55 lines
1.4 KiB
Plaintext
55 lines
1.4 KiB
Plaintext
func sum(f, start, from, to) {
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var s = 0;
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RangeNum(start, to, from-start).each { |i|
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s += f(i);
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}
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return s
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}
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func leftrect(f, a, b, n) {
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var h = ((b - a) / n);
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h * sum(f, a, a+h, b-h);
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}
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func rightrect(f, a, b, n) {
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var h = ((b - a) / n);
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h * sum(f, a+h, a + 2*h, b);
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}
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func midrect(f, a, b, n) {
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var h = ((b - a) / n);
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h * sum(f, a + h/2, a + h + h/2, b - h/2)
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}
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func trapez(f, a, b, n) {
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var h = ((b - a) / n);
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h/2 * (f(a) + f(b) + sum({ f(_)*2 }, a+h, a + 2*h, b-h));
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}
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func simpsons(f, a, b, n) {
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var h = ((b - a) / n);
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var h2 = h/2;
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var sum1 = f(a + h2);
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var sum2 = 0;
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sum({|i| sum1 += f(i + h2); sum2 += f(i); 0 }, a+h, a+h+h, b-h);
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h/6 * (f(a) + f(b) + 4*sum1 + 2*sum2);
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}
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func tryem(label, f, a, b, n, exact) {
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say "\n#{label}\n in [#{a}..#{b}] / #{n}";
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say(' exact result: ', exact);
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say(' rectangle method left: ', leftrect(f, a, b, n));
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say(' rectangle method right: ', rightrect(f, a, b, n));
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say(' rectangle method mid: ', midrect(f, a, b, n));
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say('composite trapezoidal rule: ', trapez(f, a, b, n));
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say(' quadratic simpsons rule: ', simpsons(f, a, b, n));
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}
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tryem('x^3', { _ ** 3 }, 0, 1, 100, 0.25);
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tryem('1/x', { 1 / _ }, 1, 100, 1000, log(100));
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tryem('x', { _ }, 0, 5_000, 5_000_000, 12_500_000);
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tryem('x', { _ }, 0, 6_000, 6_000_000, 18_000_000);
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