Andrei Makarov amkisko
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simplay
/ Ruby_Lambda_Fun_Numerical _Integration_Trapezoid.rb
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April 22, 2022 15:23
# Numerical Integraion over real domain of real 1d valued functions using Newton-Cotes approximation.
# NB1: Error of approximation in O(f'' * (b-a)^3 )
# NB2: In practice quite usable for many common functions, like affine, trigonomatric function
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| # D subset |R Domain over which we integrate - sample D = [1,10] | |
| D = (1..10).to_a | |
| # f:|R->|R function - sample x |-> f(x) := x^2 | |
| f = lambda {|x| x*x} | |
| # summation of function values over our domain | |
| summator = lambda {|function, domain| domain.inject(0){|x,y| x += function.call(y)} } | |
| # Integrations Driver (for real valued 1d functions only) - assumption: integration steps equidistant |
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| require 'bigdecimal' | |
| def integrate (a, b, n) | |
| a = a.to_f; b = b.to_f; n = n.to_i | |
| result = 0.0 | |
| dx = (b - a) / n | |
| dx_half = dx / 2 | |
| for i in 0 ... n | |
| result += yield a + (i * dx) |
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