spmv

spmv#

Computes a sparse matrix by dense vector product.

Description and Assumptions

The oneapi::math::sparse::spmv routine computes a sparse matrix by dense vector product defined as:

\[y \leftarrow \alpha \cdot \text{op}(A) \cdot x + \beta \cdot y\]

where:

\(\alpha\) and \(\beta\) are scalars,
\(x\) is a dense vector of size n,
\(y\) is a dense vector of size m,
\(\text{op}(A)\) is a transformed sparse matrix of size m-by-n,
\(\text{op}()\) is the transform operation using the following description:

\[\begin{split}\text{op}(A) = \begin{cases} A,& \text{oneapi::math::transpose::nontrans}\\ A^\mathsf{T},& \text{oneapi::math::transpose::trans}\\ A^\mathsf{H},& \text{oneapi::math::transpose::conjtrans} \end{cases}\end{split}\]

spmv_descr#

Definition

namespace oneapi::math::sparse {

    struct spmv_descr;
    using spmv_descr_t = spmv_descr*;

}

Description

Defines spmv_descr_t as an opaque pointer to the incomplete type spmv_descr. Each backend may provide a different implementation of the type spmv_descr. The spmv_descr_t object persists through the various stages of the spmv operation to house relevant state, optimizations and workspaces.

init_spmv_descr#

Syntax

namespace oneapi::math::sparse {

    void init_spmv_descr (sycl::queue                       &queue,
                          oneapi::math::sparse::spmv_descr_t *p_spmv_descr);

}

Input parameters

queue: The SYCL command queue which will be used for SYCL kernels execution.
p_spmv_descr: The address of the p_spmv_descr object to be initialized. Must only be called on an uninitialized spmv_descr_t object.

Output parameters

p_spmv_descr: On return, the address is updated to point to a newly allocated and initialized spmv_descr_t object that can be used to perform spmv.

Throws

This function shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::math::host_bad_alloc
oneapi::math::invalid_argument
oneapi::math::unimplemented
oneapi::math::unsupported_device

release_spmv_descr#

Syntax

namespace oneapi::math::sparse {

    sycl::event release_spmv_descr (sycl::queue                       &queue,
                                    oneapi::math::sparse::spmv_descr_t spmv_descr,
                                    const std::vector<sycl::event>    &dependencies = {});

}

Input parameters

queue: The SYCL command queue which will be used for SYCL kernels execution.
spmv_descr: Descriptor initialized with init_spmv_descr.
dependencies: List of events to depend on before starting asynchronous tasks that access data on the device. Defaults to no dependencies.

Return Values

Output event that can be waited upon or added as a dependency for the completion of the function.

Throws

This function shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::math::invalid_argument
oneapi::math::unimplemented
oneapi::math::unsupported_device

spmv_alg#

Syntax

namespace oneapi::math::sparse {

    enum class spmv_alg {
        default_alg,
        no_optimize_alg,
        coo_alg1,
        coo_alg2,
        csr_alg1,
        csr_alg2,
        csr_alg3,
    };

}

Description

These algorithm enums are provided in case backends would like to implement various different algorithms for the operation. Behavior of the algorithms (e.g., bitwise reproducibility, atomics usage) and the preconditions to using specific algorithms (e.g. sortedness of matrix arrays) is implementation-defined and must be documented in the library implementing the oneAPI specification.

spmv#

Syntax

namespace oneapi::math::sparse {

    void spmv_buffer_size(
        sycl::queue                                &queue,
        oneapi::math::transpose                     opA,
        const void*                                alpha,
        oneapi::math::sparse::matrix_view           A_view,
        oneapi::math::sparse::matrix_handle_t       A_handle,
        oneapi::math::sparse::dense_vector_handle_t x_handle,
        const void*                                beta,
        oneapi::math::sparse::dense_vector_handle_t y_handle,
        oneapi::math::sparse::spmv_alg              alg,
        oneapi::math::sparse::spmv_descr_t          spmv_descr,
        std::size_t                                &temp_buffer_size);

    void spmv_optimize(
        sycl::queue                                &queue,
        oneapi::math::transpose                     opA,
        const void*                                alpha,
        oneapi::math::sparse::matrix_view           A_view,
        oneapi::math::sparse::matrix_handle_t       A_handle,
        oneapi::math::sparse::dense_vector_handle_t x_handle,
        const void*                                beta,
        oneapi::math::sparse::dense_vector_handle_t y_handle,
        oneapi::math::sparse::spmv_alg              alg,
        oneapi::math::sparse::spmv_descr_t          spmv_descr,
        sycl::buffer<std::uint8_t, 1>              workspace);

    sycl::event spmv_optimize(
        sycl::queue                                &queue,
        oneapi::math::transpose                     opA,
        const void*                                alpha,
        oneapi::math::sparse::matrix_view           A_view,
        oneapi::math::sparse::matrix_handle_t       A_handle,
        oneapi::math::sparse::dense_vector_handle_t x_handle,
        const void*                                beta,
        oneapi::math::sparse::dense_vector_handle_t y_handle,
        oneapi::math::sparse::spmv_alg              alg,
        oneapi::math::sparse::spmv_descr_t          spmv_descr,
        void*                                      workspace,
        const std::vector<sycl::event>             &dependencies = {});

    sycl::event spmv(
        sycl::queue                                &queue,
        oneapi::math::transpose                     opA,
        const void*                                alpha,
        oneapi::math::sparse::matrix_view           A_view,
        oneapi::math::sparse::matrix_handle_t       A_handle,
        oneapi::math::sparse::dense_vector_handle_t x_handle,
        const void*                                beta,
        oneapi::math::sparse::dense_vector_handle_t y_handle,
        oneapi::math::sparse::spmv_alg              alg,
        oneapi::math::sparse::spmv_descr_t          spmv_descr,
        const std::vector<sycl::event>             &dependencies = {});

}

Notes

spmv_buffer_size and spmv_optimize must be called at least once before spmv with the same arguments. spmv can then be called multiple times. Calling spmv_optimize on the same descriptor can reset some of the descriptor’s data such as the workspace.
In the general case, not calling the functions in the order specified above is undefined behavior. Not calling spmv_buffer_size or spmv_optimize at least once with a given descriptor will throw an oneapi::math::uninitialized exception. Calling spmv with arguments not matching spmv_optimize will throw a oneapi::math::invalid_argument exception, unless stated otherwise.
The data of the dense handles x_handle and y_handle and the scalars alpha and beta can be reset before each call to spmv. Changing the data of the sparse handle A_handle is undefined behavior.
The data must be available on the device when calling spmv_optimize by using event dependencies if needed.
spmv_optimize and spmv are asynchronous.
The algorithm defaults to spmv_alg::default_alg if a backend does not support the provided algorithm.
The container type of all the handles and workspace must be consistent and use either USM pointers or SYCL buffers.

Input Parameters

queue

The SYCL command queue which will be used for SYCL kernels execution.

opA

Specifies operation op() on the input matrix. The possible options are described in transpose enum class.

alpha

Host or USM pointer representing \(\alpha\). The USM allocation can be on the host or device. The requirements are:

Must use the same kind of memory as beta.
Must be a host pointer if SYCL buffers are used.
Must be of the same type as the handles’ data type.

A_view

Specifies which part of the handle should be read as described by matrix_view. The type_view field cannot be matrix_descr::diagonal. The diag_view field can be diag::unit if and only if type_view is matrix_descr::triangular.

A_handle

Sparse matrix handle object representing \(A\).

x_handle

Dense vector handle object representing \(x\).

beta

Host or USM pointer representing \(\beta\). The USM allocation can be on the host or device. The requirements are:

Must use the same kind of memory as alpha.
Must be a host pointer if SYCL buffers are used.
Must be of the same type as the handles’ data type.

y_handle

Dense vector handle object representing \(y\).

alg

Specifies the spmv algorithm to use.

spmv_descr

Initialized spmv descriptor.

temp_buffer_size

Output buffer size in bytes.

workspace

Workspace buffer or USM pointer, must be at least of size
temp_buffer_size bytes and the address aligned on the size of the
handles’ data type.
If it is a buffer, its lifetime is extended until the spmv
descriptor is released or the workspace is
reset by spmv_optimize. The workspace cannot be a sub-buffer.
If it is a USM pointer, it must not be free’d until the corresponding
spmv has completed. The data must be accessible on the device.

dependencies

List of events to depend on before starting asynchronous tasks that access data on the device. Ignored if buffers are used. Defaults to no dependencies.

Output Parameters

temp_buffer_size: Output buffer size in bytes. A temporary workspace of at least this size must be allocated to perform the specified spmv.
y_handle: Dense vector handle object representing \(y\), result of the spmv operation.

Return Values

Output event that can be waited upon or added as a dependency for the completion of the function. May be an empty event if buffers are used.

Throws

These functions shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::math::computation_error
oneapi::math::device_bad_alloc
oneapi::math::invalid_argument
oneapi::math::unimplemented
oneapi::math::uninitialized
oneapi::math::unsupported_device

Parent topic: Sparse BLAS

spmv

Contents

spmv#

spmv_descr#

init_spmv_descr#

release_spmv_descr#

spmv_alg#

spmv#