saxpy(3S)

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

SYNOPSIS
     Single precision

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

          C/C++:
               #include <scsl_blas.h>
               void saxpy( int n, float alpha, float *x, int incx, float *y,
               int incy );

     Double precision

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

          C/C++:
               #include <scsl_blas.h>
               void daxpy( int n, double alpha, double *x, int incx, double
               *y, int incy );

     Single precision complex

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

          C/C++:
               #include <scsl_blas.h>
               void caxpy( int n, scsl_complex *alpha, scsl_complex *x, int
               incx, scsl_complex *y, int incy );

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void caxpy( int n, complex<float> *alpha, complex<float> *x,int
               incx, complex<float> *y, int incy );

     Double precision complex

          Fortran:

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

          C/C++:
               #include <scsl_blas.h>
               void zaxpy( int n, scsl_zomplex *alpha, scsl_zomplex *x, int
               incx, scsl_zomplex *y, int incy );

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void zaxpy( int n, complex<double> *alpha, complex<double> *x,
               int incx, complex<double> *y, int incy );

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

     The C and C++ prototypes shown above are appropriate for the 4-byte
     integer version of SCSL. When using the 8-byte integer version, the
     variables of type int become long long and the <scsl_blas_i8.h> header
     file should be included.

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.

     See the NOTES section of this man page for information about the
     interpretation of the data types described in the following arguments.

     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: Single precision.
               DAXPY: Double precision.
               CAXPY: Single precision complex.
               ZAXPY: Double precision complex.
               If alpha = 0 these routines return without any computation.

               For C/C++, a pointer to this scalar is passed when alpha is
               complex; otherwise, alpha is passed by value.

     x         Array of dimension (n-1) * |incx| + 1.  (input)
               SAXPY: Single precision array.
               DAXPY: Double precision array.
               CAXPY: Single precision complex array.
               ZAXPY: Double precision 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: Single precision array.
               DAXPY: Double precision array.
               CAXPY: Single precision complex array.
               ZAXPY: Double precision 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)

   Data Types
     The following data types are described in this documentation:

          Term Used                     Data type

     Fortran:

          Array dimensioned n           x(n)

          Character                     CHARACTER

          Integer                       INTEGER (INTEGER*8 for -lscs_i8[_mp])

          Single precision              REAL

          Double precision              DOUBLE PRECISION

          Single precision complex      COMPLEX

          Double precision complex      DOUBLE COMPLEX

     C/C++:

          Array dimensioned n           x[n]

          Character                     char

          Integer                       int (long long for -lscs_i8[_mp])

          Single precision              float

          Double precision              double

          Single precision complex      scsl_complex

          Double precision complex      scsl_zomplex

     C++ STL:

          Array dimensioned n           x[n]

          Character                     char

          Integer                       int (long long for -lscs_i8[_mp])

          Single precision              float

          Double precision              double

          Single precision complex      complex<float>

          Double precision complex      complex<double>

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.

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS1(3S)

     INTRO_CBLAS(3S) for information about using the C interface to Fortran 77
     Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic
     Linear Algebra Subprograms Technical Forum.