Cholesky decomposition of a symmetric positive definite matrix, .
The object acts as the matrix , defines conversion to and assignment
Real[_,_], and is intended as more or less a drop-in replacement
for that type, albeit sharing, as usual for objects (i.e. copy-by-reference
rather than copy-by-value semantics). That sharing permits, for example,
multiple multivariate Gaussian distributions to share the same covariance
or precision matrix with common posterior updates performed only once.
Various functions, such as
solve, have overloads that make use of
objects for more efficient computation.
To emphasize, the matrix represented is , not , which is to say, code such as the following:
auto A <- llt(S); y <- solve(A, x);
computes the matrix-vector product , not ,
however the Cholesky decomposition will be used to solve this more
efficiently than a general matrix solve. The point of an
is to maintain the original matrix in a decomposed form for more
|compute||Decompose the matrix positive definite matrix
|update||Rank one update (or downdate) of a Cholesky decomposition.|
Member Function Details
Decompose the matrix positive definite matrix
S into this.