# integrate

package
Version: v0.9.3 Latest Latest

Go to latest
Published: Jun 30, 2021 License: BSD-3-Clause

### Gonum integrate

Package integrate provides numerical evaluation of definite integrals of single-variable functions for the Go programming language.

## Documentation ¶

### Overview ¶

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

### Constants ¶

This section is empty.

### Variables ¶

This section is empty.

### Functions ¶

#### func Romberg ¶

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 ¶

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 ¶

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

### Types ¶

This section is empty.

## Directories ¶

Path Synopsis
Package quad provides numerical evaluation of definite integrals of single-variable functions.
Package quad provides numerical evaluation of definite integrals of single-variable functions.