naginterfaces.library.lapacklin.dtptri

naginterfaces.library.lapacklin.dtptri(uplo, diag, n, ap)

dtptri computes the inverse of a real triangular matrix, using packed storage.

For full information please refer to the NAG Library document for f07uj

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07ujf.html

Parameters

uplostr, length 1

Specifies whether $A$ is upper or lower triangular.

$uplo=\text{'U'}$

$A$ is upper triangular.

$uplo=\text{'L'}$

$A$ is lower triangular.

diagstr, length 1

Indicates whether $A$ is a nonunit or unit triangular matrix.

$diag=\text{'N'}$

$A$ is a nonunit triangular matrix.

$diag=\text{'U'}$

$A$ is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be $1$.

nint

$n$, the order of the matrix $A$.

apfloat, array-like, shape $(n\times (n+1)/2)$

The $n\times n$ triangular matrix $A$, packed by columns.

Returns

apfloat, ndarray, shape $(n\times (n+1)/2)$

$A$ is overwritten by $A^{-1}$, using the same storage format as described above.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $-2$)

On entry, error in parameter $diag$.

Constraint: $diag=\text{'N'}$ or $\text{'U'}$.

(errno $-3$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

Warns

NagAlgorithmicWarning

(errno $i>0$)

Element $⟨value⟩$ of the diagonal is exactly zero. $A$ is singular its inverse cannot be computed.

Notes

dtptri forms the inverse of a real triangular matrix $A$, using packed storage. Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.

References

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