?tpmv

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

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

x includes a vector of n elements, and A is a triangular matrix obtained by expanding an n*n unit or a non-unit based on a triangle.

Interface Definition

C interface:

void cblas_stpmv(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 *Ap, float *X, const BLASINT incX);

void cblas_dtpmv(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 *Ap, double *X, const BLASINT incX);

void cblas_ctpmv(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 *Ap, void *X, const BLASINT incX);

void cblas_ztpmv(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 *Ap, void *X, const BLASINT incX);

Fortran interface:

CALL STPMV(UPLO, TRANS, DIAG, N, AP, X, INCX)

CALL DTPMV(UPLO, TRANS, DIAG, N, AP, X, INCX)

CALL CTPMV(UPLO, TRANS, DIAG, N, AP, X, INCX)

CALL ZTPMV(UPLO, TRANS, DIAG, N, AP, 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
Ap	For stpmv, Ap is of single-precision floating-point type. For dtpmv, Ap is of double-precision floating-point type. For ctpmv, Ap is of single-precision complex number type. For ztpmv, Ap is of double-precision complex number type.	The size of a compressed triangular matrix is at least (N*(N+1)/2).	Input
X	For stpmv, X is of single-precision floating-point type. For dtpmv, X is of double-precision floating-point type. For ctpmv, X is of single-precision complex number type. For ztpmv, 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}; 
    /** 
     *        |  1.0 1.0  1.0  3.0 | 
     * A   =  |  .   3.0  3.0  2.0 | 
     *        |  .    .   2.0  3.0 | 
     *        |  .    .    .   1.0 | 
     */ 
    float ap[10] = {1.0, 1.0, 3.0, 1.0, 3.0, 2.0, 3.0, 2.0, 3.0, 1.0}; 
 
    cblas_stpmv(CblasColMajor, CblasUpper, CblasTrans, CblasNonUnit, n, ap, x, incx); 
    /** 
     * Output x = |4.0, 13.0, 17.0, 25.0| 
     */

Fortran interface:

      INTEGER :: N=4, INCX=1 
      REAL(4) :: X(4), AP(10) 
      DATA X/4.0, 3.0, 2.0, 1.0/ 
      DATA AP/1.0, 1.0, 3.0, 1.0, 3.0, 2.0, 3.0, 2.0, 3.0, 1.0/ 
      EXTERNAL STPMV 
      CALL STPMV('U', 'T', 'N', N, AP, X, INCX) 
 
*     Output X = |4.0, 13.0, 17.0, 25.0|

Parent topic: KML_BLAS Level 2 Functions