get_random_diffusivity_matrix {castor}

Create a random diffusivity matrix for a Brownian motion model.

Description

Create a random diffusivity matrix for a Brownian motion model of multi-trait evolution. This may be useful for testing purposes. The diffusivity matrix is drawn from the Wishart distribution of symmetric, nonnegative-definite matrixes:

D = X^T \cdot X,\quad X[i,j]\sim N(0,V),\quad i=1,..,n, j=1,..,p,

where n is the degrees of freedom, p is the number of traits and V is a scalar scaling.

Usage

get_random_diffusivity_matrix(Ntraits, degrees=NULL, V=1)

Arguments

Ntraits

The number of traits modelled. Equal to the number of rows and the number of columns of the returned matrix.

degrees

Degrees of freedom for the Wishart distribution. Must be equal to or greater than Ntraits. Can also be NULL, which is the same as setting it equal to Ntraits.

V

Positive number. A scalar scaling for the Wishart distribution.

Value

A real-valued quadratic symmetric non-negative definite matrix of size Ntraits x Ntraits. Almost surely (in the probabilistic sense), this matrix will be positive definite.

Author(s)

Stilianos Louca

See Also

get_random_mk_transition_matrix, simulate_bm_model

Examples

# generate a 5x5 diffusivity matrix
D = get_random_diffusivity_matrix(Ntraits=5)

# check that it is indeed positive definite
if(all(eigen(D)$values>0)){ 
  cat("Indeed positive definite\n");
}else{ 
  cat("Not positive definite\n"); 
}