sspr(3S)

NAME
     SSPR, DSPR, CSPR, ZSPR - Performs symmetric rank 1 update of a real or
     complex symmetric packed matrix

SYNOPSIS
     Single precision

          Fortran:
               CALL SSPR (uplo, n, alpha, x, incx, ap)

          C/C++:
               #include <scsl_blas.h>
               void sspr (char uplo, float *n, float alpha, int x, int incx,
               float *ap);

     Double precision

          Fortran:
               CALL DSPR (uplo, n, alpha, x, incx, ap)

          C/C++:
               #include <scsl_blas.h>
               void sspr (char uplo, double *n, double alpha, int x, int incx,
               double *ap);

     Single precision complex

          Fortran:
               CALL CSPR (uplo, n, alpha, x, incx, ap)

          C/C++:
               #include <scsl_blas.h>
               void cspr (char uplo, scsl_complex *n, scsl_complex *alpha, int
               x, int incx, scsl_complex *ap);

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void cspr (char uplo, complex<float> *n, complex<float> *alpha,
               int x, int incx, complex<float> *ap);

     Double precision complex

          Fortran:
               CALL ZSPR (uplo, n, alpha, x, incx, ap)

          C/C++:
               #include <scsl_blas.h>
               void zspr (char uplo, int n, scsl_zomplex *alpha, scsl_zomplex
               *x, int incx, scsl_zomplex *ap);
          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void zspr (char uplo, complex<double> *n, complex<double>
               *alpha, int x, int incx, complex<double> *ap);

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 1 operation:

          A <- alpha xxT + A

     where xT  is the transpose of x, alpha is a real or complex scalar, x is
     an n-element vector, and A is an n-by-n symmetric packed matrix.

     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:

     uplo      Character.  (input)
               Specifies whether the upper or lower triangular part of matrix
               A is packed into the array argument ap, as follows:

               uplo= 'U' or 'u':  the upper triangular part of A is being
               supplied in the argument ap.
               uplo= 'L' or 'l':  the lower triangular part of A is being
               supplied in the argument ap.

               For C/C++, a pointer to this character is passed.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.
     alpha     Scalar alpha.  (input)
               SSPR: Single precision.
               DSPR: Double precision.
               CSPR: Single precision complex.
               ZSPR: 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)
               SSPR: Single precision array.
               DSPR: Double precision array.
               CSPR: Single precision complex array.
               ZSPR: Double precision complex array.
               Contains vector x.

     incx      Integer.  (input)
               Specifies the increment for the elements of x.  incx must not
               be 0.

     ap        Array of dimension (n(n+1))/2 .  (input and output)
               SSPR: Single precision array.
               DSPR: Double precision array.
               CSPR: Single precision complex array.
               ZSPR: Double precision complex array.

               Before entry with uplo = 'U' or 'u', array ap must contain the
               upper triangular part of the symmetric matrix packed
               sequentially, column-by-column, so that ap(1) contains A(1,1),
               ap(2) contains A(1,2), ap(3) contains A(2,2), and so on.  On
               exit, the upper triangular part of the updated matrix
               overwrites array ap.

               Before entry with uplo = 'L' or 'l', array ap must contain the
               lower triangular part of the symmetric matrix packed
               sequentially, column-by-column, so that ap(1) contains A(1,1),
               ap(2) contains A(2,1), ap(3) contains A(3,1), and so on.  On
               exit, the lower triangular part of the updated matrix
               overwrites array ap.

NOTES
     SSPR/DSPR is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS).
     CSPR/ZSPR is an extension to Level 2 BLAS.

     When working backward (incx < 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)

   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>

     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), CHPR(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.