Numerical integration: Difference between revisions

=={{header|Elixir}}==

<lang elixir>defmodule Numerical do

@funs ~w(leftrect midrect rightrect trapezium simpson)a

def leftrect(f, left,_right), do: f.(left)

def midrect(f, left, right), do: f.((left+right)/2)

def rightrect(f,_left, right), do: f.(right)

def trapezium(f, left, right), do: (f.(left)+f.(right))/2

def simpson(f, left, right), do: (f.(left) + 4*f.((left+right)/2.0) + f.(right)) / 6.0

def integrate(f, a, b, steps) when is_integer(steps) do

delta = (b - a) / steps

Enum.each(@funs, fn fun ->

total = Enum.reduce(0..steps-1, 0, fn i, acc ->

left = a + delta * i

acc + apply(Numerical, fun, [f, left, left+delta])

end)

:io.format "~10s : ~.6f~n", [fun, total * delta]

end)

end

end

f1 = fn x -> x * x * x end

IO.puts "f(x) = x^3, where x is [0,1], with 100 approximations."

Numerical.integrate(f1, 0, 1, 100)

f2 = fn x -> 1 / x end

IO.puts "\nf(x) = 1/x, where x is [1,100], with 1,000 approximations. "

Numerical.integrate(f2, 1, 100, 1000)

f3 = fn x -> x end

IO.puts "\nf(x) = x, where x is [0,5000], with 5,000,000 approximations."

Numerical.integrate(f3, 0, 5000, 5_000_000)

f4 = fn x -> x end

IO.puts "\nf(x) = x, where x is [0,6000], with 6,000,000 approximations."

Numerical.integrate(f4, 0, 6000, 6_000_000)</lang>

{{out}}

<pre>

f(x) = x^3, where x is [0,1], with 100 approximations.

leftrect : 0.245025

midrect : 0.249988

rightrect : 0.255025

trapezium : 0.250025

simpson : 0.250000

f(x) = 1/x, where x is [1,100], with 1,000 approximations.

leftrect : 4.654991

midrect : 4.604763

rightrect : 4.556981

trapezium : 4.605986

simpson : 4.605170

f(x) = x, where x is [0,5000], with 5,000,000 approximations.

leftrect : 12499997.500000

midrect : 12500000.000000

rightrect : 12500002.500000

trapezium : 12500000.000000

simpson : 12500000.000000

f(x) = x, where x is [0,6000], with 6,000,000 approximations.

leftrect : 17999997.000000

midrect : 18000000.000000

rightrect : 18000003.000000

trapezium : 18000000.000000

simpson : 18000000.000000

</pre>