rGivens: Generate Correlation Matrices with Specified Eigenvalues

In fungible: Psychometric Functions from the Waller Lab

Generate Correlation Matrices with Specified Eigenvalues

Description

rGivens generates correlation matrices with user-specified eigenvalues via a series of Givens rotations by methods described in Bendel & Mickey (1978) and Davis & Higham (2000).

Usage

rGivens(eigs, Seed = NULL)

Arguments

eigs	A vector of eigenvalues that must sum to the order of the desired correlation matrix. A fatal error will occur if sum(eigs) != length(eigs).
Seed	Either a user supplied seed for the random number generator or ‘NULL’ for a function generated seed. Default Seed = ‘NULL’.

Value

R	A correlation matrix with desired spectrum.
Frob	The Frobenius norm of the difference between the initial and final matrices with the desired spectrum.
convergence	(Logical) TRUE if rGivens converged to a feasible solution, otherwise FALSE.

References

Bendel, R. B. & Mickey, M. R. (1978). Population correlation matrices for sampling experiments, Commun. Statist. Simulation Comput., B7, pp. 163-182.

Davies, P. I, & Higham,N. J. (2000). Numerically stable generation of correlation matrices and their factors, BIT, 40 (2000), pp. 640-651.

Examples

## Example
## Generate a correlation matrix with user-specified eigenvalues

out <- rGivens(c(2.5, 1, 1, .3, .2), Seed = 123)

#> eigen(out$R)$values
#[1] 2.5 1.0 1.0 0.3 0.2

print(out)
#$R
#           [,1]       [,2]        [,3]        [,4]       [,5]
#[1,]  1.0000000 -0.1104098 -0.24512327  0.46497370  0.2392817
#[2,] -0.1104098  1.0000000  0.33564370 -0.46640155 -0.7645915
#[3,] -0.2451233  0.3356437  1.00000000 -0.02935466 -0.2024926
#[4,]  0.4649737 -0.4664016 -0.02935466  1.00000000  0.6225880
#[5,]  0.2392817 -0.7645915 -0.20249261  0.62258797  1.0000000
#
#$Frob
#[1] 2.691613
#
##$S0
#           [,1]        [,2]        [,3]        [,4]        [,5]
#[1,]  1.0349665  0.22537748 -0.46827121 -0.10448336 -0.24730565
#[2,]  0.2253775  0.31833805 -0.23208078  0.06591368 -0.14504161
#[3,] -0.4682712 -0.23208078  2.28911499  0.05430754  0.06964858
#[4,] -0.1044834  0.06591368  0.05430754  0.94884439 -0.14439623
#[5,] -0.2473056 -0.14504161  0.06964858 -0.14439623  0.40873606
#
#$convergence
#[1] TRUE

fungible documentation built on May 29, 2024, 8:28 a.m.