Posdef function

Positive definite symmetric matrices

Generates a positive definite and symmetric matrix with specified eigen-values

Posdef(p, ev = rexp(p, 1/100))

Arguments

• p: The dimension of the matrix
• ev: The eigenvalues. If not specified, eigenvalues are taken from an exponential distribution.

Returns

Returns a symmetric positive-definite matrix with eigen-values = ev.

Details

Posdef generates random positive definite covariance matrices with specified eigen-values that can be used to simulate multivariate datasets (see Uyeda et al. 2015 - and supplied R codes).

References

Uyeda J.C., Caetano D.S., Pennell M.W. 2015. Comparative Analysis of Principal Components Can be Misleading. Syst. Biol. 64:677-689.

Clavel, J., Aristide, L., Morlon, H., 2019. A Penalized Likelihood framework for high-dimensional phylogenetic comparative methods and an application to new-world monkeys brain evolution. Syst. Biol. 68:93-116.

Author(s)

J. Clavel

See Also

GIC.fit_pl.rpanda, fit_t_pl

phyl.pca_pl

Examples

if(test){
if(require(mvMORPH)){
set.seed(123)
n <- 32 # number of species
p <- 40 # number of traits

tree <- pbtree(n=n) # phylogenetic tree
R <- Posdef(p) # a random symmetric matrix (covariance)
# simulate a dataset
Y <- mvSIM(tree, model="BM1", nsim=1, param=list(sigma=R))

test <- fit_t_pl(Y, tree, model="BM", method="RidgeAlt")
GIC(test)
}
}