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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Numerical-integration/Raku/numerical-integration.raku Normal file
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use MONKEY-SEE-NO-EVAL;
sub leftrect(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
my $end = $b-$h;
my $sum = 0;
loop (my $i = $a; $i <= $end; $i += $h) { $sum += f($i) }
$h * $sum;
}
sub rightrect(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
my $sum = 0;
loop (my $i = $a+$h; $i <= $b; $i += $h) { $sum += f($i) }
$h * $sum;
}
sub midrect(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
my $sum = 0;
my ($start, $end) = $a+$h/2, $b-$h/2;
loop (my $i = $start; $i <= $end; $i += $h) { $sum += f($i) }
$h * $sum;
}
sub trapez(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
my $partial-sum = 0;
my ($start, $end) = $a+$h, $b-$h;
loop (my $i = $start; $i <= $end; $i += $h) { $partial-sum += f($i) * 2 }
$h / 2 * ( f($a) + f($b) + $partial-sum );
}
sub simpsons(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
my $h2 = $h/2;
my ($start, $end) = $a+$h, $b-$h;
my $sum1 = f($a + $h2);
my $sum2 = 0;
loop (my $i = $start; $i <= $end; $i += $h) {
$sum1 += f($i + $h2);
$sum2 += f($i);
}
($h / 6) * (f($a) + f($b) + 4*$sum1 + 2*$sum2);
}
sub integrate($f, $a, $b, $n, $exact) {
my $e = 0.000001;
my $r0 = "$f\n in [$a..$b] / $n\n"
~ ' exact result: '~ $exact.round($e);
my ($r1,$r2,$r3,$r4,$r5);
my &f;
EVAL "&f = $f";
my $p1 = Promise.start( { $r1 = ' rectangle method left: '~ leftrect(&f, $a, $b, $n).round($e) } );
my $p2 = Promise.start( { $r2 = ' rectangle method right: '~ rightrect(&f, $a, $b, $n).round($e) } );
my $p3 = Promise.start( { $r3 = ' rectangle method mid: '~ midrect(&f, $a, $b, $n).round($e) } );
my $p4 = Promise.start( { $r4 = 'composite trapezoidal rule: '~ trapez(&f, $a, $b, $n).round($e) } );
my $p5 = Promise.start( { $r5 = ' quadratic simpsons rule: '~ simpsons(&f, $a, $b, $n).round($e) } );
await $p1, $p2, $p3, $p4, $p5;
$r0, $r1, $r2, $r3, $r4, $r5;
}
.say for integrate '{ $_ ** 3 }', 0, 1, 100, 0.25; say '';
.say for integrate '1 / *', 1, 100, 1000, log(100); say '';
.say for integrate '*.self', 0, 5_000, 5_000_000, 12_500_000; say '';
.say for integrate '*.self', 0, 6_000, 6_000_000, 18_000_000;