?hemv
Compute the product of a vector and a Hermitian matrix.
That is, 
. alpha and beta are multiplication coefficients, x and y are vectors including n elements each, 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 the matrix A is used.
|
Input |
N |
Integer |
Order of the matrix A. N must be greater than or equal to 0. |
Input |
alpha |
|
Coefficient. |
Input |
A |
|
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 |
|
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 |
|
Multiplication coefficient. |
Input |
Y |
|
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 |
Dependency
#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)