naginterfaces.library.lapacklin.dtbtrs

naginterfaces.library.lapacklin.dtbtrs(uplo, trans, diag, kd, ab, b)

dtbtrs solves a real triangular band system of linear equations with multiple right-hand sides, $AX=B$ or $A^{T}X=B$.

For full information please refer to the NAG Library document for f07ve

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f07/f07vef.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.

transstr, length 1

Indicates the form of the equations.

$trans=\text{'N'}$

The equations are of the form $AX=B$.

$trans=\text{'T'}$ or $\text{'C'}$

The equations are of the form $A^{T}X=B$.

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 $1$.

kdint

$k_d$, the number of superdiagonals of the matrix $A$ if $uplo=\text{'U'}$, or the number of subdiagonals if $uplo=\text{'L'}$.

abfloat, array-like, shape $(kd+1,n)$

The $n\times n$ triangular band matrix $A$.

bfloat, array-like, shape $(n,\text{nrhs})$

The $n\times r$ right-hand side matrix $B$.

Returns

bfloat, ndarray, shape $(n,\text{nrhs})$

The $n\times r$ solution matrix $X$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $uplo$.

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

(errno $-2$)

On entry, error in parameter $trans$.

Constraint: $trans=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

(errno $-3$)

On entry, error in parameter $diag$.

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

(errno $-4$)

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

Constraint: $n\ge 0$.

(errno $-5$)

On entry, error in parameter $kd$.

Constraint: $kd\ge 0$.

(errno $-6$)

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

Constraint: $\text{nrhs}\ge 0$.

Warns

NagAlgorithmicWarning

(errno $i>0$)

Element $⟨value⟩$ of the diagonal is exactly zero. $A$ is singular and the solution has not been computed.

Notes

dtbtrs solves a real triangular band system of linear equations $AX=B$ or $A^{T}X=B$.

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore

Higham, N J, 1989, The accuracy of solutions to triangular systems, SIAM J. Numer. Anal. (26), 1252–1265