NAG Library Routine Document

F06HCF

+− Contents

1 Purpose

9 Example

F06HCF multiplies a complex vector by a complex diagonal matrix.

SUBROUTINE F06HCF (

INTEGER	N, INCD, INCX
COMPLEX (KIND=nag_wp)	D(), X()

F06HCF performs the operation

x \leftarrow D x

where

x

is an

n

-element complex vector and

D = diag (d)

is a complex diagonal matrix.

Equivalently, the routine performs the element-by-element product of the vectors

x

and

d

x_{i} = d_{i} x_{i}, i = 1, 2, \dots, n .

None.

1: N – INTEGERInput: On entry: $n$ , the number of elements in $d$ and $x$ .
2: D( $*$ ) – COMPLEX (KIND=nag_wp) arrayInput: Note: the dimension of the array D must be at least $\max (1, 1 + (N - 1) \times |INCD|)$ .
On entry: the vector $d$ .
If $INCD > 0$ , $d_{i}$ must be stored in $D (1 + (i - 1) \times INCD)$ , for $i = 1, 2, \dots, N$ .

If $INCD < 0$ , $d_{i}$ must be stored in $D (1 - (N - i) \times INCD)$ , for $i = 1, 2, \dots, N$ .
3: INCD – INTEGERInput: On entry: the increment in the subscripts of D between successive elements of $d$ .
4: X( $*$ ) – COMPLEX (KIND=nag_wp) arrayInput/Output: Note: the dimension of the array X must be at least $\max (1, 1 + (N - 1) \times |INCX|)$ .
On entry: the array X must contain 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 $i = 1, 2, \dots, N$ .

On exit: the updated vector $x$ stored in the array elements used to supply the original vector $x$ .
Intermediate elements of X are unchanged.
5: INCX – INTEGERInput: On entry: the increment in the subscripts of X between successive elements of $x$ .