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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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Task/Numerical-integration/Standard-ML/numerical-integration.ml Normal file
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fun integrate (f, a, b, steps, meth) = let
val h = (b - a) / real steps
fun helper (i, s) =
if i >= steps then s
else helper (i+1, s + meth (f, a + h * real i, h))
in
h * helper (0, 0.0)
end
fun leftRect (f, x, _) = f x
fun midRect (f, x, h) = f (x + h / 2.0)
fun rightRect (f, x, h) = f (x + h)
fun trapezium (f, x, h) = (f x + f (x + h)) / 2.0
fun simpson (f, x, h) = (f x + 4.0 * f (x + h / 2.0) + f (x + h)) / 6.0
fun square x = x * x
val rl = integrate (square, 0.0, 1.0, 10, left_rect )
val rm = integrate (square, 0.0, 1.0, 10, mid_rect )
val rr = integrate (square, 0.0, 1.0, 10, right_rect)
val t = integrate (square, 0.0, 1.0, 10, trapezium )
val s = integrate (square, 0.0, 1.0, 10, simpson )