naginterfaces.library.lapacklin.dtftri

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

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://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07wkf.html

Parameters
transrstr, length 1

Specifies whether the RFP representation of is normal or transposed.

The matrix is stored in normal RFP format.

The matrix is stored in transposed RFP format.

uplostr, length 1

Specifies whether is upper or lower triangular.

is upper triangular.

is lower triangular.

diagstr, length 1

Indicates whether is a nonunit or unit triangular matrix.

is a nonunit triangular matrix.

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

nint

, the order of the matrix .

arfloat, array-like, shape

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

Returns
arfloat, ndarray, shape

is overwritten by , in the same storage format as .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

Diagonal element of is exactly zero. is singular its inverse cannot be computed.

Notes

dtftri forms the inverse of a real triangular matrix , 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)