?hbmv
Compute the product of a vector and a Hermitian band 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 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 |
Indicates the expansion mode of matrix A (upper triangle or lower triangle).
|
Input |
N |
Integer |
Order of the matrix A. N must be greater than or equal to 0. |
Input |
K |
Integer |
Super diagonal order of the matrix A. K must be greater than or equal to 0. |
Input |
alpha |
|
Coefficient. |
Input |
A |
|
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 |
|
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, 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)|