| // 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 |
| } |