Elementary vector operation

SAXPY/DAXPY/CAXPY/CAXPYC/ZAXPY/ZAXPYC

 

 

Use incy = 1 if the vector y is stored contiguously in

 

 

array y; that is, if yi is stored in y(i). Refer to “BLAS

 

 

Indexing Conventions” in the introduction to this

 

 

chapter.

Output

y

If n ≤ 0 or a = 0, then y is unchanged. Otherwise, ax+y

 

 

overwrites the input.

Notes

If incx = 0, then xi

= x(1) for all i.

 

The result is unspecified if incy = 0 or if x and y overlap such that any element

 

of x shares a memory location with any element of y.

Fortran

SUBROUTINE SAXPY (N, A, X,INCX, Y,INCY)

Equivalent

REAL*4 X(*),Y(*)

 

IF ( N .LE. 0 ) RETURN

 

IF ( A .EQ. 0.0 ) RETURN

 

IX = 1

 

IY = 1

 

IF ( INCX .LT. 0 ) IX = 1 - (N-1) * INCX

 

IF ( INCY .LT. 0 ) IY = 1 - (N-1) * INCY

 

DO 10 I = 1, N

 

Y(IY) = A * X(IX) + Y(IY)

 

IX = IX + INCX

 

IY = IY + INCY

 

10 CONTINUE

 

RETURN

 

END

Example 1 Compute the REAL*8 elementary vector operation

y← 2x + y,

where x and y are vectors 10 elements long stored in one-dimensional arrays X and Y of dimension 20.

INTEGER*4 N,INCX,INCY

REAL*8

A,X(20),Y(20)

N =

10

 

A =

2.0D0

 

INCX = 1

INCY = 1

CALL DAXPY (N,A,X,INCX,Y,INCY)

Example 2 Subtract 3 times the 4th row of a 10-by-10 matrix from the 5th row. The matrix is stored in a two-dimensional array B of dimension 20-by-21.

INTEGER*4

N

REAL*8

A,B(20,21)

N =

10

 

A =

-3.0D0

 

CALL DAXPY (N,A,B(4,1),20,B(5,1),20)

Chapter 2 Basic Vector Operations 67