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?her

That is, . A is an n*n Hermitian matrix, alpha is a multiplication coefficient, and x is a vector with n elements.

Interface Definition

C interface:

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

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

Fortran interface:

CALL CHER(UPLO, N, ALPHA, X, INCX, A, LDA)

CALL ZHER(UPLO, N, ALPHA, X, INCX, A, LDA)

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

Indicates the storage mode of the 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
  • Single-precision floating-point type for cher
  • Double-precision floating-point type for zher

Multiplication coefficient.

Input

X
  • Single-precision complex type for cher
  • Double-precision complex type for zher

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
  • Single-precision complex type for cher
  • Double-precision complex type for zher

Matrix A (lda, n).

Output

lda

Integer

Length of the main dimension of matrix A. The value of lda must be greater than or equal to max(1, n).

Input

Dependency

#include "kblas.h"

Examples

C interface:
    int n = 3; 
    float alpha = 2.9; 
    int incx = 1; 
    /** 
     *              |  (1.0, 0.0)  (13.0, 5.0)  (12.0, 0) | 
     *         A =  | (13.0, -5.0)  (2.0, 0.0)  (4.0, -18.0) | 
     *              |  (12.0, 0)  (4.0, 18.0)   (3.0, 0.0) | 
     */ 
    float ap[18] = {1.0, 0, 13.0, -5.0, 12.0, 0, 13.0, 5.0, 2.0, 0, 4.0, 18.0, 12.0, 0, 4.0, -18.0, 3.0, 0}; 
    float x[6] = {2.0, -2.0, 14.0, 1, 3.0, 4.0}; 
 
    cblas_cher(CblasColMajor, CblasLower, n, alpha, x, incx, ap, 3); 
    /** 
     *             | (24.200001, 0.000000)  (13.000000   5.000000)     (12.000000  0.000000)  | 
     * Output  A = | (88.400002, 82.000000) (573.300049  0.000000)     (4.000000   -18.000000)| 
     *             | (6.200001, 40.600002)  (137.400009  171.700012)   (75.500000   0.000000) |

     */

Fortran interface:

      INTEGER :: N=3 
      REAL(4) :: ALPHA=2.9 
      INTEGER :: INCX=1 
      COMPLEX(4) :: AP(3, 3) 
      DATA AP/(1.0, 0), (13.0, -5.0), (12.0, 0), (13.0, 5.0), (2.0, 0), (4.0, 18.0), (12.0, 0), (4.0, -18.0), (3.0, 0)/ 
      COMPLEX(4) :: X(3) 
      DATA X/(2.0, -2.0), (14.0, 1), (3.0, 4.0)/ 
      EXTERNAL CHER 
      CALL CHER('L', N, ALPHA, X, INCX, AP, LDA) 
 
*                 | (24.200001, 0.000000)  (13.000000   5.000000)     (12.000000  0.000000)  | 
*     Output  A = | (88.400002, 82.000000) (573.300049  0.000000)     (4.000000   -18.000000)| 
*                 | (6.200001, 40.600002)  (137.400009  171.700012)   (75.500000   0.000000) |