# gbmv¶

Computes a matrix-vector product with a general band matrix.

Description

The gbmv routines compute a scalar-matrix-vector product and add the result to a scalar-vector product, with a general band matrix. The operation is defined as

$y \leftarrow alpha*op(A)*x + beta*y$

where:

op(A) is one of op(A) = A, or op(A) = AT, or op(A) = AH,

alpha and beta are scalars,

A is an m-by-n matrix with kl sub-diagonals and ku super-diagonals,

x and y are vectors.

gbmv supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## gbmv (Buffer Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
void gbmv(sycl::queue &queue,
onemkl::transpose trans,
std::int64_t m,
std::int64_t n,
std::int64_t kl,
std::int64_t ku,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &x,
std::int64_t incx,
T beta,
sycl::buffer<T,1> &y,
std::int64_t incy)
}

namespace oneapi::mkl::blas::row_major {
void gbmv(sycl::queue &queue,
onemkl::transpose trans,
std::int64_t m,
std::int64_t n,
std::int64_t kl,
std::int64_t ku,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &x,
std::int64_t incx,
T beta,
sycl::buffer<T,1> &y,
std::int64_t incy)
}


Input Parameters

queue

The queue where the routine should be executed.

trans

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

m

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

n

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

kl

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

ku

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

alpha

Scaling factor for the matrix-vector product.

a

Buffer holding input matrix A. Must have size at least lda*n if column major layout is used or at least lda*m if row major layout is used. See Matrix Storage for more details.

lda

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

x

Buffer holding input vector x. The length len of vector x is n if A is not transposed, and m if A is transposed. The buffer must be of size at least (1 + (len - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

beta

Scaling factor for vector y.

y

Buffer holding input/output vector y. The length len of vector y is m, if A is not transposed, and n if A is transposed. The buffer must be of size at least (1 + (len - 1)*abs(incy)) where len is this length. See Matrix Storage for more details.

incy

Stride of vector y.

Output Parameters

y

Buffer holding the updated vector y.

## gbmv (USM Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event gbmv(sycl::queue &queue,
onemkl::transpose trans,
std::int64_t m,
std::int64_t n,
std::int64_t kl,
std::int64_t ku,
T alpha,
const T *a,
std::int64_t lda,
const T *x,
std::int64_t incx,
T beta,
T *y,
std::int64_t incy,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event gbmv(sycl::queue &queue,
onemkl::transpose trans,
std::int64_t m,
std::int64_t n,
std::int64_t kl,
std::int64_t ku,
T alpha,
const T *a,
std::int64_t lda,
const T *x,
std::int64_t incx,
T beta,
T *y,
std::int64_t incy,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

trans

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

m

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

n

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

kl

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

ku

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

alpha

Scaling factor for the matrix-vector product.

a

Pointer to input matrix A. The array holding input matrix A must have size at least lda*n if column major layout is used or at least lda*m if row major layout is used. See Matrix Storage for more details.

lda

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

x

Pointer to input vector x. The length len of vector x is n if A is not transposed, and m if A is transposed. The array holding input vector x must be of size at least (1 + (len - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

beta

Scaling factor for vector y.

y

Pointer to input/output vector y. The length len of vector y is m, if A is not transposed, and n if A is transposed. The array holding input/output vector y must be of size at least (1 + (len - 1)*abs(incy)) where len is this length. See Matrix Storage for more details.

incy

Stride of vector y.

dependencies

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

Output Parameters

y

Pointer to the updated vector y.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: BLAS Level 2 Routines