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Ingy döt Net 2013-04-10 23:57:08 -07:00
parent 47bf37c096
commit b83f433714
12433 changed files with 156208 additions and 123 deletions
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51
Task/Numerical-integration/Perl-6/numerical-integration-1.pl6 Normal file
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sub leftrect(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
$h * [+] do f($_) for $a, *+$h ... $b-$h;
}
sub rightrect(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
$h * [+] do f($_) for $a+$h, *+$h ... $b;
}
sub midrect(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
$h * [+] do f($_) for $a+$h/2, *+$h ... $b-$h/2;
}
sub trapez(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
$h / 2 * [+] f($a), f($b), do f($_) * 2 for $a+$h, *+$h ... $b-$h;
}
sub simpsons(&f, $a, $b, $n) {
my $h = ($b - $a) / $n;
my $h2 = $h/2;
my $sum1 = f($a + $h2);
my $sum2 = 0;
for $a+$h, *+$h ... $b-$h {
$sum1 += f($_ + $h2);
$sum2 += f($_);
}
($h / 6) * (f($a) + f($b) + 4*$sum1 + 2*$sum2);
}
sub tryem($f, $a, $b, $n, $exact) {
say "\n$f\n in [$a..$b] / $n";
eval "my &f = $f;
say ' exact result: ', $exact;
say ' rectangle method left: ', leftrect &f, $a, $b, $n;
say ' rectangle method right: ', rightrect &f, $a, $b, $n;
say ' rectangle method mid: ', midrect &f, $a, $b, $n;
say 'composite trapezoidal rule: ', trapez &f, $a, $b, $n;
say ' quadratic simpsons rule: ', simpsons &f, $a, $b, $n;"
}
tryem '{ $_ ** 3 }', 0, 1, 100, 0.25;
tryem '1 / *', 1, 100, 1000, log(100);
tryem '{$_}', 0, 5_000, 10_000, 12_500_000;
tryem '{$_}', 0, 6_000, 12_000, 18_000_000;

35
Task/Numerical-integration/Perl-6/numerical-integration-2.pl6 Normal file
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{ $_ ** 3 }
in [0..1] / 100
exact result: 0.25
rectangle method left: 0.245025
rectangle method right: 0.255025
rectangle method mid: 0.2499875
composite trapezoidal rule: 0.250025
quadratic simpsons rule: 0.25
1 / *
in [1..100] / 1000
exact result: 4.60517018598809
rectangle method left: 4.65499105751468
rectangle method right: 4.55698105751468
rectangle method mid: 4.60476254867838
composite trapezoidal rule: 4.60598605751468
quadratic simpsons rule: 4.60517038495714
{$_}
in [0..5000] / 10000
exact result: 12500000
rectangle method left: 12498750
rectangle method right: 12501250
rectangle method mid: 12500000
composite trapezoidal rule: 12500000
quadratic simpsons rule: 12500000
{$_}
in [0..6000] / 12000
exact result: 18000000
rectangle method left: 17998500
rectangle method right: 18001500
rectangle method mid: 18000000
composite trapezoidal rule: 18000000
quadratic simpsons rule: 18000000