?hbmv

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

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

Interface Definition

C interface:

void cblas_chbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const BLASINT K, 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_zhbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const BLASINT K, 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 CHBMV(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

CALL ZHBMV(UPLO, N, K, 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	Expansion mode of matrix A (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	Order of the matrix A. N must be greater than or equal to zero.	Input
K	Integer	Super diagonal order of the matrix A. K must be greater than or equal to zero.	Input
alpha	For chbmv, alpha is of single-precision complex number type. For zhbmv, alpha is of double-precision complex number type.	Coefficient	Input
A	For chbmv, A is of single-precision complex number type. For zhbmv, A is of double-precision complex number type.	Hermitian band matrix A(lda, n)	Input
lda	Integer	Length of the main dimension in matrix A. The value of lda must be greater than or equal to (k + 1).	Input
X	For chbmv, X is of single-precision complex number type. For zhbmv, 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 chbmv, beta is of single-precision complex number type. For zhbmv, beta is of double-precision complex number type.	Multiplication coefficient	Input
Y	For chbmv, Y is of single-precision complex number type. For zhbmv, 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, k = 1, lda = 3; 
    float alpha[2] = {1.0, 0}, beta[2] = {1.0, 0}; 
    int incx = 1, incy = 1; 
    /* 
     *            | 1.0, 0.0  7.0, 0.0, 6.0, 0 | 
     *      ap =  | 3.0,-5.0  4.0, 8.0     *   | 
     *            |    *         *         *   | 
     */ 
    float ap[18] = {1.0, 0, 3.0, -5.0, 0, 0, 7.0, 0, 4.0, 8.0, 0.0, 0.0, 6.0, 0, 0, 0, 0, 0}; 
    float x[6] = {3.0, 0.0, 2.0, 0.0, 1.0, 0.0}; 
    float y[6] = {1.0, 0.0, 2.0, 0.0, 3.0, 0.0}; 
 
    cblas_chbmv(CblasColMajor,CblasLower, n, k, alpha, ap, lda, x, incx, beta, y, incy); 
    /* 
     * Output y = | 10.0, 10.0, 29.0, -23.0, 17.0, 16.0| 
     */

Fortran interface:

      INTEGER :: N=3 
      INTEGER :: K=1 
      INTEGER :: LDA=3 
      COMPLEX(4) :: ALPHA=(1.0, 0.0) 
      COMPLEX(4) :: BETA=(1.0, 0.0) 
      INTEGER :: INCX=1 
      INTEGER :: INCY=1 
      COMPLEX(4) :: A(3, 3) 
      DATA A/(1.0, 0), (3.0, -5.0), (0, 0), 
     $       (7.0, 0), (4.0, 8.0), (0.0, 0.0), 
     $       (6.0, 0), (0, 0), (0, 0)/ 
      COMPLEX(4) :: X(3), Y(3) 
      DATA X/(3.0, 0.0), (2.0, 0.0), (1.0, 0.0)/ 
      DATA Y/(1.0, 0.0), (2.0, 0.0), (3.0, 0.0)/ 
      EXTERNAL CHBMV 
      CALL CHBMV('L', N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) 
 
*     Output Y = | (10.0000000, 10.0000000) (29.0000000, -23.0000000) (17.0000000, 16.0000000)|

Parent topic: KML_BLAS Level 2 Functions