force-defpos: Force Positive Definiteness of a Matrix
In stsm: Structural Time Series Models

Description Usage Arguments Details Value References

This function transforms a matrix to be positive definite.

1	force.defpos(m, tol = 0.001, debug = FALSE)

`m`	a matrix.
`tol`	tolerance.
`debug`	logical. If `TRUE`, it is checked that the output matrix is positive definite.

The scoring algorithm maxlik.fd.scoring requires a positive definite matrix to project the gradient into the optimal direction. If that matrix happens to be non-positive definite then the matrix M is transformed as described in Pollock (1999) pp. 341-342:

M = M + (μ - κ) I

where I is the identity matrix, μ is a tolerance value and κ is the smallest eigenvalue of M. Other alternatives are discussed in Nocedal and Wright (2006) chapter 3.

A positive definite matrix.

Nocedal, J. and Wright, J. W. (2006). Numerical Optimization. Springer-Verlag.

Pollock, D.S.G. (1999). A Handbook of Time-Series Analysis Signal Processing and Dynamics. Academic Press.

stsm documentation built on May 2, 2019, 7:39 a.m.