naginterfaces.library.blas.ztbsv

naginterfaces.library.blas.ztbsv(uplo, trans, diag, k, a, x)

ztbsv solves a complex triangular banded system of equations with a single right-hand side.

For full information please refer to the NAG Library document for f06sk

https://www.nag.com/numeric/nl/nagdoc_30/flhtml/f06/f06skf.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

Specifies the operation to be performed.

$trans=\text{'N'}$

$x\leftarrow A^{-1}x$.

$trans=\text{'T'}$

$x\leftarrow A^{-T}x$.

$trans=\text{'C'}$

$x\leftarrow A^{-H}x$.

diagstr, length 1

Specifies whether $A$ has nonunit or unit diagonal elements.

$diag=\text{'N'}$

The diagonal elements are stored explicitly.

$diag=\text{'U'}$

The diagonal elements are assumed to be $1$, and are not referenced.

kint

$k$, the number of subdiagonals or superdiagonals of the matrix $A$.

acomplex, array-like, shape $(k+1,n)$

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

xcomplex, array-like, shape $\left(n\right)$

The vector $x$.

Returns

xcomplex, ndarray, shape $\left(n\right)$

The updated vector $x$.

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 $k$.

Constraint: $k\ge 0$.

(errno $9$)

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

Constraint: $\text{incx}\ne 0$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

ztbsv performs one of the matrix-vector operations

$$x\leftarrow A^{-1}x\text{,}x\leftarrow A^{-T}x\text{or}x\leftarrow A^{-H}x\text{,}$$

where $A$ is an $n\times n$ complex triangular band matrix with $k$ subdiagonals or superdiagonals, and $x$ is an $n$-element complex vector. $A^{-T}$ denotes ${\left(A^T\right)}^{-1}$ or equivalently ${\left(A^{-1}\right)}^T$; $A^{-H}$ denotes ${\left(A^H\right)}^{-1}$ or equivalently ${\left(A^{-1}\right)}^H$.

No test for singularity or near-singularity of $A$ is included in this function. Such tests must be performed before calling this function.