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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 estimates the integral of a function f // \int_a^b f(x) dx // from a set of evaluations of the function using the trapezoidal rule. // The trapezoidal rule makes piecewise linear approximations to the function, // and estimates // \int_x[i]^x[i+1] f(x) dx // as // (x[i+1] - x[i]) * (f[i] + f[i+1])/2 // where f[i] is the value of the function at x[i]. // More details on the trapezoidal rule can be found at: // https://en.wikipedia.org/wiki/Trapezoidal_rule // // The (x,f) input data points must be sorted along x. // One can use github.com/gonum/stat.SortWeighted to do that. // The x and f slices must be of equal length and have length > 1. func Trapezoidal(x, f []float64) float64 { switch { case len(x) != len(f): panic("integrate: slice length mismatch") case len(x) < 2: panic("integrate: input data too small") case !sort.Float64sAreSorted(x): panic("integrate: input must be sorted") } integral := 0.0 for i := 0; i < len(x)-1; i++ { integral += 0.5 * (x[i+1] - x[i]) * (f[i+1] + f[i]) } return integral }