?tbmv
Compute the product of a vector and a triangular band matrix.
That is, 
. x is a vector including n elements, and A is an n*n unit or non-unit triangular band matrix.
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 |
Whether the matrix is in row- or column-major order. |
Input |
Uplo |
Enumeration type CBLAS_UPLO |
Whether matrix A is an upper triangular matrix or a lower triangular matrix.
|
Input |
TransA |
Enumeration type CBLAS_TRANSPOSE |
Whether matrix A is non-transposed, transposed, or conjugated.
|
Input |
Diag |
Enumeration type CBLAS_DIAG |
Whether A is a unit triangular matrix.
|
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 |
A |
|
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 |
|
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 |
Dependency
#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|