rMAP: Generate Correlation Matrices with Specified Eigenvalues

In fungible: Psychometric Functions from the Waller Lab

Generate Correlation Matrices with Specified Eigenvalues

Description

rMAP uses the method of alternating projections (MAP) to generate correlation matrices with specified eigenvalues.

Usage

rMAP(eigenval, eps = 1e-12, maxits = 5000, Seed = NULL)

Arguments

eigenval	A vector of eigenvalues that must sum to the order of the desired correlation matrix. A fatal error will occur if sum(eigenval) != length(eigenval).
eps	Convergence criterion. Default = 1e-12.
maxits	Maximm number of iterations of MAP.
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 the desired spectrum.
evals	Eigenvalues of the returned matrix, R.
convergence	(Logical) TRUE if MAP converged to a feasible solution, otherwise FALSE.

Author(s)

Niels Waller

References

Waller, N. G. (2016). Generating correlation matrices with specified eigenvalues using the method of alternating projections.

Examples

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

R <- rMAP(c(2.5, 1, 1, .3, .2), Seed = 123)$R
print(R, 2)

#       [,1]    [,2]   [,3]    [,4]   [,5]
#[1,]  1.000  0.5355 -0.746 -0.0688 -0.545
#[2,]  0.535  1.0000 -0.671 -0.0016 -0.056
#[3,] -0.746 -0.6711  1.000  0.0608  0.298
#[4,] -0.069 -0.0016  0.061  1.0000  0.002
#[5,] -0.545 -0.0564  0.298  0.0020  1.000


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

fungible documentation built on March 31, 2023, 5:47 p.m.