naginterfaces.library.det.real_​sym

naginterfaces.library.det.real_sym(a)

real_sym computes the determinant of a real $n\times n$ symmetric positive definite matrix $A$. lapacklin.dpotrf must be called first to supply the symmetric matrix $A$ 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 $A$ are referenced.

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

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f03/f03bff.html

Parameters

afloat, array-like, shape $(n,n)$

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

Returns

dfloat

The determinant of $A$ is given by $d\times {2.0}^{dexp}$. It is given in this form to avoid overflow or underflow.

dexpint

The determinant of $A$ is given by $d\times {2.0}^{dexp}$. It is given in this form to avoid overflow or underflow.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n>0$.

(errno $4$)

The matrix $A$ is not positive definite.

Notes

real_sym computes the determinant of a real $n\times n$ symmetric positive definite matrix $A$ that has been factorized as $A=U^{T}U$, where $U$ is upper triangular, or $A=L{L}^T$, where $L$ is lower triangular. The determinant is the product of the squares of the diagonal elements of $U$ or $L$. 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