Documentation ¶
Overview ¶
Package integrate provides functions to compute an integral given a specific list of evaluations.
Index ¶
Constants ¶
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Variables ¶
This section is empty.
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 equallyspaced 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
Types ¶
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Directories ¶
Path  Synopsis 

Package quad provides numerical evaluation of definite integrals of singlevariable functions.

Package quad provides numerical evaluation of definite integrals of singlevariable functions. 
Package testquad provides integrals for testing quadrature algorithms.

Package testquad provides integrals for testing quadrature algorithms. 