F06FAF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06FAF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

F06FAF computes the cosine of the angle between two real vectors.

2  Specification

FUNCTION F06FAF ( N, J, TOLX, X, INCX, TOLY, Y, INCY)
REAL (KIND=nag_wp) F06FAF
INTEGER  N, J, INCX, INCY
REAL (KIND=nag_wp)  TOLX, X(*), TOLY, Y(*)

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
xTy x2y2 .  
If 1jn, y is taken to be the unit vector ej, in which case the array Y is not referenced.
If x2tolx, the routine returns 2.0; if x2>tolx but y2toly, the routine returns -2.0; otherwise the value returned is in the range -1.0,1.0.

4  References

None.

5  Parameters

1:     N – INTEGERInput
On entry: n, the number of elements in x and y.
2:     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 ej to be used as y.
3:     TOLX – REAL (KIND=nag_wp)Input
On entry: the value tolx, used to determine whether x2 is effectively zero.
If TOLX is negative, the value zero is used.
4:     X* – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array X must be at least max1, 1+N-1 ×INCX .
On entry: the n-element vector x.
If INCX>0, xi must be stored in X1+i-1×INCX, for i=1,2,,N.
If INCX<0, xi must be stored in X1-N-i×INCX, for i=1,2,,N.
Intermediate elements of X are not referenced.
5:     INCX – INTEGERInput
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 y2 is effectively zero.
If TOLY is negative, the value zero is used.
7:     Y* – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array Y must be at least max1, 1+N-1 ×INCY .
On entry: if 1JN, Y is not referenced. Otherwise, Y holds the vector y.
If INCY>0, yi must be stored in Y1+i-1×INCY, for i=1,2,,N.
If INCY<0, yi must be stored in Y1-N-i×INCY, for i=1,2,,N.
Intermediate elements of Y are not referenced.
8:     INCY – INTEGERInput
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

Not applicable.

9  Further Comments

None.

10  Example

None.

F06FAF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015