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tbmv

Computes a matrix-vector product using a triangular band matrix.

Description

The tbmv routines compute a matrix-vector product with 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

• x is a vector of length n

tbmv supports the following precisions:

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

tbmv (Buffer Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    void tbmv(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 tbmv(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

Numbers 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 updated vector x.

tbmv (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event tbmv(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 tbmv(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

Numbers 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 updated vector x.

Return Values

Output event to wait on to ensure computation is complete.

syr2 tbsv