# syrk_batch¶

Computes a group of syrk operations.

Description

The syrk_batch routines are batched versions of syrk, performing multiple syrk operations in a single call. Each syrk operation perform a rank-k update with general matrices.

syrk_batch supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## syrk_batch (Buffer Version)¶

Description

The buffer version of syrk_batch supports only the strided API.

The strided API operation is defined as:

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

op(A) is n x k and C is n x n.

The a 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 and c buffers is given by the batch_size parameter.

Strided API

Syntax

namespace oneapi::mkl::blas::column_major {
void syrk_batch(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
std::int64_t stridea,
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 syrk_batch(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
std::int64_t stridea,
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.

upper_lower

Specifies whether data in C is stored in its upper or lower triangle. For more details, see oneMKL Defined Datatypes.

trans

Specifies op(A) the transposition operation applied to the matrix A. Conjugation is never performed, even if trans = transpose::conjtrans. See oneMKL Defined Datatypes for more details.

n

Number of rows and columns of C. Must be at least zero.

k

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

alpha

Scaling factor for the rank-k update.

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 n.

lda must be at least k.

Row major

lda must be at least k.

lda must be at least n.

stridea

Stride between different A 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 n.

stridec

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

batch_size

Specifies the number of rank-k update operations to perform.

Output Parameters

c

Output buffer, overwritten by batch_size rank-k update operations of the form alpha * op(A)*op(A)^T + beta * C.

## syrk_batch (USM Version)¶

Description

The USM version of syrk_batch supports the group API and strided API.

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] and c[idx]
C := alpha[i] * op(A) * op(A)^T + beta[i] * C
idx = idx + 1
end for
end for


The strided API operation is defined as

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

op(A) is n x k and C is n x n.

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

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

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

Group API

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event syrk_batch(sycl::queue &queue,
uplo *upper_lower,
transpose *trans,
std::int64_t *n,
std::int64_t *k,
T *alpha,
const T **a,
std::int64_t *lda,
T *beta,
T **c,
std::int64_t *ldc,
std::int64_t group_count,
std::int64_t *group_size,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event syrk_batch(sycl::queue &queue,
uplo *upper_lower,
transpose *trans,
std::int64_t *n,
std::int64_t *k,
T *alpha,
const T **a,
std::int64_t *lda,
T *beta,
T **c,
std::int64_t *ldc,
std::int64_t group_count,
std::int64_t *group_size,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Array of group_count onemkl::upper_lower values. upper_lower[i] specifies whether data in C for every matrix in group i is in upper or lower triangle.

trans

Array of group_count onemkl::transpose values. trans[i] specifies the form of op(A) used in the rank-k update in group i. See oneMKL Defined Datatypes for more details.

n

Array of group_count integers. n[i] specifies the number of rows and columns of C for every matrix in group i. All entries must be at least zero.

k

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

alpha

Array of group_count scalar elements. alpha[i] specifies the scaling factor for every rank-k update in group i.

a

Array of pointers to input matrices A with size total_batch_count.

See Matrix Storage for more details.

lda

Array 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 n[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 n[i].

beta

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

c

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

See Matrix Storage for more details.

ldc

Array 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 n[i].

group_count

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

group_size

Array of group_count integers. group_size[i] specifies the number of rank-k update 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 n[i]-by-n[i] matrix calculated by (alpha[i] * op(A)*op(A)^T + beta[i] * C) for group i.

Return Values

Output event to wait on to ensure computation is complete.

Strided API

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event syrk_batch(sycl::queue &queue,
uplo upper_lower,
transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
const T *a,
std::int64_t lda,
std::int64_t stride_a,
T beta,
T *c,
std::int64_t ldc,
std::int64_t stride_c,
std::int64_t batch_size,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event syrk_batch(sycl::queue &queue,
uplo upper_lower,
transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
const T *a,
std::int64_t lda,
std::int64_t stride_a,
T beta,
T *c,
std::int64_t ldc,
std::int64_t stride_c,
std::int64_t batch_size,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether data in C is stored in its upper or lower triangle. For more details, see oneMKL Defined Datatypes.

trans

Specifies op(A) the transposition operation applied to the matrices A. Conjugation is never performed, even if trans = transpose::conjtrans. See oneMKL Defined Datatypes for more details.

n

Number of rows and columns of C. Must be at least zero.

k

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

alpha

Scaling factor for the rank-k updates.

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 n.

lda must be at least k.

Row major

lda must be at least k.

lda must be at least n.

stridea

Stride between different A 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 n.

stridec

Stride between different C matrices.

batch_size

Specifies the number of rank-k update 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 rank-k update operations of the form alpha * op(A)*op(A)^T + beta * C.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: BLAS-like Extensions