?tbsv
That is, 
, 
, or 
. b and x are vectors including n elements each, and A is an n*n unit/non-unit, upper/lower triangular band matrix.
Interface Definition
C interface:
void cblas_stbsv(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_dtbsv(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_ctbsv(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_ztbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLOUplo, 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 STBSV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CALL DTBSV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CALL CTBSV(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CALL ZTBSV(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.
|
Input |
TransA |
Enumeration type CBLAS_TRANSPOSE |
Indicates whether matrix A is a conventional matrix, a transpose matrix, or a conjugate matrix.
|
Input |
Diag |
Enumeration type CBLAS_DIAG |
Indicates whether A is a unit trigonometric 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] = {12.0, 12.0, 20.0, 26.0, 9.0, 13.0, 12.0};
cblas_stbsv(CblasColMajor, CblasUpper, CblasNoTrans, CblasNonUnit, n, k, a, lda, x, incx);
/**
* Output x = |2.000000 2.000000 1.000000 2.000000 1.000000 3.000000 4.000000|
*/
Fortran interface:
PROGRAM TBMV
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/12.0, 12.0, 20.0, 26.0, 9.0, 13.0, 12.0/
EXTERNAL STBMV
CALL STBSV('U', 'N', 'N', N, K, A, LDA, X, INCX)
WRITE(*,*) X
END
* Output X = |2.00000000, 2.0000000, 1.00000000, 2.00000000, 1.00000000, 3.00000000, 4.00000000|