Computation of “square root” of symmetric positive definite matrix
mat_sqrt is not usually directly called by users, but arguments may be passed to it through higher-level calls (see Examples).
For given matrix C, it computes a factor L such that C = L * t(L), handling issues with nearly-singular matrices. The default behavior is to try Cholesky factorization, and use eigen if it fails.
Matrix roots are not unique (for example, they are lower triangular for t(chol(.)), and symmetric for svd(.). As matrix roots are used to simulate samples under the fitted model (in particular in the parametric bootstrap implemented in fixedLRT), this implies that for given seed of random numbers, these samples will differ with these different methods (although their distribution should be identical).
mat_sqrt(m = NULL, symSVD = NULL, try.chol = TRUE, condnum=1e12)
m |
The matrix whose 'root' is to be computed. This argument is ignored if |
symSVD |
A list representing the symmetric singular value decomposition of the matrix which 'root' is to be computed. Must have elements |
try.chol |
If |
condnum |
(large) numeric value. In the case |
For non-NULL m, its matrix root, with rows and columns labelled according to the columns of the original matrix.
If eigen was used, the symmetric singular value decomposition (a list with members u (matrix of eigenvectors) and d (vector of eigenvalues)) is given as attribute.
## Not run:
## try.chol argument passed to mat_sqrt
## through the '...' argument of higher-level functions
## such as HLCor, corrHLfit, fixedLRT:
data("scotlip")
HLCor(cases~I(prop.ag/10) +adjacency(1|gridcode)+offset(log(expec)),
ranPars=list(rho=0.174),adjMatrix=Nmatrix,family=poisson(),
data=scotlip,try.chol=FALSE)
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