chol performs a Cholesky decomposition of
a symmetric positive definite sparse matrix
a of class
matrix.csr using the block sparse Cholesky algorithm of Ng and
Peyton (1993). The structure of the resulting
object is relatively complicated. If necessary it can be coerced back
matrix.csr object as usual with
backsolve does triangular back-fitting to compute
the solutions of a system of linear equations. For systems of linear equations
that only vary on the right-hand-side, the result from
can be reused. Contrary to the behavior of
backsolve in base R,
the default behavior of
backsolve(C,b) when C is a
is to produce a solution to the system \(Ax = b\) where
C <- chol(A), see
the example section. When the flag
FALSE then backsolve
solves the system \(Cx = b\), up to a permutation -- see the comments below.
backsolve, and will
compute the inverse of a matrix if the right-hand-side is missing.
The determinant of the Cholesky factor is returned providing a
means to efficiently compute the determinant of sparse positive
definite symmetric matrices.
There are several integer storage parameters that are set by default in the call
to the Cholesky factorization, these can be overridden in any of the above
functions and will be passed by the usual "dots" mechanism. The necessity
to do this is usually apparent from error messages like: Error
in local(X...) increase tmpmax. For example, one can use,
solve(A,b, tmpmax = 100*nrow(A)). The current default for tmpmax
50*nrow(A). Some experimentation may be needed to
select appropriate values, since they are highly problem dependent. See
the code of chol() for further details on the current defaults.