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?tbmv

Compute the product of a vector and a triangular band matrix.

, or .

x is a vector including n elements, and A is a triangular band matrix of an n*n unit or a non-unit.

Interface Definition

C interface:

void cblas_stbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, const BLASINT N, const BLASINT K, const float *A, const BLASINT lda, float *X, const BLASINT incX);

void cblas_dtbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, const BLASINT N, const BLASINT K, const double *A, const BLASINT lda, double *X, const BLASINT incX);

void cblas_ctbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, const BLASINT N, const BLASINT K, const void *A, const BLASINT lda, void *X, const BLASINT incX);

void cblas_ztbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, const BLASINT N, const BLASINT K, const void *A, const BLASINT lda, void *X, const BLASINT incX);

Fortran interface:

CALL STBMV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)

CALL DTBMV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)

CALL CTBMV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)

CALL ZTBMV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)

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 matrix A is an upper triangular matrix or a lower triangular matrix.

  • If Uplo = CblasUpper, A is an upper triangular matrix.
  • If Uplo = CblasLower, A is the lower triangular matrix.

Input

TransA

Enumeration type CBLAS_TRANSPOSE

Indicates whether the matrix A is a conventional matrix, a transpose matrix, or a conjugate matrix.

  • If trans = CblasNoTrans, then .
  • If trans = CblasTrans, then .
  • If trans = CblasConjTrans, then .

Input

Diag

Enumeration type CBLAS_DIAG

Indicates whether A is a unit trigonometric matrix.

  • If Diag = CblasUnit, A is a unit triangular matrix.
  • If Diag = CblasNonUnit, A is not a unit triangular matrix.

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

A
  • For stbmv, A is of single-precision floating-point type.
  • For dtbmv, A is of double-precision floating-point type.
  • For ctbmv, A is of single-precision complex number type.
  • For ztbmv, A is of double-precision complex number type.

Triangular band matrix A(lda, n)

Input

lda

Integer

Leading dimension of matrix A. The value of lda must be greater than or equal to (k + 1).

Input

X
  • For stbmv, X is of single-precision floating-point type.
  • For dtbmv, X is of double-precision floating-point type.
  • For ctbmv, X is of single-precision complex number type.
  • For ztbmv, X is of double-precision complex number type.

Vector X. The vector scale is at least (1+(N-1)*abs(incX)).

Input/Output

incX

Integer

Increment for elements in X. The value cannot be 0.

Input

Dependencies

#include "kblas.h"

Examples

C interface:

    int n = 7, k = 3, lda = 5, incx = 1; 
    /** 
     *        |  .    .    .   2.0  2.0  3.0 1.0 | 
     *        |  .    .   2.0  1.0  2.0  4.0 0.0 | 
     *        |  .   2.0  2.0  3.0  4.0  2.0 1.0 | 
     *  A  =  | 1.0  3.0  3.0  3.0  3.0  3.0 3.0 | 
     *        |  .    .    .    .    .    .   .  | 
     */ 
    float a[35] = {0, 0, 0, 1.0, 0, 
                   0, 0, 2.0, 3.0, 0, 
                   0, 2.0, 2.0, 3.0, 0, 
                   2.0, 1.0, 3.0, 3.0, 0, 
                   2.0, 2.0, 4.0, 3.0, 0, 
                   3.0, 4.0, 2.0, 3.0, 0, 
                   1.0, 0.0, 1.0, 3.0, 0}; 
    float x[7] = {2.0, 2.0, 1.0, 2.0, 1.0, 3.0, 4.0}; 
 
    cblas_stbmv(CblasColMajor,CblasUpper, CblasNoTrans, CblasNonUnit, n, k, a, lda, x, incx); 
    /** 
     * Output x = |12.0, 12.0, 20.0, 26.0, 9.0, 13.0, 12.0| 
     */

Fortran interface:

      INTEGER :: N=7, K=3 
      INTEGER :: LDA=5, INCX=1 
      REAL(4) :: A(35), X(7) 
      DATA A/0, 0, 0, 1.0, 0, 
     $       0, 0, 2.0, 3.0, 0, 
     $       0, 2.0, 2.0, 3.0, 0, 
     $       2.0, 1.0, 3.0, 3.0, 0, 
     $       2.0, 2.0, 4.0, 3.0, 0, 
     $       3.0, 4.0, 2.0, 3.0, 0, 
     $       1.0, 0.0, 1.0, 3.0, 0/ 
      DATA X/2.0, 2.0, 1.0, 2.0, 1.0, 3.0, 4.0/ 
      EXTERNAL STBMV 
      CALL STBMV('U', 'N', 'N', N, K, A, LDA, X, INCX) 
 
*     Output X = |12.0, 12.0, 20.0, 26.0, 9.0, 13.0, 12.0|