| // 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 |
| } |