Matrix (version 0.999375-2)

nearPD: Nearest Matrix to a Positive Definite Matrix

Description

Computes the nearest positive definite matrix to an approximate one, typically a correlation or variance-covariance matrix.

Usage

nearPD(x, corr = FALSE,
       eig.tol = 1e-06, conv.tol = 1e-07, posd.tol = 1e-08,
       do2eigen = TRUE, maxit = 100, verbose = FALSE)

Arguments

x

numeric $n \times n$ approximately positive definite matrix, typically an approximation to a correlation or covariance matrix.

corr

logical indicating if the matrix should be a correlation matrix.

eig.tol

defines relative positiveness of eigenvalues compared to largest one.

conv.tol

convergence tolerance for algorithm.

posd.tol

tolerance for enforcing positive definiteness.

do2eigen

logical indicating if a posdefify() eigen step should be applied to the result of the Hingham algorithm.

maxit

maximum number of iterations allowed.

verbose

logical; if TRUE the iterations are monitored by print out.

Value

• an S3 object of class "nearPD", basically a list with components
• mat
  a matrix of class dpoMatrix, the computed positive-definite matrix.
• corr
  logical, just the argument corr.
• normF
  the Frobenius norm (norm(x-X, "F")) of the difference between the original and the resulting matrix.
• iterations
  number of iterations needed.
• converged
  logical indicating if iterations converged.

Details

Note that setting corr = TRUE just sets diag(.) <- 1 within the algorithm.

References

Cheng, Sheung Hun and Higham, Nick (1998) A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization; SIAM J. Matrix Anal. Appl., 19, 1097--1110.

Highham (2002) Computing the nearest correlation matrix - a problem from finance; IMA Journal of Numerical Analysis 22, 329--343.

See Also

More simple versions with a similar purpose by posdefify().

Examples

set.seed(27)
 m <- matrix(round(rnorm(25),2), 5, 5)
 m <- m + t(m)
 diag(m) <- pmax(0, diag(m)) + 1
 (m <- round(cov2cor(m), 2))

 str(near.m <- nearPD(m))
 round(near.m$mat, 2)
 norm(m - near.m$mat) # 1.102

 if(require("sfsmisc")) {
    m2 <- posdefify(m) # a simpler approach
    norm(m - m2)  # 1.185, i.e., slightly "less near"
 }