integrals: Numerical integration using adaptive quadrature

In bschneidr/schneidr: Utilities for data visualization, data wrangling, and mathematical statistics.

Description

Numerical integration using adaptive quadrature

Usage

double_integrate(fn, x1_lims, x2_lims)

triple_integrate(fn, x1_lims, x2_lims, x3_lims)

Arguments

fn	A function that takes two or three numeric arguments (for double_integrate or triple_integrate, respectively) and which returns a single number
x1_lims	A length-two numeric vector giving the lower and upper bound of integration (e.g. c(0, 100))
x2_lims	A length-two numeric vector giving the lower and upper bound of integration (e.g. c(0, 2*pi))
x3_lims	A length-two numeric vector giving the lower and upper bound of integration (e.g. c(-Inf, Inf))

Value

A single number, representing the numeric integral calculated using adaptive quadrature.

Examples

# Area of a cylinder!
# Radius 2, height 5

  perimeter_of_circle <- function(r) {
     2*pi*r
  }

  double_integrate(function(r, height) perimeter_of_circle(r),
                   x1_lims = c(0, 2),
                   x2_lims = c(0, 5))

# Joint density of three standard normal variables
  d_x1x2x3 <- function(x1, x2, x3) {
     dnorm(x1)*dnorm(x2)*dnorm(x3)
  }

  triple_integrate(d_x1x2x3, c(-Inf, Inf), c(-Inf, Inf), c(-Inf, Inf))

# Probability that sum of three squared standard normal variables
  is less than 9

   supported_density <- function(k, x1, x2, x3) {
      sum_squares <- sum(c(x1, x2, x3)^2)
      if (sum_squares <= k) {
         dnorm(x1)*dnorm(x2)*dnorm(x3)
      } else {
         0
      }
   }

   triple_integrate(fn = function(x1, x2, x3) {
                            supported_density(k = 9, x1, x2, x3)
                    },
                    x1_lims = c(-Inf, Inf),
                    x2_lims = c(-Inf, Inf),
                    x3_lims = c(-Inf, Inf))

  # Compare to the analytic result (Chi-squared distribution)

    pchisq(9, df = 3)

bschneidr/schneidr documentation built on Dec. 25, 2021, 4:55 p.m.