NAG Library Routine Document

F06ETF (DAXPYI)

+− Contents

1 Purpose

9 Example

F06ETF (DAXPYI) adds a scaled sparse real vector, stored in compressed form, to an unscaled real vector.

SUBROUTINE F06ETF (

INTEGER	NZ, INDX(*)
REAL (KIND=nag_wp)	A, X(), Y()

The routine may be called by its BLAS name daxpyi.

F06ETF (DAXPYI) performs the operation

y \leftarrow α x + y

where

x

is a sparse real vector, stored in compressed form, and

y

is a real vector in full storage form.

Dodson D S, Grimes R G and Lewis J G (1991) Sparse extensions to the Fortran basic linear algebra subprograms ACM Trans. Math. Software 17 253–263

1: NZ – INTEGERInput: On entry: the number of nonzeros in the sparse vector $x$ .
2: A – REAL (KIND=nag_wp)Input: On entry: the scalar $α$ .
3: X( $*$ ) – REAL (KIND=nag_wp) arrayInput: Note: the dimension of the array X must be at least $\max (1, NZ)$ .
On entry: the nonzero elements of the sparse vector $x$ .
4: INDX( $*$ ) – INTEGER arrayInput: Note: the dimension of the array INDX must be at least $\max (1, NZ)$ .
On entry: $INDX (i)$ must contain the index of $X (i)$ in the sparse vector $x$ , for $i = 1, 2, \dots, NZ$ .
Constraint: the indices must be distinct.
5: Y( $*$ ) – REAL (KIND=nag_wp) arrayInput/Output: Note: the dimension of the array Y must be at least $\max_{k} \{INDX (k)\}$ .
On entry: the vector $y$ . Only elements corresponding to indices in INDX are accessed.

On exit: the updated vector $y$ .