runif_ellipsoid: Uniform sampling on/in ellipsoid

In uniformly: Uniform Sampling

Uniform sampling on/in ellipsoid

Description

Uniform sampling on an ellipsoid or in an ellipsoid (arbitrary dimension).

Usage

runif_on_ellipsoid(n, A, r)

runif_in_ellipsoid(n, A, r)

Arguments

n	number of simulations
A	symmetric positive-definite matrix defining the ellipsoid (see Details)
r	"radius" (see Details)

Details

The ellipsoid is the set of vectors x satisfying t(x) %*% A %*% x == r^2.

Value

The simulations in a matrix with n rows.

Examples

A <- rbind(c(2, 1), c(1, 1))
r <- 2
sims <- runif_on_ellipsoid(30, A, r)
plot(sims, xlim = c(-2, 2), ylim = c(-3, 3), asp = 1, pch = 19)
sims <- runif_in_ellipsoid(100, A, r)
plot(sims, xlim = c(-2, 2), ylim = c(-3, 3), asp = 1, pch = 19)
# 3D example
A <- matrix(c(5,1,1, 1,3,1, 1,1,1), ncol = 3L)
r <- 2
# draw the ellipsoid
library(misc3d)
x <- seq(-1, 1, len = 50)
y <- seq(-1.5, 1.5, len = 50)
z <- seq(-2.7, 2.7, len = 50)
g <- as.matrix(expand.grid(x = x, y = y, z = z))
voxel <- 
  array(apply(g, 1L, function(v) t(v) %*% A %*% v), dim = c(50, 50, 50))
isosurface <- computeContour3d(voxel, max(voxel), r^2, x = x, y = y, z = z)
drawScene.rgl(makeTriangles(isosurface, alpha = 0.3))
# simulate and plot points on ellipsoid
library(rgl)
sims <- runif_on_ellipsoid(200, A, r)
points3d(sims)

uniformly documentation built on March 18, 2022, 6:44 p.m.