naginterfaces.library.blas.ztpsv

naginterfaces.library.blas.ztpsv(uplo, trans, diag, ap, x)

ztpsv solves a complex triangular system of equations, stored in packed form, with a single right-hand side.

For full information please refer to the NAG Library document for f06sl

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06slf.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.

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

The $n\times n$ triangular matrix $A$, packed by columns.

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 $7$)

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.

ztpsv 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 matrix, stored in packed form, 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.