R: Convert upper triangular part of a matrix to symmetric matrix - r

Question

I have the upper triangular part of matrix in R (without diagonal) and want to generate a symmetric matrix from the upper triangular part (with 1 on the diagonal but that can be adjusted later). I usually do that like this:
res.upper <- rnorm(4950)
res <- matrix(0, 100, 100)
res[upper.tri(res)] <- res.upper
rm(res.upper)
diag(res) <- 1
res[lower.tri(res)] <- t(res)[lower.tri(res)]
This works fine but now I want to work with very large matrices. Thus, I would want to avoid having to store res.upper and res (filled with 0) at the same time. Is there any way I can directly convert res.upper to a symmetric matrix without having to initialize the matrix res first?

Answer 1

I think there are two issues here.
now I want to work with very large matrices
Then do not use R code to do this job. R will use much more memory than you expect. Try the following code:
res.upper <- rnorm(4950)
res <- matrix(0, 100, 100)
tracemem(res) ## trace memory copies of `res`
res[upper.tri(res)] <- res.upper
rm(res.upper)
diag(res) <- 1
res[lower.tri(res)] <- t(res)[lower.tri(res)]
This is what you will get:
> res.upper <- rnorm(4950) ## allocation of length 4950 vector
> res <- matrix(0, 100, 100) ## allocation of 100 * 100 matrix
> tracemem(res)
[1] "<0xc9e6c10>"
> res[upper.tri(res)] <- res.upper
tracemem[0xc9e6c10 -> 0xdb7bcf8]: ## allocation of 100 * 100 matrix
> rm(res.upper)
> diag(res) <- 1
tracemem[0xdb7bcf8 -> 0xdace438]: diag<- ## allocation of 100 * 100 matrix
> res[lower.tri(res)] <- t(res)[lower.tri(res)]
tracemem[0xdace438 -> 0xdb261d0]: ## allocation of 100 * 100 matrix
tracemem[0xdb261d0 -> 0xccc34d0]: ## allocation of 100 * 100 matrix
In R, you have to use 5 * (100 * 100) + 4950 double words to finish these operations. While in C, you only need at most 4950 + 100 * 100 double words (In fact, 100 * 100 is all that is needed! Will talk about it later). It is difficult to overwrite object directly in R without extra memory assignment.
Is there any way I can directly convert res.upper to a symmetric matrix without having to initialize the matrix res first?
You do have to allocate memory for res because that is what you end up with; but there is no need to allocate memory for res.upper. You can initialize the upper triangular, while filling in the lower triangular at the same time. Consider the following template:
#include <Rmath.h> // use: double rnorm(double a, double b)
#include <R.h> // use: getRNGstate() and putRNGstate() for randomness
#include <Rinternals.h> // SEXP data type
## N is matrix dimension, a length-1 integer vector in R
## this function returns the matrix you want
SEXP foo(SEXP N) {
int i, j, n = asInteger(N);
SEXP R_res = PROTECT(allocVector(REALSXP, n * n)); // allocate memory for `R_res`
double *res = REAL(R_res);
double tmp; // a local variable for register reuse
getRNGstate();
for (i = 0; i < n; i++) {
res[i * n + i] = 1.0; // diagonal is 1, as you want
for (j = i + 1; j < n; j++) {
tmp = rnorm(0, 1);
res[j * n + i] = tmp; // initialize upper triangular
res[i * n + j] = tmp; // fill lower triangular
}
}
putRNGstate();
UNPROTECT(1);
return R_res;
}
The code has not been optimized, as using integer multiplication j * n + i for addressing in the innermost loop will result in performance penalty. But I believe you can move multiplication outside the inner loop, and only leave addition inside.

Answer 2

To get a symmetric matrix from an upper or lower triangular matrix you can add the matrix to its transpose and subtract the diagonal elements. The equation is linked below.
diag(U) is a diagonal matrix with the diagonal elements of U.
ultosymmetric=function(m){
m = m + t(m) - diag(diag(m))
return (m)}
If you want the diagonal elements to be 1 you can do this.
ultosymmetric_diagonalone=function(m){
m = m + t(m) - 2*diag(diag(m)) + diag(1,nrow=dim(m)[1])
return (m)}