# The Vectorized Multivariate Random Deviates This function is the vectorized version of the rmvnorm from the mvtnorm library. It provides a random number generator for the multivariate normal distribution with varying vectors of means and varying covariance matrixes. ```r rmultinormal(n, mean, sigma, method=c("eigen", "svd", "chol")) dmultinormal(x, mean, sigma, log=FALSE) ``` ## Examples ```r ## including equivalence with dmvnorm ## mean and sigma as vectors (mean <- c(10, 0)) (sigma <- matrix(c(1, 2, 2, 10), ncol=2)) sigma <- as.vector(sigma) (x <- matrix(c(9, 8, 1, -1), ncol=2)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x, mean, matrix(sigma, ncol=2)) ## mean as matrix (mean <- matrix(c(10, 0, 0, 10), ncol=2)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x[1, ], mean[1, ], matrix(sigma, ncol=2)) dmvnorm(x[2, ], mean[2, ], matrix(sigma, ncol=2)) ## sigma as matrix (mean <- c(10, 0)) (sigma <- matrix(c(1, 2, 2, 10, 10, 2, 2, 1), nrow=2, byrow=TRUE)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x[1, ], mean, matrix(sigma[1, ], ncol=2)) dmvnorm(x[2, ], mean, matrix(sigma[2, ], ncol=2)) ## mean and sigma as matrix (mean <- matrix(c(10, 0, 0, 10), ncol=2)) (sigma <- matrix(c(1, 2, 2, 10, 10, 2, 2, 1), nrow=2, byrow=TRUE)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x[1, ], mean[1, ], matrix(sigma[1, ], ncol=2)) dmvnorm(x[2, ], mean[2, ], matrix(sigma[2, ], ncol=2)) (mean <- c(10, 0)) (sigma <- matrix(c(1, 2, 2, 10, 10, 2, 2, 1), nrow=2, byrow=TRUE)) x <- rmultinormal(1000, mean, sigma) plot(x) ``` ## Arguments - `x`: Vector or matrix of quantiles. If x is a matrix, each row is taken to be a quantile. - `n`: Number of observations. If length(n) \> 1 , the length is taken to be the number required. - `mean`: Vector or matrix of means. If a matrix, each row is taken to be a quantile. Default is a vector of 0 of convenient length. - `sigma`: Covariance vector corresponding to the coercion of the covariance matrix into a vector (if unique for all n or x ) or array of covariance vectors (if varying according to n or x ). default is a diagonal matrix of convenient size. - `method`: Matrix decomposition used to determine the matrix root of sigma, possible methods are eigenvalue decomposition ("eigen", default), singular value decomposition ("svd"), and Cholesky decomposition ("chol"). - `log`: Logical; if TRUE , densities d are given as log(d). ## Details rmvnorm(n, m, s) is equivalent to rmultinormal(n, m, as.vector(s)) . dmvnorm(x, m, s) is equivalent to dmultinormal(x, m, as.vector(s)) . If mean and/or sigma is a matrix, the first random deviate will use the first row of mean and/or sigma , the second random deviate will use the second row of mean and/or sigma , ... recycling being permitted by raw. If mean is a vector of length l or is a matrix with l columns, sigma should be a vector of length l x l or a matrix of number of l x 2 columns. ## Note The use of a varying sigma may be very time consuming.

multinormal function