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|
package PDL::Demos::GSL_RNG;
sub info {('gsl_rng', 'GSL randomness functions (Req.: PDL::Graphics::Simple)')}
my @demo = (
[act => q|
# This demo illustrates the PDL::GSL::RNG module.
# It shows the power of PDL with a concise way to generate graphs of
# different random number distributions.
use PDL::Graphics::Simple;
use PDL::GSL::RNG;
$x = zeroes(100)->xlinvals(-5,5);
$w = pgswin();
# Exponential Power Distribution
$w->plot(
with=>'lines', key=>'a=1 b=2.5', $x, ran_exppow_pdf($x, 1, 2.5),
with=>'lines', key=>'a=1 b=0.5', $x, ran_exppow_pdf($x, 1, 0.5),
{le=>'tr', yrange=>[0,0.8], title=>'Exponential Power Distribution',
xlabel=>'x', ylabel=>'p(x)'}
);
|],
[act => q|
# Cauchy Distribution
$w->plot(
with=>'lines', key=>'a=1', $x, ran_cauchy_pdf($x, 1),
with=>'lines', key=>'a=2', $x, ran_cauchy_pdf($x, 2),
{le=>'tr', yrange=>[0,0.4], title=>'Cauchy Distribution',
xlabel=>'x', ylabel=>'p(x)'}
);
|],
[act => q|
# Rayleigh Tail Distribution
$x = zeroes(100)->xlinvals(0,5);
$w->plot(
with=>'lines', key=>'a=1 sigma=1', $x, ran_rayleigh_tail_pdf($x, 1, 1),
with=>'lines', key=>'a=0.5 sigma=2', $x, ran_rayleigh_tail_pdf($x, 0.5, 2),
{le=>'tr', yrange=>[0,1.1], title=>'Rayleigh Tail Distribution',
xlabel=>'x', ylabel=>'p(x)'}
);
|],
[act => q|
# Gamma Distribution
$x = zeroes(100)->xlinvals(0,5);
$w->plot(
with=>'lines', key=>'a=1 b=1', $x, ran_gamma_pdf($x, 1, 1),
with=>'lines', key=>'a=2 b=1', $x, ran_gamma_pdf($x, 2, 1),
with=>'lines', key=>'a=3 b=1', $x, ran_gamma_pdf($x, 3, 1),
{le=>'tr', yrange=>[0,1], title=>'Gamma Distribution',
xlabel=>'x', ylabel=>'p(x)'}
);
|],
[act => q|
# Bivariate Gaussian Distribution
# inspired by https://www.perlmonks.org/?node_id=11104262
$points = pdl '[219 88 2.7; 38 95 1.7; 45 268 0.8]';
($XSIZE, $YSIZE) = (300, 300);
($xcoord, $ycoord, $weight) = $points # xyw nweights
->slice(",*$XSIZE,*$YSIZE,") # xyw nx ny nweights
->using(0..2); # nx ny nweights
$xbase = xvals($XSIZE)->slice(",*$YSIZE"); # nx ny
$ybase = xvals($YSIZE)->slice("*$XSIZE,"); # nx ny
for (1..90) {
$h = (
$weight * ran_bivariate_gaussian_pdf(
$xcoord-$xbase, $ycoord-$ybase, $_, $_, 0
) # nx ny nweights
)->mv(-1,0)->sumover; # nx ny
$w->plot(with=>'image', $h, {title=>'Bivariate Gaussian Distribution',j=>1});
}
|],
[act => q|
# Same, but with a colourful heatmap (if you have the right libraries)
sub as_heatmap {
my ($d) = @_;
my $max = $d->max;
die "as_heatmap: can't work if max == 0" if $max == 0;
$d /= $max; # negative OK
my $hue = (1 - $d)*240;
$d = cat($hue, pdl(1), pdl(1));
(hsv_to_rgb($d->mv(-1,0)) * 255)->byte->mv(0,-1);
}
if (eval 'use PDL::Graphics::ColorSpace; 1') {
for (1..90) {
$h = (
$weight * ran_bivariate_gaussian_pdf(
$xcoord-$xbase, $ycoord-$ybase, $_, $_, 0
) # nx ny nweights
)->mv(-1,0)->sumover; # nx ny
$w->plot(
with=>'image', as_heatmap($h),
{title=>'Bivariate Gaussian Distribution (heatmap)',j=>1}
);
}
}
|],
[comment => q|
See https://www.gnu.org/software/gsl/doc/html/randist.html for more.
|],
);
sub demo { @demo }
sub done {'
undef $w;
'}
1;
|
