naginterfaces.library.det.real_​gen

naginterfaces.library.det.real_gen(a, ipiv)

real_gen computes the determinant of a real $n\times n$ matrix $A$. lapacklin.dgetrf must be called first to supply the matrix $A$ in factorized form.

For full information please refer to the NAG Library document for f03ba

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f03/f03baf.html

Parameters

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

The $n\times n$ matrix $A$ in factorized form as returned by lapacklin.dgetrf.

ipivint, array-like, shape $\left(n\right)$

The row interchanges used to factorize matrix $A$ as returned by lapacklin.dgetrf.

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: $n\ge 1$.

(errno $4$)

The matrix $A$ is approximately singular.

Notes

real_gen computes the determinant of a real $n\times n$ matrix $A$ that has been factorized by a call to lapacklin.dgetrf. The determinant of $A$ is the product of the diagonal elements of $U$ with the correct sign determined by the row interchanges.

References

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