Data commit

Task/Numerical-integration/Perl/numerical-integration.pl

@@ -0,0 +1,81 @@
+use feature 'say';
+
+sub leftrect {
+    my($func, $a, $b, $n) = @_;
+    my $h = ($b - $a) / $n;
+    my $sum = 0;
+    for ($_ = $a; $_ < $b; $_ += $h) { $sum += $func->($_) }
+    $h * $sum
+}
+
+sub rightrect {
+    my($func, $a, $b, $n) = @_;
+    my $h = ($b - $a) / $n;
+    my $sum = 0;
+    for ($_ = $a+$h; $_ < $b+$h; $_ += $h) { $sum += $func->($_) }
+    $h * $sum
+}
+
+sub midrect {
+    my($func, $a, $b, $n) = @_;
+    my $h = ($b - $a) / $n;
+    my $sum = 0;
+    for ($_ = $a + $h/2; $_ < $b; $_ += $h) { $sum += $func->($_) }
+    $h * $sum
+}
+
+sub trapez {
+    my($func, $a, $b, $n) = @_;
+    my $h = ($b - $a) / $n;
+    my $sum = $func->($a) + $func->($b);
+    for ($_ = $a+$h; $_ < $b; $_ += $h) { $sum += 2 * $func->($_) }
+    $h/2 * $sum
+}
+sub simpsons {
+    my($func, $a, $b, $n) = @_;
+    my $h = ($b - $a) / $n;
+    my $h2 = $h/2;
+    my $sum1 = $func->($a + $h2);
+    my $sum2 = 0;
+
+    for ($_ = $a+$h; $_ < $b; $_ += $h) {
+        $sum1 += $func->($_ + $h2);
+        $sum2 += $func->($_);
+    }
+    $h/6 * ($func->($a) + $func->($b) + 4*$sum1 + 2*$sum2)
+}
+
+# round where needed, display in a reasonable format
+sub sig {
+    my($value) = @_;
+    my $rounded;
+    if ($value < 10) {
+        $rounded = sprintf '%.6f', $value;
+        $rounded =~ s/(\.\d*[1-9])0+$/$1/;
+        $rounded =~ s/\.0+$//;
+    } else {
+        $rounded = sprintf "%.1f", $value;
+        $rounded =~ s/\.0+$//;
+    }
+    return $rounded;
+}
+
+sub integrate {
+    my($func, $a, $b, $n, $exact) = @_;
+
+    my $f = sub { local $_ = shift; eval $func };
+
+    my @res;
+    push @res, "$func\n   in [$a..$b] / $n";
+    push @res, '              exact result: ' . rnd($exact);
+    push @res, '     rectangle method left: ' . rnd( leftrect($f, $a, $b, $n));
+    push @res, '    rectangle method right: ' . rnd(rightrect($f, $a, $b, $n));
+    push @res, '      rectangle method mid: ' . rnd(  midrect($f, $a, $b, $n));
+    push @res, 'composite trapezoidal rule: ' . rnd(   trapez($f, $a, $b, $n));
+    push @res, '   quadratic simpsons rule: ' . rnd( simpsons($f, $a, $b, $n));
+    @res;
+}
+say for integrate('$_ ** 3', 0, 1, 100, 0.25); say '';
+say for integrate('1 / $_', 1, 100, 1000, log(100)); say '';
+say for integrate('$_', 0, 5_000, 5_000_000, 12_500_000); say '';
+say for integrate('$_', 0, 6_000, 6_000_000, 18_000_000);