gbmv

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

Syntax

void gbmv(queue &exec_queue, transpose trans, std::int64_t m, std::int64_t n, std::int64_t kl, std::int64_t ku, T alpha, buffer<T, 1> &a, std::int64_t lda, buffer<T, 1> &x, std::int64_t incx, T beta, buffer<T, 1> &y, std::int64_t incy)

gbmv supports the following precisions and devices.

T

Devices Supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

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 <- 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.

Input Parameters

exec_queue

The queue where the routine should be executed.

trans

Specifies op(A), the transposition operation applied to A. See Data Types 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

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.

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 and Vector 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 and Vector Storage for more details.

incy

Stride of vector y.

Output Parameters

y

Buffer holding the updated vector y.