?hemv

Compute the product of a vector and a Hermitian matrix, that is, $\text{[math]}$ .

alpha and beta are multiplication coefficients, x and y are vectors including n elements, and A is an n-order Hermitian matrix.

Interface Definition

C interface:

void cblas_chemv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const void *alpha, const void *A, const BLASINT lda, const void *X, const BLASINT incX, const void *beta, void *Y, const BLASINT incY);

void cblas_zhemv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const void *alpha, const void *A, const BLASINT lda, const void *X, const BLASINT incX, const void *beta, void *Y, const BLASINT incY);

Fortran interface:

CALL CHEMV(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

CALL ZHEMV(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

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 whether the upper triangle or the lower triangle of matrix A is used. If Uplo = CblasUpper, the upper triangle of A is used. If Uplo = CblasLower, the lower triangle of A is used.	Input
N	Integer	Order of the matrix A. N must be greater than or equal to zero.	Input
alpha	For chemv, alpha is of single-precision complex number type. For zhemv, alpha is of double-precision complex number type.	Coefficient	Input
A	For chemv, A is of single-precision complex number type. For zhemv, A is of double-precision complex number type.	Hermitian matrix A(lda, n)	Input
lda	Integer	Length of the leading dimension in matrix A. The value of lda must be greater than or equal to (k + 1).	Input
X	For chemv, X is of single-precision complex number type. For zhemv, X is of double-precision complex number type.	Vector X. The vector scale is at least (1+(N-1)*abs(incX)).	Input
incX	Integer	Increment for elements in X. The value cannot be 0.	Input
beta	For chemv, beta is of single-precision complex number type. For zhemv, beta is of double-precision complex number type.	Multiplication coefficient	Input
Y	For chemv, Y is of single-precision complex number type. For zhemv, Y is of double-precision complex number type.	Vector Y. The vector scale is at least (1+(N-1)*abs(incY)).	Input/Output
incY	Integer	Increment for elements in Y. The value cannot be 0.	Input

Dependencies

#include "kblas.h"

Examples

C interface:

    int n = 3, lda = 3; 
    float alpha[2] = {1.0, 0}, beta[2] = {1.0, 0}; 
    int incx = 1, incy = 1; 
    /*            |  (21.0,  * )      *           *      | 
     *      A =   | (1.0, -1.0)  (3.0,  * )       *      | 
     *            |  (1.0, 3.0)  (2.0, 2.0)   (2.0, *  ) | 
     */ 
    float a[18] = {21.0, 0, 1.0, -1.0, 1.0, 3.0, 0, 0, 3.0, 0, 2.0, 2.0, 0, 0, 0, 0, 2.0, 0}; 
    float x[6] = {3.0, 2.0, 1.0, 2.0, -1.0, 1.0}; 
    float y[6] = {1.0, 2.0, 3.0, 2.0, -1.0, 1.0}; 
 
    cblas_chemv(CblasColMajor,CblasLower, n, alpha, a, lda, x, incx, beta, y, incy); 
    /* 
     * Output y = | 65.0, 51.0, 11.0, 11.0, -8.0, 20.0| 
     */

Fortran interface:

      INTEGER :: N=3 
      INTEGER :: LDA=3 
      COMPLEX(4) :: ALPHA=(1.0, 0) 
      COMPLEX(4) :: BETA=(1.0, 0) 
      INTEGER :: INCX=1 
      INTEGER :: INCY=1 
      COMPLEX(4) :: A(3, 3) 
      DATA A/(21.0, 0), (1.0, -1.0), (1.0, 3.0), 
     $       (0, 0), (3.0, 0), (2.0, 2.0), 
     $       (0, 0), (0, 0), (2.0, 0)/ 
 
      COMPLEX(4) :: X(3) 
      DATA X/(3.0, 2.0), (1.0, 2.0), (-1.0, 1.0)/ 
      COMPLEX(4) :: Y(3) 
      DATA Y/(1.0, 2.0), (3.0, 2.0), (-1.0, 1.0)/ 
      EXTERNAL CHEMV 
      CALL CHEMV('L', N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
 
*     Output Y : (65.0, 51.0), (11.0, 11.0), (-8.0, 20.0)

Parent topic: KML_BLAS Level 2 Functions