- 総標本数Nでr1xr2x...というような任意の形の分割表を列挙したいとする
- とりあえず興味があるのは2x2x...という限られたパターンとしよう
- 分割表のセル数MについてNをM分割して
の場合を考える、というのもありだが、2x2x...の場合には２分割を再帰的に実施してもよさそうだ
- nの２分割は(0,n),(1,n-1),...,(n,0)のn+1通り、と単純なことがありがたい
divide.2 <- function(v,depth=1){
tmp <- list()
for(i in 1:length(v)){
tmp[[i]] <- 0:v[i]
}
tmp2 <- expand.grid(tmp)
tmp3 <- NULL
for(i in 1:length(tmp2[1,])){
tmp3 <- cbind(tmp3,tmp2[,i],v[i]-tmp2[,i])
}
if(depth==1){
return(list(tmp3))
}else{
ret <- list()
for(i in 1:length(tmp3[,1])){
ret[[i]] <- divide.2(tmp3[i,],depth=depth-1)
}
return(ret)
}
}
divide.2(c(3),depth=4)
> divide.2(c(2),depth=3)
[[1]]
[[1]][[1]]
[[1]][[1]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 0 0 0 0 2
[2,] 0 0 0 0 0 0 1 1
[3,] 0 0 0 0 0 0 2 0
[[1]][[2]]
[[1]][[2]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 0 0 1 0 1
[2,] 0 0 0 0 1 0 0 1
[3,] 0 0 0 0 0 1 1 0
[4,] 0 0 0 0 1 0 1 0
[[1]][[3]]
[[1]][[3]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 0 0 2 0 0
[2,] 0 0 0 0 1 1 0 0
[3,] 0 0 0 0 2 0 0 0
[[2]]
[[2]][[1]]
[[2]][[1]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 1 0 0 0 1
[2,] 0 0 1 0 0 0 0 1
[3,] 0 0 0 1 0 0 1 0
[4,] 0 0 1 0 0 0 1 0
[[2]][[2]]
[[2]][[2]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 1 0 0 0 0 0 1
[2,] 1 0 0 0 0 0 0 1
[3,] 0 1 0 0 0 0 1 0
[4,] 1 0 0 0 0 0 1 0
[[2]][[3]]
[[2]][[3]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 1 0 1 0 0
[2,] 0 0 1 0 0 1 0 0
[3,] 0 0 0 1 1 0 0 0
[4,] 0 0 1 0 1 0 0 0
[[2]][[4]]
[[2]][[4]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 1 0 0 0 1 0 0
[2,] 1 0 0 0 0 1 0 0
[3,] 0 1 0 0 1 0 0 0
[4,] 1 0 0 0 1 0 0 0
[[3]]
[[3]][[1]]
[[3]][[1]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 0 0 2 0 0 0 0
[2,] 0 0 1 1 0 0 0 0
[3,] 0 0 2 0 0 0 0 0
[[3]][[2]]
[[3]][[2]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 1 0 1 0 0 0 0
[2,] 1 0 0 1 0 0 0 0
[3,] 0 1 1 0 0 0 0 0
[4,] 1 0 1 0 0 0 0 0
[[3]][[3]]
[[3]][[3]][[1]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0 2 0 0 0 0 0 0
[2,] 1 1 0 0 0 0 0 0
[3,] 2 0 0 0 0 0 0 0
