NAG Library Routine Document

F06FAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the number of elements in $x$ and $y$.

2:     $\mathrm{J}$ – INTEGERInput

On entry: if the vector $y$ is supplied in Y, J should be set to $0$. Otherwise, J specifies the index $j$ of the unit vector $e_j$ to be used as $y$.

3:     $\mathrm{TOLX}$ – REAL (KIND=nag_wp)Input

On entry: the value $\mathit{tolx}$, used to determine whether ${‖x‖}_2$ is effectively zero.

If TOLX is negative, the value zero is used.

4:     $\mathrm{X}\left(*\right)$ – REAL (KIND=nag_wp) arrayInput

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

On entry: the $n$-element vector $x$.

If $\mathbf{INCX}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{X}\left(1+\left(\mathit{i}-1\right)\times \mathbf{INCX}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

If $\mathbf{INCX}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{X}\left(1-\left(\mathbf{N}-\mathit{i}\right)\times \mathbf{INCX}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

Intermediate elements of X are not referenced.

5:     $\mathrm{INCX}$ – INTEGERInput

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

6:     $\mathrm{TOLY}$ – REAL (KIND=nag_wp)Input

On entry: the value $\mathit{toly}$, used to determine whether ${‖y‖}_2$ is effectively zero.

If TOLY is negative, the value zero is used.

7:     $\mathrm{Y}\left(*\right)$ – REAL (KIND=nag_wp) arrayInput

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

On entry: if $1\le \mathbf{J}\le \mathbf{N}$, Y is not referenced. Otherwise, Y holds the vector $y$.

If $\mathbf{INCY}>0$, $y_{\mathit{i}}$ must be stored in $\mathbf{Y}\left(1+\left(\mathit{i}-1\right)\times \mathbf{INCY}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

If $\mathbf{INCY}<0$, $y_{\mathit{i}}$ must be stored in $\mathbf{Y}\left(1-\left(\mathbf{N}-\mathit{i}\right)\times \mathbf{INCY}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

Intermediate elements of Y are not referenced.

8:     $\mathrm{INCY}$ – INTEGERInput

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

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example