tbsv

Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference

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ID 772045

Date 12/16/2022

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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:

where:

op(A) is one of op(A) = A, or op(A) = A^T, or op(A) = A^H
A is n x 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,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::transpose trans,
              oneapi::mkl::diag unit_diag,
              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,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::transpose trans,
              oneapi::mkl::diag unit_diag,
              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 matrix A is upper or lower triangular. See Data Types for more details.
trans: Specifies op(A), the transposition operation applied to matrix A. See Data Types for more details.
unit_diag: Specifies whether matrix A is unit triangular or not. See Data Types for more details.
n: Number of rows and columns of matrix A. Must be at least zero.
k: Number of sub/super-diagonals of matrix A. Must be at least zero.
a: Buffer holding input matrix A. Size of the buffer must be 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. Size of the buffer must be at least (1 + (n - 1)*abs(incx)). See Matrix Storage for more details.
incx: Stride of vector x.

Output Parameters

x: Buffer holding solution vector x.

tbsv (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event tbsv(sycl::queue &queue,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     oneapi::mkl::diag unit_diag,
                     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,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     oneapi::mkl::diag unit_diag,
                     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 matrix A is upper or lower triangular. See Data Types for more details.
trans: Specifies op(A), the transposition operation applied to matrix A. See Data Types for more details.
unit_diag: Specifies whether matrix A is unit triangular or not. See Data Types for more details.
n: Number of rows and columns of matrix A. Must be at least zero.
k: Number of sub/super-diagonals of matrix A. Must be at least zero.
a: Pointer to input matrix A. Size of the array holding input matrix A must be 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. Size of the array holding input vector x must be 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 solution vector x.

Return Values

Output event to wait on to ensure computation is complete.

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Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference

tbsv

Description

tbsv (Buffer Version)

tbsv (USM Version)