What is the fast way to turn this vector into symmetric matrix?

Question

everyone! Suppose I have a vector of length n(n+1)/2:

a = (a_11, a_12, a_22, ...., a_nn) 

Now I'd like to turn it into a symmetric matrix, mean

I could assign the value one by one, but I'm wondering if there is some faster to create this matrix? Thanks so much!!

Answer 1

You could write a function that does this:

IF you had your vector as a11,a12,a13..a1n,a22,a23..a2n, a33,..a3n,..ann They you could do:

vec2mat <- function(x){
  p <- sqrt(1 + 8 * length(x))/ 2 - 0.5
  m <- matrix(0, p, p)
  m[lower.tri(m, diag = TRUE)] <- x
  m[upper.tri(m)] <- (t(m))[upper.tri(m)]
  m
}

Now:

vec2mat(1:6)
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    4    5
[3,]    3    5    6
vec2mat(1:10)
     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    2    5    6    7
[3,]    3    6    8    9
[4,]    4    7    9   10

if you had a11, a12,a22,a31, a32, a33...

vec2mat <- function(x){
  p <- sqrt(1 + 8 * length(x))/ 2 - 0.5
  m <- matrix(0, p, p)
  m[upper.tri(m, diag = TRUE)] <- x
  m[lower.tri(m)] <- t(m)[lower.tri(m)]
  m
}
 vec2mat(1:10)
     [,1] [,2] [,3] [,4]
[1,]    1    2    4    7
[2,]    2    3    5    8
[3,]    4    5    6    9
[4,]    7    8    9   10