chpr(3S)

NAME
     CHPR, ZHPR - Performs Hermitian rank 1 update of a packed complex
     Hermitian matrix

SYNOPSIS
     Single precision complex

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

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

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

     Double precision complex

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

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

          C++ STL:
               #include <complex.h>
               #include <scsl_blas.h>
               void zhpr (char uplo, complex<double> *n, 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 Hermitian rank 1 operation:

          A <- alpha xxH + A

     where alpha is a real scalar, x is an n-element vector, xH is the
     conjugate transpose of x, 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 supplied in
               the argument ap.
               uplo= 'L' or 'l': the lower triangular part of A is supplied in
               the argument ap.

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

     alpha     Scalar alpha.  (input)
               CHPR: Real.
               ZHPR: Double precision.

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               CHPR: Single precision complex array.
               ZHPR: 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)
               CHPR: Single precision complex array.
               ZHPR: 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
     CHPR/ZHPR is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS).

     When working backward (incx < 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)


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

          Term Used                     Data type

     Fortran:

          Array dimensioned n           x(n)

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

          Character                     CHARACTER

          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_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.