naginterfaces.library.det.real_​sym

naginterfaces.library.det.real_sym(a)[source]

real_sym computes the determinant of a real symmetric positive definite matrix . lapacklin.dpotrf must be called first to supply the symmetric matrix in Cholesky factorized form. The storage (upper or lower triangular) used by lapacklin.dpotrf is not relevant to real_sym since only the diagonal elements of the factorized are referenced.

For full information please refer to the NAG Library document for f03bf

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f03/f03bff.html

Parameters
afloat, array-like, shape

The lower or upper triangle of the Cholesky factorized form of the positive definite symmetric matrix . Only the diagonal elements are referenced.

Returns
dfloat

The determinant of is given by . It is given in this form to avoid overflow or underflow.

dexpint

The determinant of is given by . It is given in this form to avoid overflow or underflow.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

The matrix is not positive definite.

Notes

real_sym computes the determinant of a real 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 lapacklin.dpotrf.

References

Wilkinson, J H and Reinsch, C, 1971, Handbook for Automatic Computation II, Linear Algebra, Springer–Verlag