?tpsv

Solve linear equations. The coefficient matrix is a triangular matrix expanded according to the triangle.

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

b and x are vectors including n elements, and A is a triangular matrix of n*n units or non-units expanded according to a triangle.

Interface Definition

C interface:

void cblas_stpsv(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_dtpsv(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_ctpsv(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_ztpsv(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 STPSV(UPLO, TRANS, DIAG, N, AP, X, INCX)

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

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

CALL ZTPSV(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	Storage expansion mode of matrix A (upper triangle or lower triangle) If Uplo = CblasUpper, the upper triangle of A is used for expansion. If Uplo = CblasLower, the lower triangle of A is used for expansion.	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 stpsv, Ap is of single-precision floating-point type. For dtpsv, Ap is of double-precision floating-point type. For ctpsv, Ap is of single-precision complex number type. For ztpsv, 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 stpsv, X is of single-precision floating-point type. For dtpsv, X is of double-precision floating-point type. For ctpsv, X is of single-precision complex number type. For ztpsv, X is of double-precision complex number type.	Vector X. The vector scale is at least (1+(N-1)*abs(incX)). The output is updated after the equation is solved.	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_stpsv(CblasColMajor, CblasUpper, CblasTrans, CblasNonUnit, n, ap, x, incx); 
    /** 
     * Output x = |4.000000, -0.333333, -0.500000, -8.833333| 
     */

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 STPSV 
      CALL STPSV('U', 'T', 'N', N, AP, X, INCX) 
 
*     Output X = |4.000000, -0.333333, -0.500000, -8.833333|

Parent topic: KML_BLAS Level 2 Functions