.rst .pdf

tbsv

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

Syntax

void tbsv(queue &exec_queue, uplo upper_lower, transpose trans, diag unit_nonunit, std::int64_t n, std::int64_t k, buffer<T, 1> &a, std::int64_t lda, buffer<T, 1> &x, std::int64_t incx)

tbsv supports the following precisions and devices.

T	Devices Supported
float	Host, CPU, and GPU
double	Host, CPU, and GPU
std::complex<float>	Host, CPU, and GPU
std::complex<double>	Host, CPU, and GPU

Description

The tbsv routines solve a system of linear equations whose coefficients are in a triangular band matrix. The operation is defined as

op(A)*x = b

where:

op(A) is one of op(A) = A, or op(A) = A^T, or op(A) = A^H,

A is an n-by-n unit or non-unit, upper or lower triangular band matrix, with (k + 1) diagonals,

b and x are vectors of length n.

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See Data Types for more details.

trans

Specifies op(A), the transposition operation applied to A. See Data Types for more details.

unit_nonunit

Specifies whether the matrix A is unit triangular or not. See Data Types for more details.

n

Number of rows and columns of A. Must be at least zero.

k

Number of sub/super-diagonals of the matrix A. Must be at least zero.

a

Buffer holding input matrix A. Must have size at least lda*n. See Matrix and Vector Storage for more details.

lda

Leading dimension of matrix A. Must be at least (k + 1), and positive.

x

Buffer holding input vector x. The buffer must be of size at least (1 + (n - 1)*abs(incx)). See Matrix and Vector Storage for more details.

incx

Stride of vector x.

Output Parameters

x

Buffer holding the solution vector x.

tbmv (USM Version) tbsv (USM Version)