spagmix (version 0.3-5)

sgmix: Bivariate Gaussian mixture density generation

Description

Generates a pixel image of a specified bivariate normal mixture density observed on a bounded window.

Usage

sgmix(mean, vcv, window, p0 = 0, p = NULL, resolution = 128, int = 1)

Arguments

mean

A \(2 \times N\) matrix specifying the means of each of \(N\) contributing normal densities.

vcv

Either a \(2 \times 2 \times N\) array specifying the variance-covariance matrices of each contributing density, or a numeric vector of length \(N\) giving the isotropic standard deviations of each contributing density. An error is thrown if the function encounters anything but a symmetric, positive-definite covariation specification for each component.

window

An object of class owin giving the observational window on which the mixture density is defined.

p0

The proportion of uniform density that contributes to the mixture (default is 0).

p

A numeric vector of the \(N\) proportions for each contributing density (default is equal proportions for each density, after subtracting p0). Together, p0 and p must sum to exactly 1.

resolution

The number of pixels along each side of the grid for the pixel image (default is 128).

int

A positive numeric value for post-hoc rescaling of the density (useful if the user wishes to return an intensity function). Defaults to 1 for no change in scaling.

Value

An object of class im giving the mixture density.

Details

This function generates a pixel image of a 2D density function made of a mixture of \(N\) bivariate normals; each component is restricted to conserve probability mass over a bounded subset of the plane. A warning will appear if less than 1% of the integral of each Gaussian bump is inside the observational window.

Examples

# NOT RUN {
# Example using isotropic standard deviations
m1 <- c(0.4,0.5)
m2 <- c(0.2,0.7)
s1 <- 0.1
s2 <- 0.025
dens1 <- sgmix(mean=cbind(m1,m2),vcv=c(s1,s2),window=toywin,p0=0.3,p=c(0.5,0.2))

plot(dens1,log=TRUE)
pts1 <- rpoint(200,dens1) # generate random points via spatstat.core::rpoint
points(pts1)


# Example using full covariance matrices
mn <- cbind(c(0.25,0.8),c(0.31,0.82),c(0.43,0.64),c(0.63,0.62),c(0.21,0.26))
v1 <- matrix(c(0.0023,-0.0009,-0.0009,0.002),2)
v2 <- matrix(c(0.0016,0.0015,0.0015,0.004),2)
v3 <- matrix(c(0.0007,0.0004,0.0004,0.0011),2)
v4 <- matrix(c(0.0023,-0.0041,-0.0041,0.0099),2)
v5 <- matrix(c(0.0013,0.0011,0.0011,0.0014),2)
vr <- array(NA,dim=c(2,2,5))
for(i in 1:5) vr[,,i] <- get(paste("v",i,sep=""))
dens2 <- sgmix(mean=mn,vcv=vr,window=toywin,p0=0.1)

plot(dens2,log=TRUE)
pts2 <- rpoint(200,dens2)
points(pts2)
# }