## package integrate

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

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

### Index ¶

- func Romberg(f []float64, dx float64) float64
- func Simpsons(x, f []float64) float64
- func Trapezoidal(x, f []float64) float64

### Functions ¶

#### func Romberg ¶

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 ¶

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.

See https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule_for_irregularly_spaced_data for more information.

#### func Trapezoidal ¶

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

### Source Files ¶

doc.go romberg.go simpsons.go trapezoidal.go

### Directories ¶

Path | Synopsis |
---|---|

integrate/quad | Package quad provides numerical evaluation of definite integrals of single-variable functions. |

integrate/testquad | Package testquad provides integrals for testing quadrature algorithms. |

- Version
- v0.14.0 (latest)
- Published
- Aug 19, 2023
- Platform
- linux/amd64
- Imports
- 3 packages
- Last checked
- 6 days ago –

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