matrix code simplification and generalization

Question

Good day, Please i need assistance trying to generalize this code for any matrix the data PoliticalDemocracy is available in the lavaan library

What I tried

library(lavaan)
R<-chol(cor(PoliticalDemocracy[1:8]))
diag(R)<-NA
R<-round(R,3)
R
R[R==0]<-NA
R

d<-matrix(NA,nrow(R),ncol(R))
d[,1]<-acos(R[1,])
d


d[,2]<-acos(R[2,]/sin(d[,1]))
d[,3]<-acos(R[3,]/sin(d[,1])*sin(d[,2]))
d[,4]<-acos(R[4,]/sin(d[,1])*sin(d[,2])*sin(d[,3]))
d[,5]<-acos(R[5,]/sin(d[,1])*sin(d[,2])*sin(d[,3])*sin(d[,4]))
d[,6]<-acos(R[6,]/sin(d[,1])*sin(d[,2])*sin(d[,3])*sin(d[,4])*sin(d[,5]))
d[,7]<-acos(R[7,]/sin(d[,1])*sin(d[,2])*sin(d[,3])*sin(d[,4])*sin(d[,5])*sin(d[,6]))
d[,8]<-acos(R[8,]/sin(d[,1])*sin(d[,2])*sin(d[,3])*sin(d[,4])*sin(d[,5])*sin(d[,6])*sin(d[,7]))

I tried using the loop but was having errors and an empty matrix d

d<-matrix(NA,nrow(R),ncol(R))
d[,1]<-acos(R[1,])
d


for (i in 2:nrow(d)){
  d[,i]<-acos(R[i,])/prod(sin(d[,i-1]))
  d
}
d

@AllanCameron

Answer 1

You could use Reduce function as shown below

(Reduce(function(x, y) 
  cbind(x, acos(y/matrixStats::rowProds(sin(x)))),
  data.frame(t(R)), init = matrix(rep(pi/2), nrow(R)))[,-1])