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) = 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.

tbsv supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

T
`float`
`double`
`std::complex<float>`
`std::complex<double>`

tbsv (Buffer Version)#

Syntax

namespace oneapi::math::blas::column_major {
    void tbsv(sycl::queue &queue,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose trans,
              oneapi::math::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::math::blas::row_major {
    void tbsv(sycl::queue &queue,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose trans,
              oneapi::math::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 oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to A. See oneMath defined datatypes for more details.
unit_nonunit: Specifies whether the matrix A is unit triangular or not. See oneMath 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. Must not be zero.

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::math::invalid_argument

oneapi::math::unsupported_device

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

tbsv (USM Version)#

Syntax

namespace oneapi::math::blas::column_major {
    sycl::event tbsv(sycl::queue &queue,
                     oneapi::math::uplo upper_lower,
                     oneapi::math::transpose trans,
                     oneapi::math::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::math::blas::row_major {
    sycl::event tbsv(sycl::queue &queue,
                     oneapi::math::uplo upper_lower,
                     oneapi::math::transpose trans,
                     oneapi::math::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 oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to A. See oneMath defined datatypes for more details.
unit_nonunit: Specifies whether the matrix A is unit triangular or not. See oneMath 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. Must not be zero.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.