CHPR(3S)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.
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CHPR(3S)CHPR(3S)
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
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CHPR(3S)CHPR(3S)
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])
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CHPR(3S)CHPR(3S)
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 ALSOINTRO_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.
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