NAG Library Routine Document

f06faf (dvcos)

1

Purpose

2

Specification

3

Description

4

References

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Arguments

1:     $\mathbf{n}$ – IntegerInput

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

2:     $\mathbf{j}$ – 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:     $\mathbf{tolx}$ – 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:     $\mathbf{x}\left(*\right)$ – 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:     $\mathbf{incx}$ – IntegerInput

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

6:     $\mathbf{toly}$ – 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:     $\mathbf{y}\left(*\right)$ – 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:     $\mathbf{incy}$ – IntegerInput

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

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Error Indicators and Warnings

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Accuracy

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Parallelism and Performance

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Further Comments

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Example