R help

Dear all,
  I need to generate numbers from multivariate normal with large dimensions
(5,000,000).
Below is my code and the error I got from R. Sigma in the code is the
covariance
matrix. Can anyone give some idea on how to take care of this error. Thank
you.
                Hannah

m <- 5000000
m1 <- 0.5*m
rho <- 0.5
Sigma <- rho* matrix(1, m, m)+diag(1-rho, m)

Error in matrix(1, m, m) : too many elements specified

Hi.

The matrix of dimension m times m does not fit into memory,
since it requires 8*m^2 = 2e+14 bytes = 2e+05 GB.

Generating a multivariate normal with a covariance matrix
with 1 on the diagonal and rho outside of the diagonal may
be done also as follows.

  m <- 10 # can be 5000000
  rho <- 0.5
  # single vector
  x <- rnorm(1, sd=sqrt(rho)) + rnorm(m, sd=sqrt(1 - rho))

  # several vectors
  a <- t(replicate(10000, rnorm(1, sd=sqrt(rho)) + rnorm(m, sd=sqrt(1 - rho))))

  # check the sample covariance matrix if m is not too large
  sigma <- cov(a)
  range(diag(sigma)) # elements on the diagonal

  [1] 0.9963445 1.0196015

  diag(sigma) <- NA 
  range(sigma, na.rm=TRUE) # elements outside of the diagonal

  [1] 0.4935129 0.5162836

Generating several vectors using replicate() may not be efficient.
The following can be used instead.

  n <- 10000
  a <- matrix(rnorm(n*m, sd=sqrt(1 - rho)), nrow=n, ncol=m) + rnorm(n, sd=sqrt(rho))

Note that the size of "a" is n times m and it should fit into the memory.

Hope this helps.

Petr Savicky.