mchol {fastmatrix} | R Documentation |
The modified Cholesky factorization
Description
Compute the Cholesky factorization of a real symmetric but not necessarily positive definite matrix.
Usage
mchol(x)
Arguments
x |
a symmetric but not necessarily positive definite matrix to be factored. |
Value
The lower triangular factor of modified Cholesky decomposition, i.e., the matrix
such that
, where
is a nonnegative diagonal matrix that is zero if
es sufficiently positive
definite.
References
Gill, P.E., Murray, W., Wright, M.H. (1981). Practical Optimization. Academic Press, London.
Nocedal, J., Wright, S.J. (1999). Numerical Optimization. Springer, New York.
See Also
Examples
# a non-positive-definite matrix
a <- matrix(c(4,2,1,2,6,3,1,3,-.004), ncol = 3)
try(chol(a)) # fails
z <- mchol(a)
z # triangular factor
# modified 'a' matrix
tcrossprod(z)
[Package fastmatrix version 0.5-772 Index]