SAXPY

SAXPY (Single-precision real Alpha X Plus Y^[1]) is one of the functions in the Basic Linear Algebra Subprograms (BLAS) package, and is a common operation in computations with vector processors. SAXPY is a combination of scalar multiplication and vector addition,

$\mathbf{z} = \alpha \mathbf{x} + \mathbf{y}, \,$

where α is a scalar, and $\mathbf{x}$ and $\mathbf{y}$ are vectors. As with most functions, there exist four variants of SAXPY in the BLAS package, namely SAXPY, DAXPY, CAXPY and ZAXPY. These variants differ only in the datatype of scalar α. Description of these routines can be found in showed external links.

Different datatypes

SAXPY

SAXPY ^[2] is not only the generic term for the combined scalar multiplication plus vector addition operation, but also the specific variant where the scalar α and the vectors $\mathbf{x}$ and $\mathbf{y}$ are of single precision.

DAXPY

DAXPY denotes SAXPY with double precision α, $\mathbf{x}$ and $\mathbf{y}$.

CAXPY

CAXPY denotes SAXPY with complex α, $\mathbf{x}$ and $\mathbf{y}$.

ZAXPY

ZAXPY denotes SAXPY with double precision complex α, $\mathbf{x}$ and $\mathbf{y}$.

Generic implementation

The most generic C implementation of SAXPY looks like the following:

void saxpy(float* x, float* y, int n, float a) {
  int i;
  for (i = 0; i < n; ++i)
    y[i] += a * x[i];
}

References

1. ^ http://www.gnu.org/software/gsl/manual/html_node/BLAS-Support.html
2. ^ G. H. Golub, C. F. Loan, Matrix Computations, 3rd edition, Johns Hopkins, 1996. ISBN 0801854148.

External links

• http://download.oracle.com/docs/cd/E19059-01/stud.9/817-6700/
• http://www.netlib.org/blas/