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regenerate demos using (in PDL checkout):
perl -Mblib utils/harness ../pdl-www/content/demos/
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‎content/demos/bad.html‎

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either because it does not make sense or it's too much work to do!
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<p/>
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To find out the status of a particular routine, use the 'badinfo'
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command in perldl or pdl2 shell (this information is also included
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command in perldl shell (this information is also included
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when you do 'help'), or the '-b' switch of pdldoc.
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<hr/>

‎content/demos/cartography.html‎

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<hr/>
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There are a large number of map projections -- to list them all,
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say "??cartography" in the perldl or pdl2 shell. Here are four
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say "??cartography" in the perldl shell. Here are four
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of them:
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<pre>
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undef $w; # Close old window

‎content/demos/index.html‎

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@@ -16,6 +16,7 @@ <h1 class='title'>Demos and Examples</h1>
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<li><a href="?page=demos/gsl_rng">gsl_rng - GSL randomness functions</a></li>
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<li><a href="?page=demos/proj">proj - Transforms with PROJ</a></li>
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<li><a href="?page=demos/simplex">simplex - Simplex optimisation</a></li>
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<li><a href="?page=demos/stats">stats - Statistics, linear modelling</a></li>
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<li><a href="?page=demos/transform">transform - Coordinate transformations</a></li>
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<li><a href="?page=demos/plot2D">2D plotting with PGPLOT</a></li>
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<li><a href="?page=screenshots/index">3D plots</a></li>

‎content/demos/pdl.html‎

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of the basic capabilities of PDL.
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<p/>
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We encourage you to play with these commands in
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the perldl or pdl2 shell and use its online help support
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the perldl shell and use its online help support
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to find out more about these and other commands and
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features of PDL.
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<p/>

‎content/demos/stats.html‎

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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>stats - Statistics, linear modelling</title>
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</head>
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<body>
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<h1>stats - Statistics, linear modelling</h1>
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This demo illustrates the <a href="https://metacpan.org/pod/PDL::Stats">PDL::Stats</a> module,
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which lets you analyse statistical data in a number of ways.
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<pre>
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use <a href="https://metacpan.org/pod/PDL::Stats">PDL::Stats</a>;
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$w = pgswin(); # <a href="https://metacpan.org/pod/PDL::Graphics::Simple">PDL::Graphics::Simple</a> window
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srandom(5); # for reproducibility
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</pre>
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<hr/>
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First, <a href="https://metacpan.org/pod/PDL::Stats::TS">PDL::Stats::TS</a> - let's show three sets of random data, against
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the de-seasonalised version
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<pre>
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$data = random(12, 3);
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$data->plot_dseason( 12, { win=>$w } );
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</pre>
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<h4>Output</h4>
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<img src="images/demos/stats/output-1.png"/>
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<hr/>
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Now let's show the seasonal means of that data
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<pre>
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($m, $ms) = $data->season_m( 6, { plot=>1, win=>$w } );
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print "m=$m\nms=$ms";
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</pre>
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<h4>Output</h4>
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<pre>
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m=
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[
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[ 0.63660469 0.21671189 0.31362712 0.65773141 0.44697942 0.44024627]
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[ 0.77400156 0.24928771 0.54476702 0.42999148 0.80334015 0.63420928]
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[ 0.89574201 0.28036099 0.43392446 0.31499982 0.16980532 0.29458511]
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]
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ms=
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[
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[ 0.022649418 0.027603922 0.065493262 5.6366038e-06 0.0097363653 0.053513471]
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[ 0.026704068 0.026384061 0.18308074 0.14584601 0.012937776 0.081424333]
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[ 0.0031311796 0.011825565 0.012130112 0.043369421 0.00970367 7.9067403e-05]
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]
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</pre>
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<img src="images/demos/stats/output-2.png"/>
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<hr/>
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Now, auto-correlation of a random sound-sample.
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See <a href="https://pdl.perl.org/advent/blog/2024/12/15/pitch-detection/">https://pdl.perl.org/advent/blog/2024/12/15/pitch-detection/</a> for more!
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<pre>
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random(100)->plot_acf( 50, { win=>$w } );
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</pre>
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<h4>Output</h4>
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<img src="images/demos/stats/output-3.png"/>
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<hr/>
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<a href="https://metacpan.org/pod/PDL::Stats::Kmeans">PDL::Stats::Kmeans</a> clusters data points into "k" (a supplied number) groups
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<pre>
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$data = grandom(200, 2); # two rows = two dimensions
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%k = $data->kmeans; # use default of 3 clusters
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print "$_\t@{[$k{$_} =~ /^\n*(.*?)\n*\z/s]}\n" for sort keys %k;
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$w->plot(
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(map +(with=>'points', style=>$_+1, ke=>"Cluster ".($_+1),
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$data->dice_axis(0,which($k{cluster}->slice(",$_")))->dog),
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0 .. $k{cluster}->dim(1)-1),
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(map +(with=>'circles', style=>$_+1, ke=>"Centroid ".($_+1), $k{centroid}->slice($_)->dog, 0.1),
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0 .. $k{centroid}->dim(0)-1),
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{le=>'tr'},
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);
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</pre>
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<h4>Output</h4>
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<pre>
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R2 0.562033919028588
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centroid [
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[ -1.1856909 0.045429685 0.76406539]
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[ 0.54058456 -1.07968 0.4569263]
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]
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cluster [
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[0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0]
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[1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1]
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[0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0]
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]
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n [59 71 70]
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ss [
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[ 26.674205 40.003228 26.652344]
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[ 36.077374 23.989678 31.197273]
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]
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</pre>
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<img src="images/demos/stats/output-4.png"/>
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<hr/>
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There's also a principal component analysis (PCA) clustering function
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<pre>
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$data = qsort random 10, 5; # 10 obs on 5 variables
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%r = $data->pca( { plot=>1, win=>$w } );
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</pre>
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Here we can see that very nearly all the variance is in the first component.
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<h4>Output</h4>
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<img src="images/demos/stats/output-5.png"/>
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<hr/>
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From that PCA we can plot the original vs PCA-transformed scores
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along the first two components
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<pre>
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$data->plot_scores( $r{eigenvector}, {win=>$w} );
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</pre>
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<h4>Output</h4>
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<img src="images/demos/stats/output-6.png"/>
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<hr/>
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Suppose this is a person's ratings for top 10 box office movies
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ascending sorted by box office
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<pre>
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$y = pdl '[1 1 2 2 2 2 4 4 5 5]';
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$x = cat sequence(10), sequence(10)**2; # IV with linear and quadratic component
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</pre>
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We do an ordinary least squares (OLS), or multiple linear regression,
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to get the underlying linear model. Here we also plot how far the real
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data was from our calculated model.
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<pre>
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%m = $y->ols( $x, { plot=>1, win=>$w } );
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print "$_\t@{[$m{$_} =~ /^\n*(.*?)\n*\z/s]}\n" for sort keys %m;
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</pre>
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<h4>Output</h4>
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<pre>
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F 40.4225352112676
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F_df [2 7]
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F_p 0.000142834216344756
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R2 0.920314253647587
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b [0.981818181818215 0.212121212121208 0.0303030303030304]
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b_p [0.0399105086044558 0.328001176835915 0.203034040562643]
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b_se [0.389875811466657 0.201746929168937 0.021579988884181]
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b_t [2.51828442017153 1.05142225953578 1.40421899499882]
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ss_model 19.8787878787879
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ss_residual 1.72121212121212
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ss_total 21.6
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y_pred [0.981818181818215 1.22424242424245 1.52727272727275 1.89090909090911 2.31515151515153 2.80000000000002 3.34545454545456 3.95151515151516 4.61818181818182 5.34545454545455]
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</pre>
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<img src="images/demos/stats/output-7.png"/>
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<hr/>
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<pre>
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$y = pdl '[1 1 2 2 3 3 3 3 4 5 5 5]'; # suppose this is ratings for 12 apples
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$a = pdl '[1 2 3 1 2 3 1 2 3 1 2 3]'; # IV for types of apple
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@b = qw( y y y y y y n n n n n n ); # IV for whether we baked the apple
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</pre>
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First let's look at the raw data, categorised in each independent variable:
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<pre>
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$y->plot_stripchart( $a, \@b, { IVNM=>[qw(apple bake)], win=>$w } );
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</pre>
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Looks like there's a visible partition in the "bake" IV
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<h4>Output</h4>
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<img src="images/demos/stats/output-8.png"/>
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<hr/>
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Let's try the analysis of variance (ANOVA) in <a href="https://metacpan.org/pod/PDL::Stats::GLM">PDL::Stats::GLM</a>
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<pre>
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%m = $y->anova( $a, \@b, { IVNM=>[qw(apple bake)], plot=>0, win=>$w } );
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print "$_\t@{[$m{$_} =~ /^\n*(.*?)\n*\z/s]}\n" for sort keys %m;
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</pre>
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The p-value of variance explained by "bake" is ~0.015 - significant
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Let's plot the means of the interaction of all IVs
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<pre>
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$m{'| apple ~ bake | m'}->plot_means($m{'| apple ~ bake | se'},
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{ IVNM=>[qw(apple bake)], plot=>1, win=>$w });
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</pre>
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<h4>Output</h4>
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<pre>
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F 2.46666666666667
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F_df [5 6]
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F_p 0.151168719948632
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ms_model 3.08333333333333
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ms_residual 1.25
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ss_model 15.4166666666667
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ss_residual 7.5
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ss_total 22.9166666666667
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| apple | F 0.466666666666667
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| apple | F_p 0.648078345471096
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| apple | df 2
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| apple | m [2.75 3 3.5]
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| apple | ms 0.583333333333334
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| apple | se [0.853912563829966 0.816496580927726 0.645497224367903]
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| apple | ss 1.16666666666667
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| apple || err df 6
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| apple ~ bake | F 0.0666666666666671
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| apple ~ bake | F_p 0.936190104380701
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| apple ~ bake | df 2
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| apple ~ bake | m [
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[1.5 2 2.5]
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[ 4 4 4.5]
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]
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| apple ~ bake | ms 0.0833333333333339
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| apple ~ bake | se [
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[0.5 1 0.5]
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[ 1 1 0.5]
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]
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| apple ~ bake | ss 0.166666666666668
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| apple ~ bake || err df 6
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| bake | F 11.2666666666667
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| bake | F_p 0.015294126084452
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| bake | df 1
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| bake | m [2 4.16666666666667]
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| bake | ms 14.0833333333333
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| bake | se [0.365148371670111 0.401386485959742]
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| bake | ss 14.0833333333333
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| bake || err df 6
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</pre>
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<img src="images/demos/stats/output-9.png"/>
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<hr/>
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This concludes the demo.
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<p/>
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Be sure to check the documentation for <a href="https://metacpan.org/pod/PDL::Stats">PDL::Stats</a>, to see further
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possibilities.
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</body>
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</html>

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