41 lines
1.4 KiB
Text
41 lines
1.4 KiB
Text
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F left_rect((Float -> Float) f, Float x, Float h) -> Float
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R f(x)
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F mid_rect((Float -> Float) f, Float x, Float h) -> Float
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R f(x + h / 2)
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F right_rect((Float -> Float) f, Float x, Float h) -> Float
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R f(x + h)
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F trapezium((Float -> Float) f, Float x, Float h) -> Float
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R (f(x) + f(x + h)) / 2.0
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F simpson((Float -> Float) f, Float x, Float h) -> Float
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R (f(x) + 4 * f(x + h / 2) + f(x + h)) / 6.0
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F cube(Float x) -> Float
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R x * x * x
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F reciprocal(Float x) -> Float
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R 1 / x
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F identity(Float x) -> Float
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R x
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F integrate(f, a, b, steps, meth)
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V h = (b - a) / steps
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V ival = h * sum((0 .< steps).map(i -> @meth(@f, @a + i * @h, @h)))
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R ival
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L(a, b, steps, func, func_name) [(0.0, 1.0, 100, cube, ‘cube’),
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(1.0, 100.0, 1000, reciprocal, ‘reciprocal’),
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(0.0, 5000.0, 5'000'000, identity, ‘identity’),
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(0.0, 6000.0, 6'000'000, identity, ‘identity’)]
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L(rule, rule_name) [(left_rect, ‘left_rect’),
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(mid_rect, ‘mid_rect’),
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(right_rect, ‘right_rect’),
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(trapezium, ‘trapezium’),
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(simpson, ‘simpson’)]
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print("#. integrated using #.\n from #. to #. (#. steps) = #.".format(
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func_name, rule_name, a, b, steps, integrate(func, a, b, steps, rule)))
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