gonum: gonum.org/v1/gonum/integrate

package integrate

import "gonum.org/v1/gonum/integrate"

Package integrate provides functions to compute an integral given a specific list of evaluations.

func Romberg¶Uses

func Romberg(f []float64, dx float64) float64

Romberg returns an approximate value of the integral

\int_a^b f(x)dx


computed using the Romberg's method. The function f is given as a slice of equally-spaced samples, that is,

f[i] = f(a + i*dx)


and dx is the spacing between the samples.

The length of f must be 2^k + 1, where k is a positive integer, and dx must be positive.

See https://en.wikipedia.org/wiki/Romberg%27s_method for a description of the algorithm.

func Simpsons¶Uses

func Simpsons(x, f []float64) float64

Simpsons returns an approximate value of the integral

\int_a^b f(x)dx


computed using the Simpsons's method. 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 3.

func Trapezoidal¶Uses

func Trapezoidal(x, f []float64) float64

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

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