On 24-Mar-07 19:26:21, Ted Harding wrote: > On 24-Mar-07 14:00:44, Ted Harding wrote: >> [...] > [...] > Well, I've written some rather crude code to implement the > above. Even allowing for possible "editorial" improvements, > the more I look at it the more I think there may be a better > way! (Of doing it directly, I mean, raher than a rejection > method). > > Still, it seems to work (and quite slickly) ... > > And now I've done what I should have donein the first place: the code for rdiric() in VGAM is "stand-alone" and can simply be copied, so:
## library(VGAM) gives the following code for function rdiric() rdiric<-function(n, shape, dimension = NULL) { dimension = if (!is.numeric(dimension)) length(shape) shape = rep(shape, len = dimension) ans = if (is.R()) rgamma(n * dimension, rep(shape, rep(n, dimension))) else rgamma(n * dimension, rep(shape, each = n)) dim(ans) = c(n, dimension) ans = ans/apply(ans, 1, sum) ans } ## Make some random points, get their CH and centroid, and draw them X<-cbind(rnorm(10),rnorm(10)) plot(X[,1],X[,2],pch="+",col="green") H<-chull(X) C<-colMeans(X[H,]) points(C[1],C[2],pch="+",col="red") ## Draw the CH and the triangulation H<-c(H,H[1]) ## To close the contour K<-length(H)-1 ## No of triangles lines(X[H,1],X[H,2],col="blue") for(i in (1:K)){lines(c(X[H[i],1],C[1]),c(X[H[i],2],C[2]),col="red")} ## Set up the sampling by triangles As<-numeric(K) Ns<-numeric(K) ## Get the areas of the triangles for(i in (1:(K))){ V1<-X[H[i],] V2<-X[H[i+1],] V3<-C As[i]<-abs(det(rbind(V1-V3,V2-V3))) } ## As illustration, 1000 points over the CH N<-1000 ## How many points to go in eavh triangle Cuts<-cumsum(As)/sum(As) R<-runif(N) Ns[1]<-sum(R<=Cuts[1]) for(i in (2:K)){Ns[i]<-sum(R<=Cuts[i])-sum(R<=Cuts[i-1])} ## Uniform distribution over each triangle for(i in (1:(K))){ V1<-X[H[i],] V2<-X[H[i+1],] V3<-C ## The Dirichlet sample: T<-rbind(X[H[i],],X[H[i+1],],C) D<-rdiric(Ns[i],c(1,1,1)) Z<-D%*%T points(Z[,1],Z[,2],pch="+",col="blue") } Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 25-Mar-07 Time: 11:26:58 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.