saxpby(3S)

NAME
     SAXPBY, DAXPBY, CAXPBY, ZAXPBY - Adds a scalar multiple of a Single
     precision or complex vector x to a scalar multiple of another Single
     precision or complex vector y

SYNOPSIS
     Single precision

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

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

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

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

     Single precision complex

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

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

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

     Double precision complex

          Fortran:

               CALL ZAXPBY (n, alpha, x, incx, beta, y, incy)

          C/C++:
               #include <scsl_blas.h>
               void zaxpby( int n, scsl_zomplex *alpha, scsl_zomplex *x, int
               incx, scsl_zomplex *beta, scsl_zomplex *y, int incy );
          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void zaxpby( int n, complex<double> *alpha, complex<double> *x,
               int incx, complex<double> *beta, 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
     SAXPBY/DAXPBY adds a scalar multiple of a real vector x to a scalar
     multiple of a real vector y.

     CAXPBY/ZAXPBY adds a scalar multiple of a complex vector x to a scalar
     multiple of a complex vector y:

          y <- alpha x + beta y

     where x and y are n-vectors and alpha and beta are scalars.

     The following special cases are recognized:

     *   alpha = 0:  equivalent to SSCAL, DSCAL, CSCAL, ZSCAL

     *   alpha = 1, beta = 0:  equivalent to SCOPY, CCOPY, DCOPY, ZCOPY

     *   alpha not equal to 1, beta = 0:  like SCOPY, CCOPY, DCOPY, ZCOPY with
         scaling

     *   alpha not equal to 0, beta = 1:  equivalent to SAXPY, CAXPY, DAXPY,
         ZAXPY

     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 of the vectors x and y.

     alpha     Scalar alpha (input).
               SAXPBY: Single precision.
               DAXPBY:  Double precision.
               CAXPBY: Single precision complex.
               ZAXPBY:  Double precision complex.

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

     x         Array of dimension (1+(n-1) *|incx|).  (input)
               SAXPBY: Single precision array.
               DAXPBY: Double precision array.
               CAXPBY: Single precision omplex array.
               ZAXPBY: Double precision complex array.
               The vector x.  If incx > 0, the i-th element of the vector x is
               located in x(1+(i-1) * |incx|).  If incx < 0, the i-th element
               of the vector x is located in x(1+(n-i) * |incx|).

     incx      Integer.  (input)
               Increment between elements of the vector x.  If incx < 0, x is
               processed in reverse order.

     beta      Scalar beta. (input)
               SAXPBY: Single precision scalar.
               DAXPBY:  Double precision scalar.
               CAXPBY: Single precision complex scalar.
               ZAXPBY:  Double precision complex scalar.

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

     y         Array of dimension (1+(n-1) * |incy|).  (input/output)
               SAXPBY: Single precision array.
               DAXPBY: Double precision array.
               CAXPBY: Single precision complex array.
               ZAXPBY: Double complex array.
               On entry, the vector y.  If incy > 0, the i-th element of the
               vector y is located in y(1+(i-1) * |incy|).  If incy < 0, the
               i-th element of the vector y is located in y(1+(n-i) * |incy|).

               On exit, y is overwritten with the vector sum alphax+ betay.

     incy      Integer.  (input)
               Increment between elements of y.  If incy < 0, y is processed
               in reverse order.

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


   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>

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.