Compute the upper Cholesky factor, R, of the real symmetric
or complex Hermitian positive definite matrix A.
The upper Cholesky factor R is computed by using the upper
triangular part of matrix A and is defined by
Calling chol using the optional "upper" flag has the
same behavior. In contrast, using the optional "lower" flag,
chol returns the lower triangular factorization, computed by using
the lower triangular part of matrix A, such that
Called with one output argument chol fails if matrix A is
not positive definite. Note that if matrix A is not real symmetric
or complex Hermitian then the lower triangular part is considered to be
the (complex conjugate) transpose of the upper triangular part, or vice
versa, given the "lower" flag.
Called with two or more output arguments p flags whether the matrix
A was positive definite and chol does not fail. A zero value
of p indicates that matrix A is positive definite and R
gives the factorization. Otherwise, p will have a positive value.
If called with three output arguments matrix A must be sparse and
a sparsity preserving row/column permutation is applied to matrix A
prior to the factorization. That is R is the factorization of
A(Q,Q) such that
The sparsity preserving permutation is generally returned as a matrix.
However, given the optional flag "vector", Q will be
returned as a vector such that
In general the lower triangular factorization is significantly faster for
sparse matrices.
See also: hess, lu, qr, qz, schur, svd, ichol, cholinv, chol2inv, cholupdate, cholinsert, choldelete, cholshift.