# dSnorm: Density of a multivariate normal with Toeplitz variance... In SuperGauss: Superfast Likelihood Inference for Stationary Gaussian Time Series

## Description

Efficient density evaluation for the multivariate normal distribution with Toeplitz variance matrix.

## Usage

 ```1 2 3``` ```dSnorm(X, mu, acf, log = FALSE) dSnormDL(X, mu, acf, log = FALSE) ```

## Arguments

 `X` Vector or matrix, of which each column is a multivariate observation. `mu` Vector or matrix of mean values of compatible dimensions with `X`. Defaults to all zeros. `acf` Vector containing the first column of the Toeplitz variance matrix. For `dSnorm`, can also be a `Toeplitz` object. `log` Logical, whether to return the multivariate normal density on the log scale.

## Details

`dSnorm` and `dSnormDL` have identical outputs, with the former using the generalized Schur algorithm and the latter, the Durbin-Levinson algorithm, which is more common but slower. `dSnormDL` is provided mainly for speed comparisons.

## Value

Vector of (log-)densities, one for each column of `X`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```N <- 10 d <- 4 X <- matrix(rnorm(N*d), N, d) theta <- 0.1 lambda <- 2 mu <- theta^2 * rep(1, N) acf <- exp(-lambda * (1:N - 1)) acf <- Toeplitz(acf = acf) dSnorm(X, mu, acf, log = TRUE) ```

SuperGauss documentation built on May 1, 2019, 7:58 p.m.