?gbmv

Compute the product of a vector and a band matrix.

That is, $\text{[math]}$ , $\text{[math]}$ , or $\text{[math]}$ .

For the Fortran interface, $\text{[math]}$ , $\text{[math]}$ , or $\text{[math]}$ .

alpha and beta are multiplication coefficients, x and y are vectors, and A is a band matrix of m*n.

Interface Definition

C interface:

void cblas_sgbmv(const enum CBLAS_ORDER order, const enum CBLAS_TRANSPOSE TransA, const BLASINT M, const BLASINT N, const BLASINT KL, const BLASINT KU, const float alpha, const float *A, const BLASINT lda, const float *X, const BLASINT incX, const float beta, float *Y, const BLASINT incY);

void cblas_dgbmv(const enum CBLAS_ORDER order, const enum CBLAS_TRANSPOSE TransA, const BLASINT M, const BLASINT N, const BLASINT KL, const BLASINT KU, const double alpha, const double *A, const BLASINT lda, const double *X, const BLASINT incX, const double beta, double *Y, const BLASINT incY);

void cblas_cgbmv(const enum CBLAS_ORDER order, const enum CBLAS_TRANSPOSE TransA, const BLASINT M, const BLASINT N, const BLASINT KL, const BLASINT KU, 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_zgbmv(const enum CBLAS_ORDER order, const enum CBLAS_TRANSPOSE TransA, const BLASINT M, const BLASINT N, const BLASINT KL, const BLASINT KU, 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 SGBMV(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

CALL DGBMV(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

CALL CGBMV(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)

CALL ZGBMV(TRANS, M, N, KL, KU, 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
TransA	Enumeration type CBLAS_TRANSPOSE	Indicates whether matrix A is a conventional matrix, a transpose matrix, or a conjugate matrix. If TransA = CblasNoTrans, then $\text{[math]}$ . If TransA = CblasTrans, then $\text{[math]}$ . If TransA = CblasConjTrans, then $\text{[math]}$ . For the Fortran interface: If TransA = R, $\text{[math]}$ . If TransA = S, $\text{[math]}$ . If TransA = D, $\text{[math]}$ .	Input
M	Integer	Number of rows in matrix A. The value of M must be greater than or equal to 0.	Input
N	Integer	Number of columns of matrix A. The value of N must be greater than or equal to 0.	Input
KL	Integer	Subdiagonal order of A. The value of KL must be greater than or equal to 0.	Input
KU	Integer	Hyperdiagonal order of A. The value of KU must be greater than or equal to 0.	Input
alpha	Single-precision floating-point type for sgbmv Double-precision floating-point type for dgbmv Single-precision complex type for cgbmv Double-precision complex type for zgbmv	Multiplication coefficient.	Input
A	Single-precision floating-point type for sgbmv Double-precision floating-point type for dgbmv Single-precision complex type for cgbmv Double-precision complex type for zgbmv	Band matrix. The matrix size is lda*N.	Input
lda	Integer	Length of the leading dimension in matrix A. The value of lda must be greater than or equal to (KL + KU + 1).	Input
X	Single-precision floating-point type for sgbmv Double-precision floating-point type for dgbmv Single-precision complex type for cgbmv Double-precision complex type for zgbmv	Vector X. If TransA = CblasNoTrans, the vector size is at least (1+(N-1)abs(incX)). Otherwise, the vector size must be at least (1+(M-1)abs(incX)).	Input
incX	Integer	Increment for elements in X. The value cannot be 0.	Input
beta	Single-precision floating-point type for sgbmv Double-precision floating-point type for dgbmv Single-precision complex type for cgbmv Double-precision complex type for zgbmv	Multiplication coefficient.	Input
Y	Single-precision floating-point type for sgbmv Double-precision floating-point type for dgbmv Single-precision complex type for cgbmv Double-precision complex type for zgbmv	Vector Y. If TransA = CblasNoTrans, the vector size is at least (1+(M-1)abs(incY)). Otherwise, the vector size 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 m = 5, n = 4; 
    float alpha = 2.0; 
    /** 
     *        |  .    .   2.0  2.0 | 
     *        |  .   1.0  2.0  3.0 | 
     *        | 1.0  2.0  2.0  4.0 | 
     *  A  =  | 1.0  3.0  2.0  5.0 | 
     *        | 1.0  4.0  2.0   .  | 
     *        | 1.0  5.0   .    .  | 
     *        |  .    .    .    .  | 
     *        |  .    .    .    .  | 
     */ 
    float a[32] = {0, 0, 1.0, 1.0, 1.0, 1.0, 0, 0, 
                   0, 1.0, 2.0, 3.0, 4.0, 5.0, 0, 0, 
                   2.0, 2.0, 2.0, 2.0, 2.0, 0, 0, 0, 
                   2.0, 3.0, 4.0, 5.0, 0, 0, 0, 0}; 
    float x[4] = {2.0, 2.0, 3.0, 4.0}; 
    float y[5] = {1.0, 1.0, 13.0, 4.0, 5.0}; 
 
    cblas_sgbmv(CblasColMajor,CblasNoTrans, m, n, 3, 2, alpha, a, 8, x, 1, 10.0, y, 1); 
    /** 
     *  Ouput y: 30.0, 50.0, 182.0, 104.0, 122.0 
     */

Fortran interface:

      INTEGER :: M=5 
      INTEGER :: N=4 
      REAL(4) :: ALPHA=2.0 
      REAL(4) A(8, 4) 
      DATA A /0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 3, 4, 5, 0, 0, 
              2, 2, 2, 2, 2, 0, 0, 0, 2, 3, 4, 5, 0, 0, 0, 0/ 
      REAL(4) X(4) 
      DATA X /2, 2, 3, 4/ 
      REAL(4) Y(5) 
      DATA Y /1, 1, 13, 4, 5/ 
      CALL SGBMV('N', M, N, 3, 2, ALPHA, A, 8, X, 1, 10, Y, 1) 
 
*     Ouput y: 20.0       40.0       52.0       64.0       72.0

Parent topic: KML_BLAS Level 2 Functions