README

Gonum integrate GoDoc

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.

    Index

    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.

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

        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.
          Package testquad provides integrals for testing quadrature algorithms.
          Package testquad provides integrals for testing quadrature algorithms.