On Sat, Feb 18, 2012 at 06:00:53PM -0500, li li wrote: > 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. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.