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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:
LaTex Math image.
where:
  • op(
    A
    ) is one of op(
    A
    ) =
    A
    , or op(
    A
    ) =
    A
    T
    , or op(
    A
    ) =
    A
    H
  • alpha
    and
    beta
    are scalars
  • A
    is
    m
    x
    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(queue &queue, oneapi::mkl::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(queue &queue, oneapi::mkl::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 matrix
A
. See Data Types for more details.
m
Number of rows of matrix
A
. Must be at least zero.
n
Number of columns of matrix
A
. Must be at least zero.
kl
Number of sub-diagonals of matrix
A
. Must be at least zero.
ku
Number of super-diagonals of matrix
A
. Must be at least zero.
alpha
Scaling factor for the matrix-vector product.
a
Buffer holding input matrix
A
. Size of the buffer must be 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. Size of the buffer must be 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. Size of the buffer must be at least (1 + (
len
- 1)*abs(
incy
)). See Matrix Storage for more details.
incy
Stride of vector
y
.
Output Parameters
y
Buffer holding updated vector
y
.

gbmv (USM Version)

Syntax
namespace oneapi::mkl::blas::column_major { sycl::event gbmv(queue &queue, oneapi::mkl::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(queue &queue, oneapi::mkl::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 matrix
A
. See Data Types for more details.
m
Number of rows of matrix
A
. Must be at least zero.
n
Number of columns of matrix
A
. Must be at least zero.
kl
Number of sub-diagonals of matrix
A
. Must be at least zero.
ku
Number of super-diagonals of matrix
A
. Must be at least zero.
alpha
Scaling factor for the matrix-vector product.
a
Pointer to input matrix
A
. Size of the array must be 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. Size of the array holding input vector
x
must be 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. Size of the array holding input/output vector
y
must be 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 updated vector
y
.
Return Values
Output event to wait on to ensure computation is complete.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.