cblas_?tpsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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cblas_?tpsv

Solves a system of linear equations whose coefficients are in a triangular packed matrix.

Syntax

void cblas_stpsv (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n, const float *ap, float *x, const MKL_INT incx);

void cblas_dtpsv (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n, const double *ap, double *x, const MKL_INT incx);

void cblas_ctpsv (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n, const void *ap, void *x, const MKL_INT incx);

void cblas_ztpsv (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const CBLAS_DIAG diag, const MKL_INT n, const void *ap, void *x, const MKL_INT incx);

Include Files

mkl.h

Description

The ?tpsv routines solve one of the following systems of equations

A*x = b, or A'*x = b, or conjg(A')*x = b,

where:

b and x are n-element vectors,

A is an n-by-n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.

This routine does not test for singularity or near-singularity.

Such tests must be performed before calling this routine.

Input Parameters

Layout

Specifies whether two-dimensional array storage is row-major (CblasRowMajor) or column-major (CblasColMajor).

uplo

Specifies whether the matrix A is upper or lower triangular:

uplo = CblasUpper

if uplo = CblasLower, then the matrix is low triangular.

trans

Specifies the system of equations:

if trans=CblasNoTrans, then A*x = b;

if trans=CblasTrans, then A'*x = b;

if trans=CblasConjTrans, then conjg(A')*x = b.

diag

Specifies whether the matrix A is unit triangular:

if diag = CblasUnit then the matrix is unit triangular;

if diag = CblasNonUnit , then the matrix is not unit triangular.

n

Specifies the order of the matrix A. The value of n must be at least zero.

ap

Array, size at least ((n*(n + 1))/2).

For Layout = CblasColMajor:

Before entry with uplo = CblasUpper, the array ap must contain the upper triangular part of the triangular matrix packed sequentially, column-by-column, so that ap[0] contains A_{1, 1}, ap[1] and ap[2] contain A_{1, 2} and A_{2, 2} respectively, and so on.

Before entry with uplo = CblasLower, the array ap must contain the lower triangular part of the triangular matrix packed sequentially, column-by-column, so that ap[0] contains A_{1, 1}, ap[1] and ap[2] contain A_{2, 1} and A_{3, 1} respectively, and so on.

For Layout = CblasRowMajor:

Before entry with uplo = CblasUpper, the array ap must contain the upper triangular part of the triangular matrix packed sequentially, row-by-row, ap[0] contains A_{1, 1}, ap[1] and ap[2] contain A_{1, 2} and A_{1, 3} respectively, and so on. Before entry with uplo = CblasLower, the array ap must contain the lower triangular part of the triangular matrix packed sequentially, row-by-row, so that ap[0] contains A_{1, 1}, ap[1] and ap[2] contain A_{2, 1} and A_{2, 2} respectively, and so on.

When diag = CblasUnit, the diagonal elements of a are not referenced, but are assumed to be unity.

x

Array, size at least (1 + (n - 1)*abs(incx)). Before entry, the incremented array x must contain the n-element right-hand side vector b.

incx

Specifies the increment for the elements of x.

The value of incx must not be zero.

Output Parameters

x: Overwritten with the solution vector x.

Parent topic: BLAS Level 2 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

cblas_?tpsv