# tbsv#

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

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) = AT, or op(A) = AH,

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.

tbsv supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## tbsv (Buffer Version)#

Syntax

namespace oneapi::mkl::blas::column_major {
void tbsv(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
onemkl::diag unit_nonunit,
std::int64_t n,
std::int64_t k,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &x,
std::int64_t incx)
}

namespace oneapi::mkl::blas::row_major {
void tbsv(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
onemkl::diag unit_nonunit,
std::int64_t n,
std::int64_t k,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &x,
std::int64_t incx)
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

unit_nonunit

Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes 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 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 Storage for more details.

incx

Stride of vector x.

Output Parameters

x

Buffer holding the solution vector x.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::unimplemented

## tbsv (USM Version)#

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event tbsv(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
onemkl::diag unit_nonunit,
std::int64_t n,
std::int64_t k,
const T *a,
std::int64_t lda,
T *x,
std::int64_t incx,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event tbsv(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
onemkl::diag unit_nonunit,
std::int64_t n,
std::int64_t k,
const T *a,
std::int64_t lda,
T *x,
std::int64_t incx,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

unit_nonunit

Specifies whether the matrix A is unit triangular or not. See oneMKL defined datatypes 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

Pointer to input matrix A. The array holding input matrix A must have size at least lda*n. See Matrix Storage for more details.

lda

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

x

Pointer to input vector x. The array holding input vector x must be of size at least (1 + (n - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

dependencies

List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters

x

Pointer to the solution vector x.

Return Values

Output event to wait on to ensure computation is complete.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::invalid_argument

oneapi::mkl::unsupported_device