmult(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');
defpdl(
'innerwt',
'a(n); b(n); c(n); [o]d(); ', '',
'double tmp = 0;
loop(n) %{ tmp += $a() * $b() * $c(); %}
$d() = tmp;','
=for ref
Weighted (i.e. triple) inner product
d = sum_i a(i) b(i) c(i)
=cut
');
defpdl(
'inner2',
'a(n); b(n,m); c(m); [o]d();',
'',
'double tmp=0;
loop(n,m) %{
tmp += $a() * $b() * $c();
%}
$d() = tmp;
','
=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 a and c since that would be very
wasteful. Instead, you should use a temporary for b*c.
=cut
');
defpdl(
'inner2d',
'a(n,m); b(n,m); [o]c()',
'',
'double tmp=0;
loop(n,m) %{
tmp += $a() * $b();
%}
$c() = tmp;
','
=for ref
Inner product over 2 dimensions.
Equivalent to
$c = inner($a->clump(2), $b->clump(2))
'
);
defpdl(
'inner2t',
'a(j,n); b(n,m); c(m,k); [t]tmp(n,k); [o]d(j,k));',
'',
'
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;
%}',<<'EOD');
=for ref
Efficient Triple matrix product a*b*c
Efficiency comes from by using the temporary tmp. This operation only scales as
N**3 whereas threading using inner2 would scale as 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.
=cut
EOD
=item minimum_ind(a(n),int [o]c()), maximum_ind(a(n),int [o]c())
These functions work like the previous except that they
return the index of the maximum element
=item minimum_n_ind(a(n),int [o]c(m)), maximum_n_ind(a(n),int [o]c(m))
These functions work like the previous except that they
return the indices of the I<m> maximum elements.
=cut
for $which (['minimum','<'],
['maximum','>']) {
defpdl(
$which->[0],
'a(n); [o]c();','',
'$GENERIC() cur;
loop(n) %{
if(!n || $a() '.$which->[1].' cur || IsNaN(cur)) {cur = $a();}
%}
$c() = cur;
', projectdocs($which->[0],$which->[0])
);
defpdl(
$which->[0]."_ind",
'a(n); int[o]c();','',
'$GENERIC() cur; int curind;
loop(n) %{
if(!n || $a() '.$which->[1].' cur || IsNaN(cur))
{cur = $a(); curind = n;}
%}
$c() = curind;
',"Like $which->[0] but returns the index rather than the value"
);
defpdl(
$which->[0]."_n_ind",
'a(n); int[o]c(m);','',
'$GENERIC() cur; int curind;
if($SIZE(m) > $SIZE(n)) $CROAK("n_ind: m_size > n_size");
loop(m) %{
loop(n) %{
int nm; int flag=0;
for(nm=0; nm<m; nm++) {
if($c(m=>nm) == n) {flag=1; break;}
}
if(!flag &&
(n<=m || $a() '.$which->[1].' cur || IsNaN(cur)))
{cur = $a(); curind = n;}
%}
$c() = curind;
%}
',"Returns the index of C<m> $which->[0] elements"
);
}
pp_addpm(<<'EOD'
=cut
=head2 minmaximum
=for ref
Find minimum and maximum and their indices for a given piddle;
=for usage
perldl> $a=pdl [[-2,3,4],[1,0,3]]
perldl> ($min, $max, $min_ind, $max_ind)=minmaximum($a)
perldl> p $min, $max, $min_ind, $max_ind
[-2 0] [4 3] [0 1] [2 2]
See also minmax, which clumps the piddle together.
=cut
EOD
);
pp_def( 'minmaximum',
Pars => 'a(n); [o]cmin(); [o] cmax(); int [o]cmin_ind(); int [o]cmax_ind();',
Code => '$GENERIC() curmin, curmax;
int curmin_ind, curmax_ind;
loop(n) %{
if (!n || ($a() < curmin) || IsNaN(curmin)) {curmin = $a(); curmin_ind = n;};
if (!n || ($a() > curmax) || IsNaN(curmax)) {curmax = $a(); curmax_ind = n;};
%}
$cmin() = curmin;
$cmax() = curmax;
$cmin_ind() = curmin_ind;
$cmax_ind() = curmax_ind;'
);
for (['hclip','>'],['lclip','<']) {
pp_def($_->[0],
Pars => 'a(); b(); [o] c()',
Code => '$c() = ($a() '.$_->[1].' $b()) ? $b() : $a();',
Doc => 'clip $a by $b ($b is '.($_->[0] eq 'hclip' ? 'upper' :
'lower').' bound)',
PMCode=><<"EOD",
sub PDL::$_->[0] {
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::_$_->[0]_int(\$a,\$b,\$c);
return \$c;
}
EOD
);
}
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, $x);
=cut
*clip = \&PDL::clip;
sub PDL::clip {
my($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
defpdl(
'wtstat',
'a(n); wt(n); avg(); [o]b();',
'int deg',
'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;
',<<'EOD');
=head2 wtstat
=for ref
Weighted statistical moment of given degree
This calculates a weighted statistic over the vector a.
The formula is
b() = (sum_i wt_i * (a_i ** degree - avg)) / (sum_i wt_i)
=cut
EOD
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 '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.
=head2 randsym
=for ref
Constructor which returns piddle of random numbers
=for usage
$a = randsym([type], $nx, $ny, $nz,...);
$a = randsym $b;
etc. (see 'zeroes')
This is the uniform distribution between 0 and 1 (excluding both 0 and
1, cf C<random>). The arguments are the same as C<zeroes> (q.v.) -
i.e. one can specify dimensions, types or give a template.
=cut
EOD
pp_def(
'random',
Pars=>'a();',
PMFunc => '',
Code =>
'$a() = ((double)rand()) / (RAND_MAX+1.0);',
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 $x;
}
EOD
);
pp_def(
'randsym',
Pars=>'a();',
PMFunc => '',
Code =>
'$a() = (0.5+(double)rand()) / (RAND_MAX+1.0);',
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 $b;
etc. See 'zeroes'
This is generated by summing 12 uniform random
distributions for now. Hopefully someone can be
inspired to create a better version!
Mean = 0, Stddev = 1
=cut
sub grandom { ref($_[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 'erfi';
$x .= erfi(randsym($x));
return $x;
}
EOD
pp_add_exported('','grandom');
defpdl(
'assgn',
'a(); [o]b();',
'',
'$b() = $a();',
'Plain numerical assignment. This is used to implement the ".=" operator'
);
# The last x is ignored...
pp_def('vsearch',
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 $val the index of the least larger member
of $xs (which need to be in increasing order). If the value is larger
than any member of $xs, the index to the last element of $xs is returned.
=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 C<cumusumover> function to obtain
cumulative probabilities from absolute probabilities.
EOD
pp_def('interpol',
Pars => 'i(); x(n); y(n); [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() > $x(n => m) == up)
jl = m;
else
jh = m;
}
if (jl == -1) {
if ($i() != $x(n => 0)) carp = 1;
jl = 0;
} else if (jl == n1) {
if ($i() != $x(n => n1)) carp = 1;
jl = n1-1;
}
jh = jl+1;
if ((d = $x(n => jh)-$x(n => jl)) == 0)
barf("identical abscissas");
d = ($x(n => jh)-$i())/d;
$ip() = d*$y(n => jl) + (1-d)*$y(n => jh);
%}
if (carp) warn("some values had to be extrapolated");
', Doc=><<'EOD');
=for ref
routine for 1D linear interpolation
=for usage
$interpolated_values = interpol($interpol_at, $ordered_abscissas, $yvalues)
'interpol' uses a binary search to find the suspects, er...,
interpolation indices and therefore abscissas have to be strictly
ordered (increasing or decreasing). For interpolation at lots of
closely spaced abscissas an approach that uses the last index found as
a start for the next search can be faster (compare Numerical Recipes
'hunt' routine). Feel free to implement that on top of the binary
search if you like. For out of bounds values it just does a linear
extrapolation and issues a warning upon completion.
=cut
EOD
pp_add_exported("", one2nd);
pp_addpm(<<'EOD');
=head2 one2nd
=for ref
Converts a one dimensional index piddle to a set of ND coordinates
=for usage
@coords=one2nd($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 $a clumped using clump(-1). This routine is used in 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
pp_addpm(<<'EOD'
=head2 which
=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 mask really has to be 1-D (use clump(-1)
if you need to work with ND-images)
If you want to return both the indices of non-zero values and the
complement, use the function 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 $indx
[7 8 9]
=cut
=head2 which_both
=for ref
Returns piddle of indices of non-zero values and their complement
=for usage
($i, $c_i) = which_both($mask);
This works just as which, but the complement of $i will be in $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 $big"
[5 6 7 8 9]
[0 1 2 3 4]
=cut
EOD
);
for ({Name=>'which',
Pars => 'mask(n); int [o] inds(m);',
Variables => 'int dm=0;',
Elseclause => "",
Autosize => '$SIZE(m) = sum;'},
{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".' $SIZE(q) = dpdl->dims[0]-sum;'})
{
pp_def($_->{Name},
Pars => $_->{Pars},
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
Returns indices to non-zero values or those values from another piddle.
=for usage
$i = $x->where($x+5 > 0); # $i contains elements of $x
# where mask ($x+5 > 0) is 1
Note: $i is always 1-D, even if $x is >1-D. The first argument
(the values) and the second argument (the mask) currently have to have
the same initial dimensions (or horrible things happen).
It is also possible to use the same mask for several piddles with
the same call:
($i,$j,$k) = where($x,$y,$z, $x+5>0);
There is also the following syntax, retained only for compatibility
with PDL versions <1.99.
This use is deprecated, and will be removed
in the future. Use C<which> instead.
$i = where($x > 0); # indices to $x, equivalent to 'which()'
Note: the mask has to be 1-D. See the documentation for C<which>
=cut
sub PDL::where {
if($#_ == 0) {
warn "WARNING: one argument form of where() is now deprecated - use which()\n";
return $_[0]->which();
} elsif($#_ == 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_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->dims[0] + dpdlb->dims[0];',
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 => << 'EOD',
=for ref
append two piddles by concantening along their respective 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
sum of sizes of the two argument piddles' first dims.
EOD
);
for({Name => 'histogram',
WeightPar => '',
HistType => 'int+',
HistOp => '++',
Doc1 => "",
Doc2 => "",
Doc3 => "number of\n",
Doc4 => "\nUse C<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 => '+= $wt()',
Doc1 => " from weighted data",
Doc2 => "\$weights, ",
Doc3 => "sum of the values in \$weights\nthat correspond to ",
Doc4 => "",
Doc5 => "whistogram(pdl(1,1,2), pdl(0.1,0.1,0.5), 1, 0, 4)\n [0 0.2 0.5 0]"})
{
pp_def($_->{Name},
Pars => 'in(n); '.$_->{WeightPar}.$_->{HistType}. '[o] hist(m)',
# set outdim by Par!
OtherPars => 'double step; double min; int msize => m',
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}.';
%}
%}
',
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 \$numbins bins starting from \$min, each
\$step wide. The value in each bin is the $_->{Doc3}values in \$data that lie within the bin limits.
Data below the lower limit is put in the first bin, and data above the
upper limit is put in the last bin.
The output is reset in a different threadloop so that you
can take a histogram of \$a(10,12) into \$b(15) and get the result
you want.
$_->{Doc4}
=for example
perldl> p $_->{Doc5}
=cut
EOD
}
for({Name => 'histogram2d',
WeightPar => '',
HistType => 'int+',
HistOp => '++',
Doc1 => "",
Doc2 => "",
Doc3 => "number of\n",
Doc5 => "histogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),1,0,3,1,0,3)
[
[0 0 0]
[0 2 2]
[0 1 0]
]
"},
{Name => 'whistogram2d',
WeightPar => 'float+ wt(n);',
HistType => 'float+',
HistOp => '+= $wt()',
Doc1 => " from weighted data",
Doc2 => " \$weights,",
Doc3 => "sum of the values in\n\$weights that correspond to ",
Doc5 => "whistogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),pdl(0.1,0.2,0.3,0.4,0.5),1,0,3,1,0,3)
[
[ 0 0 0]
[ 0 0.5 0.9]
[ 0 0.1 0]
]
"})
{
pp_def($_->{Name},
Pars => 'ina(n); inb(n); '.$_->{WeightPar}.$_->{HistType}. '[o] hist(ma,mb)',
# set outdim by Par!
OtherPars => 'double stepa; double mina; int masize => ma;
double stepb; double minb; int mbsize => mb;',
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))'.$_->{HistOp}.';
%}
%}
',
Doc=><<"EOD");
=for ref
Calculates a 2d histogram$_->{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 \$nbinx x \$nbiny bins, with the lower
limits of the first one at (\$minx, \$miny), and with bin size
(\$stepx, \$stepy). The value in each bin is the $_->{Doc3}values in \$datax and \$datay that lie within the bin limits.
Data below the lower limit is put in the first bin, and data above the
upper limit is put in the last bin.
=for example
perldl> p $_->{Doc5}
=cut
EOD
}
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 $c*$a and $c*$b will be zero, i.e. $c is
orthogonal to $a and $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',
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() = $vec(); %}
}',
);
pp_add_exported('','stats');
pp_addpm(<<'EOD');
=head2 stats
=for ref
Calculates useful statistics on a piddle
=for usage
($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.
=cut
*stats = \&PDL::stats;
sub PDL::stats {
barf('Usage: ($mean,[$rms]) = stats($data,[$weights])') if $#_>1;
my ($data,$weights) = @_;
my ($mean,$rms);
if ($#_==0) {
$mean = ($data->sum)/($data->nelem);
$rms = sqrt( ((($data-$mean)**2 )->sum) / ($data->nelem) );
}
else {
$mean = (($weights*$data)->sum) / (($weights)->sum);
$rms = sqrt( ( ( $weights*(($data-$mean)**2) )->sum ) / ($weights->sum) );
}
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
pp_addpm(<<'EOD'
=head2 whichND
=for ref
Returns the coordinates for non-zero values
=for usage
@coords=whichND($mask);
returns an array of piddles containing the coordinates of the elements
that are non-zero in $mask.
=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 $a->at($x,$y,$z,$w)
203
=cut
*whichND = \&PDL::whichND;
sub PDL::whichND {
my $mask = shift;
my $ind=($mask->clump(-1))->which;
return $mask->one2nd($ind);
}
EOD
);
pp_add_exported("", whichND);
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_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) and Karl Glazebrook
(kgb@aaoepp.aao.gov.au).
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
pp_done();