naginterfaces.library.matop.dtfttr

naginterfaces.library.matop.dtfttr(transr, uplo, n, ar)

dtfttr unpacks a real triangular matrix, stored in a Rectangular Full Packed (RFP) format array, to a full format array.

For full information please refer to the NAG Library document for f01vg

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f01/f01vgf.html

Parameters

transrstr, length 1

Specifies whether the normal RFP representation of $A$ or its transpose is stored.

$transr=\text{'N'}$

The RFP representation of the matrix $A$ is stored.

$transr=\text{'T'}$

The transpose of the RFP representation of the matrix $A$ is stored.

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.

nint

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

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

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

Returns

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

The triangular matrix $A$.

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 $n$.

Constraint: $n\ge 0$.

Notes

dtfttr unpacks a real $n\times n$ triangular matrix $A$, stored in RFP format to conventional storage in a full format array. This function is intended for possible use in conjunction with functions from submodule blas, submodule blast and submodule lapacklin where some functions that use triangular matrices store them in RFP format. The RFP storage format is described in the F07 Introduction.

References

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)