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?hpr2

Perform a rank-2 update of a Hermitian expansion matrix, that is, .

Where alpha is a multiplication coefficient, x and y are vectors including n elements, and A is an n*n Hermitian matrix.

Interface Definition

C interface:

void cblas_chpr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const void *alpha, const void *X, const BLASINT incX, const void *Y, const BLASINT incY, void *Ap);

void cblas_zhpr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const void *alpha, const void *X, const BLASINT incX, const void *Y, const BLASINT incY, void *Ap);

Fortran interface:

CALL CHPR2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)

CALL ZHPR2(UPLO, N, ALPHA, X, INCX, Y, INCY, 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

Hermitian matrix expansion storage mode (upper triangle expansion or lower triangle expansion)

  • 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 chpr2, alpha is of single-precision complex number type.
  • For zhpr2, alpha is of double-precision complex number type.

Multiplication coefficient

Input

X
  • For chpr2, X is of single-precision complex number type.
  • For zhpr2, 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

Y
  • For cher2, Y is of single-precision complex number type.
  • For zher2, Y is of double-precision complex number type.

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

Input

incY

Integer

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

Input

Ap
  • For chpr2, Ap is of single-precision complex number type.
  • For zhpr2, Ap is of double-precision complex number type.

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

Input/Output

Dependencies

#include "kblas.h"

Examples

C interface:

    int n = 3; 
    float alpha[2] = {1.0, 2.9}; 
    int incx = 1, incy = 1; 
    /** 
     *              |  (2.0, 0.0)  (13.0, 5.0)  (12.0, -13.0) | 
     *         A =  | (13.0, -5.0)  (2.0, 0.0)  (4.0, -18.0)  | 
     *              |  (12.0, 13.0)  (4.0, 18.0)   (1.0, 0.0) | 
     */ 
    float ap[12] = {2.0, 0, 13.0, -5.0, 12.0, 13.0, 2.0, 0, 4.0, 18.0, 1.0, 0}; 
    float x[6] = {2.0, -2.0, 14.0, 1, 3.0, 4.0}; 
    float y[6] = {2.0, -2.0, 14.0, 1, 3.0, 4.0}; 
 
    cblas_chpr2(CblasColMajor, CblasLower, n, alpha, x, incx, y, incy, ap); 
    /** 
     * Output ap = |(18.0, 0.0), (65.0, 55.0), (8.0, 41.0), (396.0, 0.0), (96.0, 124.0), (51.0, 0.0)| 
     */

Fortran interface:

     INTEGER :: N=3 
      COMPLEX(4) :: ALPHA=(1.0, 2.9) 
      INTEGER :: INCX=1, INCY=1 
      COMPLEX(4) :: AP(6), X(3), Y(3) 
      DATA AP/(2.0, 0), (13.0, -5.0), (12.0, 13.0), (2.0, 0), 
     $        (4.0, 18.0), (1.0, 0)/ 
      DATA X/(2.0, -2.0), (14.0, 1), (3.0, 4.0)/ 
      DATA Y/(2.0, -2.0), (14.0, 1), (3.0, 4.0)/ 
      EXTERNAL CHPR2 
      CALL CHPR2('L', N, ALPHA, X, INCX, Y, INCY, AP) 
 
*     Output AP = |(18.0, 0.0), (65.0, 55.0), (8.0, 41.0), (396.0, 0.0), (96.0, 124.0), (51.0, 0.0)|