say I have the matrix d, which is the result of two different realizations (rows) of a sampling procedure in two dimensions (columns). I want to develop a function that creates the fully-antithetic draws from this original matrix.
c1 <- c(0.1, 0.6);c2 <- c(0.3, 0.8);d <- rbind(c1,c2)
# [,1] [,2]
# c1 0.1 0.6
# c2 0.3 0.8
That is to say, for example, for the first realization (c(0.1, 0.6)) I want to obtain the mirror images of this random draw in two dimensions, which generated 4 (2^2) possible combinations as follows:
d1_anthi = matrix(
c( d[1,1] , d[1,2],
1 - d[1,1], d[1,2],
d[1,1] , 1 - d[1,2],
1 - d[1,1], 1 - d[1,2]), nrow=2,ncol=4)
t(d1_anthi)
# [,1] [,2]
# [1,] 0.1 0.6
# [2,] 0.9 0.6
# [3,] 0.1 0.4
# [4,] 0.9 0.4
Analogously, for the second, realization the results is the following:
d2_anthi = matrix(
c( d[2,1] , d[2,2],
1 - d[2,1], d[2,2],
d[2,1] , 1 - d[2,2],
1 - d[2,1], 1 - d[2,2]), nrow=2, ncol=4)
t(d2_anthi)
# [,1] [,2]
# [1,] 0.3 0.8
# [2,] 0.7 0.8
# [3,] 0.3 0.2
# [4,] 0.7 0.2
Accordingly, my desired object will lock is like this:
anthi_draws <- rbind(t(d1_anthi),t(d2_anthi))
# [,1] [,2]
# [1,] 0.1 0.6 <- original first realization
# [2,] 0.9 0.6
# [3,] 0.1 0.4
# [4,] 0.9 0.4
# [5,] 0.3 0.8 <- original second realization
# [6,] 0.7 0.8
# [7,] 0.3 0.2
# [8,] 0.7 0.2
Finally, I would like to create a function that, given a matrix of random numbers, is able to create this expanded matrix of antithetic draws. For example, in the picture below I have a sampling in three dimensions, then the total number of draws per original draw is 2^3 = 8.
In particular, I am having problems with the creating of the full combinatory that depends on the dimensions of the original sampling (columns of the matrix). I was planning on using expand.grid() but I couldn't create the full combinations using it. Any hints or help in order to create such a function is welcome. Thank you in advance.