npreg (version 1.1.0)

msqrt: Matrix (Inverse?) Square Root

Description

Stable computation of the square root (or inverse square root) of a positive semi-definite matrix.

Usage

msqrt(x, inverse = FALSE, symmetric = FALSE, 
      tol = .Machine$double.eps, checkx = TRUE)

Value

The matrix z that gives the (inverse?) square root of x. See Details.

Arguments

x

positive semi-definite matrix

inverse

compute inverse square root?

symmetric

does the square root need to be symmetric? See Details.

tol

tolerance for detecting linear dependencies in x

checkx

should x be checked for symmetry using isSymmetric?

Author

Nathaniel E. Helwig <[e-mail]>

Details

If symmetric = FALSE, this function computes the matrix z such that x = tcrossprod(z)

If symmetric = TRUE, this function computes the matrix z such that x = crossprod(z) = tcrossprod(z)

If inverse = TRUE, the matrix x is replaced by the pseudo-inverse of x in these equations (see psolve)

See Also

psolve

Examples

# generate x
set.seed(0)
x <- crossprod(matrix(rnorm(100), 20, 5))

# asymmetric square root (default)
xsqrt <- msqrt(x)
mean(( x - crossprod(xsqrt) )^2)
mean(( x - tcrossprod(xsqrt) )^2)

# symmetric square root
xsqrt <- msqrt(x, symmetric = TRUE)
mean(( x - crossprod(xsqrt) )^2)
mean(( x - tcrossprod(xsqrt) )^2)

# asymmetric inverse square root (default)
xsqrt <- msqrt(x, inverse = TRUE)
mean(( solve(x) - crossprod(xsqrt) )^2)
mean(( solve(x) - tcrossprod(xsqrt) )^2)

# symmetric inverse square root
xsqrt <- msqrt(x, inverse = TRUE, symmetric = TRUE)
mean(( solve(x) - crossprod(xsqrt) )^2)
mean(( solve(x) - tcrossprod(xsqrt) )^2)