NAG FL Interface
f06shf (ztpmv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{uplo}$ – Character(1) Input

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{uplo}=\text{'U'}$

$A$ is upper triangular.

$\mathbf{uplo}=\text{'L'}$

$A$ is lower triangular.

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

2: $\mathbf{trans}$ – Character(1) Input

On entry: specifies the operation to be performed.

$\mathbf{trans}=\text{'N'}$

$x\leftarrow Ax$.

$\mathbf{trans}=\text{'T'}$

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

$\mathbf{trans}=\text{'C'}$

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

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

3: $\mathbf{diag}$ – Character(1) Input

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\text{'N'}$

The diagonal elements are stored explicitly.

$\mathbf{diag}=\text{'U'}$

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

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

4: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

5: $\mathbf{ap}\left(*\right)$ – Complex (Kind=nag_wp) array Input

Note: the dimension of the array ap must be at least $\mathbf{n}\times (\mathbf{n}+1)/2$.

On entry: the $n\times n$ triangular matrix $A$, packed by columns.

More precisely,

• if $\mathbf{uplo}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+j(j-1)/2\right)$ for $i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+(2n-j)(j-1)/2\right)$ for $i\ge j$.

If $\mathbf{diag}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{diag}=\text{'N'}$ or ‘U’.

6: $\mathbf{x}\left(*\right)$ – Complex (Kind=nag_wp) array Input/Output

Note: the dimension of the array x must be at least $\max (1,1+(\mathbf{n}-1)\times \left|\mathbf{incx}\right|)$.

On entry: the vector $x$.

If $\mathbf{incx}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left(1+(\mathit{i}–1)\times \mathbf{incx}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

If $\mathbf{incx}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left(1–(\mathbf{n}–\mathit{i})\times \mathbf{incx}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

On exit: the updated vector $x$ stored in the array elements used to supply the original vector $x$.

7: $\mathbf{incx}$ – Integer Input

On entry: the increment in the subscripts of x between successive elements of $x$.

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

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example