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 // Copyright ©2016 The Gonum Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package integrate import "sort" // Trapezoidal returns an approximate value of the integral // \int_a^b f(x) dx // computed using the trapezoidal rule. The function f is given as a slice of // samples evaluated at locations in x, that is, // f[i] = f(x[i]), x[0] = a, x[len(x)-1] = b // The slice x must be sorted in strictly increasing order. x and f must be of // equal length and the length must be at least 2. // // The trapezoidal rule approximates f by a piecewise linear function and // estimates // \int_x[i]^x[i+1] f(x) dx // as // (x[i+1] - x[i]) * (f[i] + f[i+1])/2 // More details on the trapezoidal rule can be found at: // https://en.wikipedia.org/wiki/Trapezoidal_rule func Trapezoidal(x, f []float64) float64 { n := len(x) switch { case len(f) != n: panic("integrate: slice length mismatch") case n < 2: panic("integrate: input data too small") case !sort.Float64sAreSorted(x): panic("integrate: input must be sorted") } integral := 0.0 for i := 0; i < n-1; i++ { integral += 0.5 * (x[i+1] - x[i]) * (f[i+1] + f[i]) } return integral }