unfoldr (version 0.7.1)

em.spheroids: Trivariate stereological unfolding

Description

Estimate the joint size-shape-orientation distribution of spheroids

Usage

em.spheroids(P, F, maxIt, nCores = getOption("par.unfoldr", 2L))

Arguments

P

coefficient array

F

input histogram

maxIt

maximum number of EM iterations

nCores

number of cpu cores to be used

Value

trivariate histogram

Details

Given an array of coefficients P, see coefficientMatrixSpheroids and an input histogram F of measured planar characteristics of section profiles, the function estimates the spatial joint size-shape-orientation distribution of the corresponding spheroids in 3D by a discretized version of the Expectation Maximization (EM) algorithm. A number of cpu cores can be set by the option 'par.unfoldr' for parallel computations. The function is also internally called by unfold in case of spheroids.

References

Bene$\check{\text{s}}$, V. and Rataj, J. Stochastic Geometry: Selected Topics Kluwer Academic Publishers, Boston, 2004

Examples

# NOT RUN {
## Comment: Trivariate unfolding of spheroid distribution

## set number of cpu cores (optional)
options(par.unfoldr=2L)

## Intensity: mean number of spheroids per unit volume
lam <- 1000

## simulation parameters
theta <- list("size"=list("meanlog"=-2.5,"sdlog"=0.5),
		      "shape"=list(0.5),"orientation"=list("kappa"=2))
## simualtion
set.seed(1234)

S <- simPoissonSystem(theta,lam,size="rlnorm",
		orientation="rbetaiso",box=list(c(0,5)),type="prolate",pl=1)

## unfolding
sp <- verticalSection(S,2.5)
ret <- unfold(sp,c(7,6,5),kap=1.25)
cat("Intensities: ", sum(ret$N_V)/25, "vs.",lam,"\n")
# }