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?hpr

Perform a rank-1 update of a triangular expanded Hermitian matrix, that is, .

Where alpha is a scaling coefficient, x is a vector including n elements, and A is a triangularly expanded Hermitian matrix.

Interface Definition

C interface:

void cblas_chpr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const float alpha, const void *X, const BLASINT incX, void *A);

void cblas_zhpr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const double alpha, const void *X,const BLASINT incX, void *A);

Fortran interface:

CALL CHPR(UPLO, N, ALPHA, X, INCX, AP)

CALL ZHPR(UPLO, N, ALPHA, X, INCX, AP)

Parameters

Parameter

Type

Description

Input/Output

order

Enumeration type CBLAS_ORDER

Indicates whether the matrix is in row- or column-major order.

Input

Uplo

Enumeration type CBLAS_UPLO

Expansion storage mode of a Hermitian matrix (upper triangle or lower triangle)

  • If Uplo = CblasUpper, the upper triangle of A is used for expansion.
  • If Uplo = CblasLower, the lower triangle of A is used for expansion.

Input

N

Integer

Number of elements in vector X

Input

alpha
  • For chpr, alpha is of single-precision complex number type.
  • For zhpr, alpha is of double-precision complex number type.

Multiplication coefficient

Input

X
  • For chpr, X is of single-precision complex number type.
  • For zhpr, X is of double-precision complex number type.

Matrix X. The length must be at least 1+(n-1)*abs(incX).

Input

incX

Integer

Increment for elements in vector X. The value cannot be 0.

Input

A
  • For chpr, A is of single-precision complex number type.
  • For zhpr, A is of double-precision complex number type.

Matrix A: The matrix scale is at least (n*(n+1)/2).

Input/Output

Dependencies

#include "kblas.h"

Examples

C interface:

    int n = 3; 
    float alpha = 1.0; 
    int incx = 1; 
    /** 
     *              |  (2.0, 0.0)  (13.0, 5.0)  (12.0, -13.0) | 
     *         A =  | (13.0, -5.0)  (3.0, 0.0)  (4.0, -18.0)  | 
     *              |  (12.0, 13.0)  (4.0, 18.0)   (2.0, 0.0) | 
     */ 
    float ap[12] = {2.0, 0, 13.0, -5.0, 12.0, 13.0, 3.0, 0, 4.0, 18.0, 2.0, 0}; 
    float x[6] = {2.0, -2.0, 14.0, 1, 3.0, 4.0}; 
 
    cblas_chpr(CblasColMajor, CblasLower, n, alpha, x, incx, ap); 
    /** 
     * Output ap = |(10.0, 0.0), (39.0, 25.0), (10.0, 27.0), (200.0, 0.0), (50.0, 71.0), (27.0, 0.0) | 
     */

Fortran interface:

      INTEGER :: N=3 
      REAL(4) :: ALPHA=1.0 
      INTEGER :: INCX=1 
      COMPLEX(4) :: AP(6), X(3) 
      DATA AP/(2.0, 0), (13.0, -5.0), (12.0, 13.0), (3.0, 0), 
     $        (4.0, 18.0), (2.0, 0)/ 
      DATA X/(2.0, -2.0), (14.0, 1), (3.0, 4.0)/ 
      EXTERNAL CHPR 
      CALL CHPR('L', N, ALPHA, X, INCX, AP) 
 
*     Output AP = | (10.0, 0.0), (39.0, 25.0), (10.0, 27.0), (200.0, 0.0), (50.0, 71.0), (27.0, 0.0) |