naginterfaces.library.lapacklin.dgetri

naginterfaces.library.lapacklin.dgetri(a, ipiv)

dgetri computes the inverse of a real matrix $A$, where $A$ has been factorized by dgetrf().

For full information please refer to the NAG Library document for f07aj

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f07/f07ajf.html

Parameters

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

The $LU$ factorization of $A$, as returned by dgetrf().

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

The pivot indices, as returned by dgetrf().

Returns

afloat, ndarray, shape $(n,n)$

The factorization is overwritten by the $n\times n$ matrix $A^{-1}$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

Warns

NagAlgorithmicWarning

(errno $i>0$)

Element $⟨value⟩$ of the diagonal is zero. $U$ is singular, and the inverse of $A$ cannot be computed.

Notes

dgetri is used to compute the inverse of a real matrix $A$, the function must be preceded by a call to dgetrf(), which computes the $LU$ factorization of $A$ as $A=PLU$. The inverse of $A$ is computed by forming $U^{-1}$ and then solving the equation $XPL=U^{-1}$ for $X$.

References

Du Croz, J J and Higham, N J, 1992, Stability of methods for matrix inversion, IMA J. Numer. Anal. (12), 1–19