Numerical integration: Difference between revisions
Added Perl example
SqrtNegInf (talk | contribs) m (→{{header|Perl 6}}: moved commentary to top, fixed language version tag) |
SqrtNegInf (talk | contribs) (Added Perl example) |
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integrate := integral
end;</lang>
=={{header|Perl}}==
{{trans|Perl 6}}
<lang perl>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('$_', 0, 6_000, 6_000_000, 18_000_000);</lang>
{{out}}
<pre>$_ ** 3
in [0..1] / 100
exact result: 0.25
rectangle method left: 0.245025
rectangle method right: 0.255025
rectangle method mid: 0.249988
composite trapezoidal rule: 0.250025
quadratic simpsons rule: 0.25
1 / $_
in [1..100] / 1000
exact result: 4.60517
rectangle method left: 4.654991
rectangle method right: 4.556981
rectangle method mid: 4.604763
composite trapezoidal rule: 4.605986
quadratic simpsons rule: 4.60517
$_
in [0..5000] / 5000000
exact result: 12500000
rectangle method left: 12499997.5
rectangle method right: 12500002.5
rectangle method mid: 12500000
composite trapezoidal rule: 12500000
quadratic simpsons rule: 12500000
$_
in [0..6000] / 6000000
exact result: 18000000
rectangle method left: 17999997
rectangle method right: 18000003
rectangle method mid: 18000000
composite trapezoidal rule: 18000000
quadratic simpsons rule: 18000000</pre>
=={{header|Perl 6}}==
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