f06faf_ (const Integer *n, const Integer *j, const double *tolx, const double x[], const Integer *incx, const double *toly, const double y[], const Integer *incy)

The routine may be called by the names f06faf or nagf_blas_dvcos.

3 Description

f06faf returns, via the function name, the cosine of the angle between two

n

-element real vectors

x

and

y

, given by the expression

\frac{x^{T} y}{{‖ x ‖}_{2} {‖ y ‖}_{2}} .

1 \leq j \leq n

y

is taken to be the unit vector

e_{j}

, in which case the array y is not referenced.

{‖ x ‖}_{2} \leq tolx

, the routine returns

2.0

; if

{‖ x ‖}_{2} > tolx

but

{‖ y ‖}_{2} \leq tol y

, the routine returns

- 2.0

; otherwise the value returned is in the range

(- 1.0, 1.0)

4 References

None.

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of elements in $x$ and $y$ .
2: $j$ – Integer Input: 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: $tolx$ – Real (Kind=nag_wp) Input: On entry: the value $tolx$ , used to determine whether ${‖ x ‖}_{2}$ is effectively zero.
If tolx is negative, the value zero is used.
4: $x (*)$ – Real (Kind=nag_wp) array Input: Note: the dimension of the array x must be at least $\max (1, 1 + (n - 1) \times | incx |)$ .

On entry: the $n$ -element vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x (1 + (i - 1) \times incx)$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of x are not referenced.
5: $incx$ – Integer Input: On entry: the increment in the subscripts of x between successive elements of $x$ .
6: $toly$ – Real (Kind=nag_wp) Input: On entry: the value $toly$ , used to determine whether ${‖ y ‖}_{2}$ is effectively zero.
If toly is negative, the value zero is used.
7: $y (*)$ – Real (Kind=nag_wp) array Input: Note: the dimension of the array y must be at least $\max (1, 1 + (n - 1) \times | incy |)$ .

On entry: if $1 \leq j \leq n$ , y is not referenced. Otherwise, y holds the vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y (1 + (i - 1) \times incy)$ , for $i = 1, 2, \dots, n$ .

If $incy < 0$ , $y_{i}$ must be stored in $y (1 - (n - i) \times incy)$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of y are not referenced.
8: $incy$ – Integer Input: On entry: the increment in the subscripts of y between successive elements of $y$ .

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

f06faf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.