ssyr2(3S)

NAME
     SSYR2, DSYR2 - Performs symmetric rank 2 update of a real symmetric
     matrix

SYNOPSIS
     Single precision

          Fortran:
               CALL SSYR2 (uplo, n, alpha, x, incx, y, incy, a, lda)

          C/C++:
               #include <scsl_blas.h>
               void ssyr2 (char *uplo, int n, float alpha, float *x, int incx,
               float *y, int incy, float *a, int lda);

     Double precision

          Fortran:
               CALL DSYR2 (uplo, n, alpha, x, incx, y, incy, a, lda)

          C/C++:
               #include <scsl_blas.h>
               void dsyr2 (char *uplo, int n, double alpha, double *x, int
               incx, double *y, int incy, double *a, int lda);

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
     These routines perform the following symmetric rank 2 operation:

          A <- alpha xyT + alpha yxT + A

     where alpha is a real scalar, yT is the transpose of y, xT is the
     transpose of x, x and y are n-element vectors, and A is an n-by-n real
     symmetric matrix.

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

     This routine has the following arguments:

     uplo      Character.  (input)
               Specifies whether the upper or lower triangular part of matrix
               A is being supplied, as follows:

               uplo= 'U' or 'u':  only the upper triangular part of array a is
               referenced.
               uplo= 'L' or 'l':  only the lower triangular part of array a is
               referenced.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     alpha     Scalar alpha.  (input)
               SSYR2: Single precision.
               DSYR2: Double precision.

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               SSYR2: Single precision array.
               DSYR2: Double precision array.

     incx      Integer.  (input)
               On entry, incx specifies the increment for the elements of x.
               incx must not be 0.

     y         Array of dimension 1+(n-1) * |incy|.  (input)
               SSYR2: Single precision array.
               DSYR2: Double precision array.

     incy      Integer.  (input)
               On entry, incy specifies the increment for the elements of y.
               incy must not be 0.

     a         Array of dimension (lda,n).  (input and output)
               SSYR2: Real array.
               DSYR2: Double precision array.

               Before entry with  uplo='U' or 'u', the leading n-by-n upper
               triangular part of array a must contain the upper triangular
               part of the symmetric matrix and the strictly lower triangular
               part of a is not referenced.  On exit, the upper triangular
               part of the updated matrix overwrites the upper triangular part
               of array a.

               Before entry with uplo='L' or 'l', the leading n-by-n lower
               triangular part of array a must contain the lower triangular
               part of the symmetric matrix and the strictly upper triangular
               part of a is not referenced.  On exit, the lower triangular
               part of the updated matrix overwrites the lower triangular part
               of array a.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the calling
               program.  lda >= MAX(1,n).

NOTES
     SSYR2/DSYR2 is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS).

     When working backward (incx < 0 or incy < 0), this 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)

          Array of dimensions (m,n)     x(m,n)

          Character                     CHARACTER

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

          Single precision              REAL

          Double precision              DOUBLE PRECISION

     C/C++:

          Array dimensioned n           x[n]

          Array of dimensions (m,n)     x[m*n]

          Character                     char

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

          Single precision              float

          Double precision              double

     Note that you can explicitly declare multidimensional C/C++ arrays
     provided that the array dimensions are swapped with respect to the
     Fortran declaration (e.g., x[n][m] in C/C++ versus x(m,n) in Fortran).
     To avoid a compiler type mismatch error in C++ (or a compiler warning
     message in C), however, the array should be cast to a pointer of the
     appropriate type when passed as an argument to a SCSL routine.

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS2(3S), CHER2(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.