#compositional analysis
library(compositions)
x<-c(.1,.5,.4)
V<-t(ilrBase(x))
D<-rbind(c(1,0,-1),c(0,1,-1))
x_alr<-D%*%log(x)
x_ilr<-V%*%log(x)
x_alr
alr(x)
x_ilr
ilr(x,t(V))
#matrix to convert ilr to alr directly
A<-D%*%t(V)
#is A invertible?
det(A) #should be nonzero
x_alr2<-A%*%x_ilr