naginterfaces.library.det.complex_​gen

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

complex_gen computes the determinant of a complex $n\times n$ matrix $A$. lapacklin.zgetrf must be called first to supply the matrix $A$ in factorized form.

For full information please refer to the NAG Library document for f03bn

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f03/f03bnf.html

Parameters

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

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

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

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

Returns

dcomplex

The mantissa of the real and imaginary parts of the determinant.

dexpint, ndarray, shape $\left(2\right)$

The exponents for the real and imaginary parts of the determinant. The determinant, $d=(d_r,d_i)$, is returned as $d_r=D_r\times 2^j$ and $d_i=D_i\times 2^k$, where $d=(D_r,D_i)$ and $j$ and $k$ are stored in the first and second elements respectively of the array $dexp$ on successful exit.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $4$)

The matrix $A$ is approximately singular.

Notes

complex_gen computes the determinant of a complex $n\times n$ matrix $A$ that has been factorized by a call to lapacklin.zgetrf. 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