nag_det_real_sym (f03bfc) computes the determinant of a real
by
symmetric positive definite matrix
.
nag_dpotrf (f07fdc) must be called first to supply the symmetric matrix
in Cholesky factorized form. The storage (upper or lower triangular) used by
nag_dpotrf (f07fdc) is not relevant to nag_det_real_sym (f03bfc) since only the diagonal elements of the factorized
are referenced.
nag_det_real_sym (f03bfc) computes the determinant of a real
by
symmetric positive definite matrix
that has been factorized as
, where
is upper triangular, or
, where
is lower triangular. The determinant is the product of the squares of the diagonal elements of
or
. The Cholesky factorized form of the matrix must be supplied; this is returned by a call to
nag_dpotrf (f07fdc).
The accuracy of the determinant depends on the conditioning of the original matrix. For a detailed error analysis see page 25 of
Wilkinson and Reinsch (1971).
Not applicable.
This example computes a Cholesky factorization and calculates the determinant of the real symmetric positive definite matrix