NAG Library Routine Document

F06FKF

+− Contents

1 Purpose

9 Example

F06FKF computes the weighted Euclidean norm of a real vector.

FUNCTION F06FKF (

REAL (KIND=nag_wp) F06FKF

INTEGER	N, INCW, INCX
REAL (KIND=nag_wp)	W(), X()

F06FKF returns, via the function name, the weighted Euclidean norm

\sqrt{x^{T} W x}

of the

n

-element real vector

x

scattered with stride INCW and INCX respectively, where

W = diag (w)

and

w

is a vector of weights scattered with stride INCW.

None.

1: N – INTEGERInput: On entry: $n$ , the number of elements in $x$ .
2: W( $*$ ) – REAL (KIND=nag_wp) arrayInput: Note: the dimension of the array W must be at least $\max (1, 1 + (N - 1) \times |INCW|)$ .
On entry: $w$ , the vector of weights.
If $INCW > 0$ , $w_{i}$ must be stored in $W (1 + (i - 1) \times INCX)$ , for $i = 1, 2, \dots, N$ .

If $INCW < 0$ , $w_{i}$ must be stored in $W (1 - (N - i) \times INCW)$ , for $i = 1, 2, \dots, N$ .

Constraint: All weights must be non-negative.
3: INCW – INTEGERInput: On entry: the increment in the subscripts of W between successive elements of $w$ .
4: X( $*$ ) – REAL (KIND=nag_wp) arrayInput: 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 – INTEGERInput: On entry: the increment in the subscripts of X between successive elements of $x$ .