naginterfaces.library.lapacklin.dtftri

naginterfaces.library.lapacklin.dtftri(transr, uplo, diag, n, ar)

dtftri computes the inverse of a real triangular matrix stored in Rectangular Full Packed (RFP) format.

For full information please refer to the NAG Library document for f07wk

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f07/f07wkf.html

Parameters

transrstr, length 1

Specifies whether the RFP representation of $A$ is normal or transposed.

$transr=\text{'N'}$

The matrix $A$ is stored in normal RFP format.

$transr=\text{'T'}$

The matrix $A$ is stored in transposed RFP format.

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 $A$.

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

The upper or lower triangular part (as specified by $uplo$) of the $n\times n$ symmetric matrix $A$, in either normal or transposed RFP format (as specified by $transr$). The storage format is described in detail in the F07 Introduction.

Returns

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

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

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $transr$.

Constraint: $transr=\text{'N'}$ or $\text{'T'}$.

(errno $-2$)

On entry, error in parameter $uplo$.

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

(errno $-3$)

On entry, error in parameter $diag$.

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

(errno $-4$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

Warns

NagAlgorithmicWarning

(errno $i>0$)

Diagonal element $⟨value⟩$ of $A$ is exactly zero. $A$ is singular its inverse cannot be computed.

Notes

dtftri forms the inverse of a real triangular matrix $A$, stored using RFP format. The RFP storage format is described in the F07 Introduction. 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

Gustavson, F G, Waśniewski, J, Dongarra, J J and Langou, J, 2010, Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion, ACM Trans. Math. Software (37, 2)