Choleski: Choleski multiplication with Toeplitz variance matrices.

Description Usage Arguments Details Value Examples

Description

Multiplies the Choleski decomposition of the Toeplitz matrix with another matrix, or solves a system of equations with the Cholesky factor.

Usage

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cholZX(Z, acf)

cholXZ(X, acf)

Arguments

Z

Length-N or N x p matrix of residuals.

acf

Length-N autocorrelation vector of the Toeplitz variance matrix.

X

Length-N or N x p matrix of observations.

Details

If C == t(chol(toeplitz(acf))), then cholZX computes C %*% Z and cholZX computes solve(C, X). Both functions use the Durbin-Levinson algorithm.

Value

Size N x p residual or observation matrix.

Examples

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N <- 10
p <- 2
W <- matrix(rnorm(N * p), N, p)
acf <- exp(-(1:N - 1))
cholZX(Z = W, acf = acf)
cholXZ(X = W, acf = acf)

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