?trmv

Compute the product of a vector and a triangular matrix.

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

x is a vector that includes n elements, and A is a unit or non-unit triangular matrix of n x n.

Interface Definition

C interface:

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

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

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

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

Fortran interface:

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

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

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

CALL ZTRMV(UPLO, TRANS, DIAG, N, 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 to use the upper triangle or lower triangle of matrix A. If Uplo = CblasUpper, the upper triangle of A is used. If Uplo = CblasLower, the lower triangle of A is used.	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 $\text{[math]}$ . If trans = CblasTrans, then $\text{[math]}$ . If trans = CblasConjTrans, then $\text{[math]}$ .	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
A	For strmv, A is of single-precision floating-point type. For dtrmv, A is of double-precision floating-point type. For ctrmv, A is of single-precision complex number type. For ztrmv, A is of double-precision complex number type.	Triangular matrix. The minimum matrix size is lda*N.	Input
lda	Integer	Leading dimension of matrix A. The value of lda must be greater than or equal to max(1, n).	Input
X	For strmv, X is of single-precision floating-point type. For dtrmv, X is of double-precision floating-point type. For ctrmv, X is of single-precision complex number type. For ztrmv, 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 = 4, incx = 1; 
    float x[4] = {4.0, 3.0, 2.0, 1.0}; 
    /** 
    *          |  .   2.0  1.0  1.0 | 
    *   A   =  |  .    .   1.0  2.0 | 
    *          |  .    .    .   1.0 | 
    *          |  .    .    .    .  | 
    **/ 
    float a[16] = {0, 0, 0, 0, 
                   2.0, 0, 0, 0, 
                   1.0, 1.0, 0, 0, 
                   1.0, 2.0, 1.0, 0}; 
 
    cblas_strmv(CblasColMajor, CblasUpper, CblasTrans, CblasUnit, n, a, 4, x, incx); 
    /** 
    * Output x = |4.0, 11.0, 9.0, 13.0| 
    **/

Fortran interface:

      INTEGER :: N=4, INCX=1 
      REAL(4) :: X(4), AP(16) 
      DATA X/4.0, 3.0, 2.0, 1.0/ 
      DATA A/0, 0, 0, 0, 
     $       2.0, 0, 0, 0, 
     $       1.0, 1.0, 0, 0, 
     $       1.0, 2.0, 1.0, 0/ 
      EXTERNAL STRMV 
      CALL STRMV('U', 'T', 'U', N, A, 4, X, INCX) 
 
*     Output X = |4.0, 11.0, 9.0, 13.0|

Parent topic: KML_BLAS Level 2 Functions