# gemm_batch#

Computes a group of gemm operations.

Description

The gemm_batch routines are batched versions of gemm, performing multiple gemm operations in a single call. Each gemm operation perform a matrix-matrix product with general matrices.

gemm_batch supports the following precisions.

T

half

float

double

std::complex<float>

std::complex<double>

## gemm_batch (Buffer Version)#

Description

The buffer version of gemm_batch supports only the strided API.

The strided API operation is defined as:

for i = 0 … batch_size – 1
A, B and C are matrices at offset i * stridea, i * strideb, i * stridec in a, b and c.
C := alpha * op(A) * op(B) + beta * C
end for


where:

op(X) is one of op(X) = X, or op(X) = XT, or op(X) = XH,

alpha and beta are scalars,

A, B, and C are matrices,

op(A) is m x k, op(B) is k x n, and C is m x n.

The a, b and c buffers contain all the input matrices. The stride between matrices is given by the stride parameter. The total number of matrices in a, b and c buffers is given by the batch_size parameter.

Strided API

Syntax

namespace oneapi::mkl::blas::column_major {
void gemm_batch(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
std::int64_t stridea,
sycl::buffer<T,1> &b,
std::int64_t ldb,
std::int64_t strideb,
T beta,
sycl::buffer<T,1> &c,
std::int64_t ldc,
std::int64_t stridec,
std::int64_t batch_size)
}

namespace oneapi::mkl::blas::row_major {
void gemm_batch(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
std::int64_t stridea,
sycl::buffer<T,1> &b,
std::int64_t ldb,
std::int64_t strideb,
T beta,
sycl::buffer<T,1> &c,
std::int64_t ldc,
std::int64_t stridec,
std::int64_t batch_size)
}


Input Parameters

queue

The queue where the routine should be executed.

transa

Specifies op(A) the transposition operation applied to the matrices A. See oneMKL defined datatypes for more details.

transb

Specifies op(B) the transposition operation applied to the matrices B. See oneMKL defined datatypes for more details.

m

Number of rows of op(A) and C. Must be at least zero.

n

Number of columns of op(B) and C. Must be at least zero.

k

Number of columns of op(A) and rows of op(B). Must be at least zero.

alpha

Scaling factor for the matrix-matrix products.

a

Buffer holding the input matrices A with size stridea * batch_size.

lda

The leading dimension of the matrices A. It must be positive.

A not transposed

A transposed

Column major

lda must be at least m.

lda must be at least k.

Row major

lda must be at least k.

lda must be at least m.

stridea

Stride between different A matrices.

b

Buffer holding the input matrices B with size strideb * batch_size.

ldb

The leading dimension of the matricesB. It must be positive.

B not transposed

B transposed

Column major

ldb must be at least k.

ldb must be at least n.

Row major

ldb must be at least n.

ldb must be at least k.

strideb

Stride between different B matrices.

beta

Scaling factor for the matrices C.

c

Buffer holding input/output matrices C with size stridec * batch_size.

ldc

The leading dimension of the matrices C. It must be positive and at least m if column major layout is used to store matrices or at least n if column major layout is used to store matrices.

stridec

Stride between different C matrices. Must be at least ldc * n.

batch_size

Specifies the number of matrix multiply operations to perform.

Output Parameters

c

Output buffer, overwritten by batch_size matrix multiply operations of the form alpha * op(A)*op(B) + beta * C.

Notes

If beta = 0, matrix C does not need to be initialized before calling gemm_batch.

Throws

This routine 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::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::unimplemented

## gemm_batch (USM Version)#

Description

The USM version of gemm_batch supports the group API and the strided API. The group API supports pointer and span inputs.

The group API operation is defined as:

idx = 0
for i = 0 … group_count – 1
for j = 0 … group_size – 1
A, B, and C are matrices in a[idx], b[idx] and c[idx]
C := alpha[i] * op(A) * op(B) + beta[i] * C
idx = idx + 1
end for
end for


The advantage of using span instead of pointer is that the sizes of the array can vary and the size of the span can be queried at runtime. For each GEMM parameter, except the output matrices, the span can be of size 1, the number of groups or the total batch size. For the output matrices, to ensure all computation are independent, the size of the span must be the total batch size.

Depending on the size of the spans, each parameter for the GEMM computation is used as follows:

• If the span has size 1, the parameter is reused for all GEMM computation.

• If the span has size group_count, the parameter is reused for all GEMM within a group, but each group will have a different value for this parameter. This is like the gemm_batch group API with pointers.

• If the span has size equal to the total batch size, each GEMM computation will use a different value for this parameter.

The strided API operation is defined as

for i = 0 … batch_size – 1
A, B and C are matrices at offset i * stridea, i * strideb, i * stridec in a, b and c.
C := alpha * op(A) * op(B) + beta * C
end for


where:

op(X) is one of op(X) = X, or op(X) = XT, or op(X) = XH,

alpha and beta are scalars,

A, B, and C are matrices,

op(A) is m x k, op(B) is k x n, and C is m x n.

For group API, a, b and c arrays contain the pointers for all the input matrices. The total number of matrices in a, b and c are given by:

$total\_batch\_count = \sum_{i=0}^{group\_count-1}group\_size[i]$

For strided API, a, b, c arrays contain all the input matrices. The total number of matrices in a, b and c are given by the batch_size parameter.

Group API

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event gemm_batch(sycl::queue &queue,
onemkl::transpose *transa,
onemkl::transpose *transb,
std::int64_t *m,
std::int64_t *n,
std::int64_t *k,
T *alpha,
const T **a,
std::int64_t *lda,
const T **b,
std::int64_t *ldb,
T *beta,
T **c,
std::int64_t *ldc,
std::int64_t group_count,
std::int64_t *group_size,
const std::vector<sycl::event> &dependencies = {})

sycl::event gemm_batch(sycl::queue &queue,
const sycl::span<onemkl::transpose> &transa,
const sycl::span<onemkl::transpose> &transb,
const sycl::span<std::int64_t> &m,
const sycl::span<std::int64_t> &n,
const sycl::span<std::int64_t> &k,
const sycl::span<std::int64_t> &alpha,
const sycl::span<const T*> &a,
const sycl::span<std::int64_t> &lda,
const sycl::span<const T*> &b,
const sycl::span<std::int64_t> &ldb,
const sycl::span<T> &beta,
sycl::span<T*> &c,
const sycl::span<std::int64_t> &ldc,
size_t group_count,
const sycl::span<size_t> &group_sizes,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event gemm_batch(sycl::queue &queue,
onemkl::transpose *transa,
onemkl::transpose *transb,
std::int64_t *m,
std::int64_t *n,
std::int64_t *k,
T *alpha,
const T **a,
std::int64_t *lda,
const T **b,
std::int64_t *ldb,
T *beta,
T **c,
std::int64_t *ldc,
std::int64_t group_count,
std::int64_t *group_size,
const std::vector<sycl::event> &dependencies = {})

sycl::event gemm_batch(sycl::queue &queue,
const sycl::span<onemkl::transpose> &transa,
const sycl::span<onemkl::transpose> &transb,
const sycl::span<std::int64_t> &m,
const sycl::span<std::int64_t> &n,
const sycl::span<std::int64_t> &k,
const sycl::span<std::int64_t> &alpha,
const sycl::span<const T*> &a,
const sycl::span<std::int64_t> &lda,
const sycl::span<const T*> &b,
const sycl::span<std::int64_t> &ldb,
const sycl::span<T> &beta,
sycl::span<T*> &c,
const sycl::span<std::int64_t> &ldc,
size_t group_count,
const sycl::span<size_t> &group_sizes,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

transa

Array or span of group_count onemkl::transpose values. transa[i] specifies the form of op(A) used in the matrix multiplication in group i. See oneMKL defined datatypes for more details.

transb

Array or span of group_count onemkl::transpose values. transb[i] specifies the form of op(B) used in the matrix multiplication in group i. See oneMKL defined datatypes for more details.

m

Array or span of group_count integers. m[i] specifies the number of rows of op(A) and C for every matrix in group i. All entries must be at least zero.

n

Array or span of group_count integers. n[i] specifies the number of columns of op(B) and C for every matrix in group i. All entries must be at least zero.

k

Array or span of group_count integers. k[i] specifies the number of columns of op(A) and rows of op(B) for every matrix in group i. All entries must be at least zero.

alpha

Array or span of group_count scalar elements. alpha[i] specifies the scaling factor for every matrix-matrix product in group i.

a

Array of pointers or span of input matrices A with size total_batch_count.

See Matrix Storage for more details.

lda

Array or span of group_count integers. lda[i] specifies the leading dimension of A for every matrix in group i. All entries must be positive.

A not transposed

A transposed

Column major

lda[i] must be at least m[i].

lda[i] must be at least k[i].

Row major

lda[i] must be at least k[i].

lda[i] must be at least m[i].

b

Array of pointers or span of input matrices B with size total_batch_count.

See Matrix Storage for more details.

ldb

Array or span of group_count integers. ldb[i] specifies the leading dimension of B for every matrix in group i. All entries must be positive.

B not transposed

B transposed

Column major

ldb[i] must be at least k[i].

ldb[i] must be at least n[i].

Row major

ldb[i] must be at least n[i].

ldb[i] must be at least k[i].

beta

Array or span of group_count scalar elements. beta[i] specifies the scaling factor for matrix C for every matrix in group i.

c

Array of pointers or span of input/output matrices C with size total_batch_count.

See Matrix Storage for more details.

ldc

Array or span of group_count integers. ldc[i] specifies the leading dimension of C for every matrix in group i. All entries must be positive and ldc[i] must be at least m[i] if column major layout is used to store matrices or at least n[i] if row major layout is used to store matrices.

group_count

Specifies the number of groups. Must be at least 0.

group_size

Array or span of group_count integers. group_size[i] specifies the number of matrix multiply products in group i. All entries must be at least 0.

dependencies

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

Output Parameters

c

Overwritten by the m[i]-by-n[i] matrix calculated by (alpha[i] * op(A)*op(B) + beta[i] * C) for group i.

Notes

If beta = 0, matrix C does not need to be initialized before calling gemm_batch.

Return Values

Output event to wait on to ensure computation is complete.

Output Parameters

c

Overwritten by the m[i]-by-n[i] matrix calculated by (alpha[i] * op(A)*op(B) + beta[i] * C) for group i.

Notes

If beta = 0, matrix C does not need to be initialized before calling gemm_batch.

Return Values

Output event to wait on to ensure computation is complete.

Strided API

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event gemm_batch(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
T alpha,
const T *a,
std::int64_t lda,
std::int64_t stridea,
const T *b,
std::int64_t ldb,
std::int64_t strideb,
T beta,
T *c,
std::int64_t ldc,
std::int64_t stridec,
std::int64_t batch_size,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event gemm_batch(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
T alpha,
const T *a,
std::int64_t lda,
std::int64_t stridea,
const T *b,
std::int64_t ldb,
std::int64_t strideb,
T beta,
T *c,
std::int64_t ldc,
std::int64_t stridec,
std::int64_t batch_size,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

transa

Specifies op(A) the transposition operation applied to the matrices A. See oneMKL defined datatypes for more details.

transb

Specifies op(B) the transposition operation applied to the matrices B. See oneMKL defined datatypes for more details.

m

Number of rows of op(A) and C. Must be at least zero.

n

Number of columns of op(B) and C. Must be at least zero.

k

Number of columns of op(A) and rows of op(B). Must be at least zero.

alpha

Scaling factor for the matrix-matrix products.

a

Pointer to input matrices A with size stridea * batch_size.

lda

The leading dimension of the matrices A. It must be positive.

A not transposed

A transposed

Column major

lda must be at least m.

lda must be at least k.

Row major

lda must be at least k.

lda must be at least m.

stridea

Stride between different A matrices.

b

Pointer to input matrices B with size strideb * batch_size.

ldb

The leading dimension of the matricesB. It must be positive.

B not transposed

B transposed

Column major

ldb must be at least k.

ldb must be at least n.

Row major

ldb must be at least n.

ldb must be at least k.

strideb

Stride between different B matrices.

beta

Scaling factor for the matrices C.

c

Pointer to input/output matrices C with size stridec * batch_size.

ldc

The leading dimension of the matrices C. It must be positive and at least m if column major layout is used to store matrices or at least n if column major layout is used to store matrices.

stridec

Stride between different C matrices.

batch_size

Specifies the number of matrix multiply operations to perform.

dependencies

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

Output Parameters

c

Output matrices, overwritten by batch_size matrix multiply operations of the form alpha * op(A)*op(B) + beta * C.

Notes

If beta = 0, matrix C does not need to be initialized before calling gemm_batch.

Return Values

Output event to wait on to ensure computation is complete.

Throws

This routine 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::mkl::invalid_argument

oneapi::mkl::unsupported_device