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Writing it down

PWC 165 refers us to mathsisfun for the algorithm to be used. Let’s write it down.

    my $input = '333,129  39,189 140,156 292,134 393,52  160,166 362,122  13,193
                341,104 320,113 109,177 203,152 343,100 225,110  23,186 282,102
                284,98  205,133 297,114 292,126 339,112 327,79  253,136  61,169
                128,176 346,72  316,103 124,162  65,181 159,137 212,116 337,86
                215,136 153,137 390,104 100,180  76,188  77,181  69,195  92,186
                275,96  250,147  34,174 213,134 186,129 189,154 361,82  363,89';

    my @points = $input.words».split(',')».Int;

    my \term:<x²> := @points[*;0]».&(*²);
    my \xy = @points[*;0] »*« @points[*;1];
    my \Σx = [+] @points[*;0];
    my \Σy = [+] @points[*;1];
    my \term:<Σx²> = [+] x²;
    my \Σxy = [+] xy;
    my \N = +@points;

    my $m = (N * Σxy - Σx * Σy) / (N * Σx² - (Σx)²);
    my $b = (Σy - $m * Σx) / N;

    say [$m, $b];

That was exceedingly simple. If the point cloud is large, this might also be exceedingly slow. There are no side effects and everything is nice and constant. Should be easy to get the CPU busy.

    sub delayed(&c) is rw {
        my $p = start { c };
        Proxy.new: STORE => method (|) {}, FETCH => method { await $p; $p.result }
    }

    my \term:<x²> = delayed { @points[*;0]».&(*²) };
    my \xy = delayed { @points[*;0] »*« @points[*;1] };
    my \Σx = delayed { [+] @points[*;0] };
    my \Σy = delayed { [+] @points[*;1] }
    my \term:<Σx²> = delayed { [+] x² };
    my \Σxy = delayed { [+] xy };
    my \N = +@points;

    my $m = (N * Σxy - Σx * Σy) / (N * Σx² - (Σx)²);
    my $b = (Σy - $m * Σx) / N;

    say [$m, $b];

Since I use sigil-less symbols, I get binding for free. This in turn makes using Proxy easy. The await $p part is called more then once per Proxy but not in a loop so there is no real need to optimise here. On my box the Proxyed version is almost twice as fast. A nice win for such a simple change.

I somehow feel this solution might please a mathematician — as Raku should.

Categories: Raku
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  1. May 23, 2022 at 16:15

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