计算矩阵 R 列表的元素分位数

Question

I have a list of matrices that looks like this:

matrix.list <- list()
for(i in 1:1000){
  matrix.list[[i]] <- matrix(rnorm(9), ncol=3, nrow=3)
}

I can calculate element wise means and standard deviations in a straightforward way, following this stackoverflow question :

matrix.mean <- apply(simplify2array(matrix.list), 1:2, mean)
matrix.sd   <- apply(simplify2array(matrix.list), 1:2, sd  )

However, I would like to calculate the 0.025 and 0.975 quantiles. I would do this on a vector like this:

my.vec <- rnorm(1000)
q.0.025 <- quantile(my.vec, probs = 0.025)
q.0.975 <- quantile(my.vec, probs = 0.975)

But how can I calculate these element-wise quantiles across my list of matrices, similar to what I can do for mean and sd? As soon as I pass parameters to function apply it fails.

Answer 1

Q <- apply(simplify2array(matrix.list), 1:2, quantile, prob = c(0.025, 0.975))

apply would simplify the result to an array, and since the function quantile returns more than one values, you have a 3D array. But extraction is straightforward:

Q[1, , ]  ## 0.025 quantile
#          [,1]      [,2]      [,3]
#[1,] -2.046691 -1.925256 -2.075718
#[2,] -1.981182 -1.999648 -1.887588
#[3,] -1.931738 -1.743275 -1.854083

Q[2, , ]  ## 0.975 quantile
#         [,1]     [,2]     [,3]
#[1,] 1.953820 2.042508 1.836591
#[2,] 2.065854 2.006068 1.899495
#[3,] 1.885080 2.021729 1.943645