axpy(3F)

NAME
     SAXPY, CAXPY, DAXPY, ZAXPY - Adds a scalar multiple of a real or
     complex vector to another real or complex vector

SYNOPSIS
     Real

        CALL SAXPY (n, alpha, x, incx, y, incy)

     Double precision

        CALL DAXPY (n, alpha, x, incx, y, incy)

     Complex

        CALL CAXPY (n, alpha, x, incx, y, incy)

     Double complex

        CALL ZAXPY (n, alpha, x, incx, y, incy)

DESCRIPTION
     SAXPY/DAXPY adds a scalar multiple of a real vector to another real
     vector.

     CAXPY/ZAXPY adds a scalar multiple of a complex vector to another
     complex vector.

     These routines perform the following vector operation:

          y  <-  alpha * x + y

     where alpha is a real or complex scalar, and x and y are real or
     complex vectors.

     These routines have the following arguments:

     n         Integer.  (input)
               Number of elements in the vectors.  If n <= 0, these
               routines return without any computation.

     alpha     Scalar. (input)
               SAXPY: Real.
               DAXPY: Double precision.
               CAXPY: Complex.
               ZAXPY: Double complex.
               If alpha = 0 these routines return without any computation.

     x         Array of dimension (n-1) * |incx| + 1.  (input)
               SAXPY: Real array.
               DAXPY: Double precision array.
               CAXPY: Complex array.
               ZAXPY: Double complex array.
               Contains the vector to be scaled before summation.

     incx      Integer.  (input)
               Increment between elements of x.  If incx = 0, the results
               will be unpredictable.

     y         Array of dimension (n-1) * |incy| + 1.  (input and output)
               SAXPY: Real array.
               DAXPY: Double precision array.
               CAXPY: Complex array.
               ZAXPY: Double complex array.
               Before calling the routine, y contains the vector to be
               summed.  After the routine ends, y contains the result of
               the summation.

     incy      Integer.  (input)
               Increment between elements of y.  If incy = 0, the results
               will be unpredictable.

NOTES
     These routines are Level 1 Basic Linear Algebra Subprograms (Level 1
     BLAS).

     When working backward (incx < 0 or incy < 0), each routine starts at
     the end of the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)), ..., x(1)

          y(1-incy * (n-1)), y(1-incy * (n-2)), ..., y(1)

RETURN VALUES
     When n <= 0, real alpha = 0., or complex alpha = 0 = 0.+0.i, these
     routines return immediately with no change in their arguments.