chpr2(3S)

NAME
     CHPR2, ZHPR2 - Performs Hermitian rank 2 update of a packed complex
     Hermitian matrix

SYNOPSIS
     Single precision complex

          Fortran:
               CALL CHPR2 (uplo, n, alpha, x, incx, y, incy, ap)

          C/C++:
               #include <scsl_blas.h>
               void chpr2 (char uplo, scsl_complex *n, scsl_complex *alpha,
               scsl_complex *x, int incx, scsl_complex *y, int incy,
               scsl_complex *ap);

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void chpr2 (char uplo, complex<float> *n, complex<float>
               *alpha, complex<float> *x, int incx, complex<float> *y, int
               incy, complex<float> *ap);

     Double precision complex

          Fortran:
               CALL ZHPR2 (uplo, n, alpha, x, incx, y, incy, ap)

          C/C++:
               #include <scsl_blas.h>
               void zhpr2 (char uplo, scsl_zomplex *n, scsl_zomplex *alpha,
               scsl_zomplex *x, int incx, scsl_zomplex *y, int incy,
               scsl_zomplex ap);

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void zhpr2 (char uplo, complex<double> *n, complex<double>
               *alpha, complex<double> *x, int incx, complex<double> *y, int
               incy, 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 Hermitian rank 2 operation:

          A  <- alpha xyH + (complex conjugate of alpha)* yxH + A

     where alpha is a scalar, x and y are n-element vectors, xH and yH
     conjugate transposes of x and y, respectively, and A is an n-by-n packed
     complex Hermitian 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).
               CHPR2: Single precision complex.
               ZHPR2: Double precision complex.

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

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               CHPR2: Single precision complex array.
               ZHPR2: Double precision complex array.
               Contains vector x.

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

     y         Array of dimension 1+(n-1) * |incy|.  (input)
               CHPR2: Single precision complex array.
               ZHPR2: Double precision complex array.
               Contains vector y.

     incy      Integer.  (input)
               Increment for the elements of y.  Argument incy must not be 0.

     ap        Array of dimension (n(n+1))/2 .  (input and output)
               CHPR2: Single precision complex array.
               ZHPR2: Double precision complex array.

               Before entry with uplo = 'U' or 'u', array ap must contain the
               upper triangular part of the Hermitian 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 Hermitian 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.

               The imaginary parts of the diagonal elements need not be set.
               They are assumed to be 0; on exit, they are set to 0.

NOTES
     CHPR2/ZHPR2 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)

          Character                     CHARACTER

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

          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 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 complex      complex<float>

          Double precision complex      complex<double>

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