# syr2k¶

Performs a symmetric rank-2k update.

Description

The syr2k routines perform a rank-2k update of an n x n symmetric matrix C by general matrices A and B.

If trans = transpose::nontrans, the operation is defined as:

$C \leftarrow alpha*(A*B^T + B*A^T) + beta*C$

where A is n x k and B is k x n.

If trans = transpose::trans, the operation is defined as:

$C \leftarrow alpha*(A^T*B + B^T*A) + beta * C$

where A is k x n and B is n x k.

In both cases:

alpha and beta are scalars,

C is a symmetric matrix and A,B are general matrices,

The inner dimension of both matrix multiplications is k.

syr2k supports the following precisions:

T

float

double

std::complex<float>

std::complex<double>

## syr2k (Buffer Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
void syr2k(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,
sycl::buffer<T,1> &b,
std::int64_t ldb,
T beta,
sycl::buffer<T,1> &c,
std::int64_t ldc)
}

namespace oneapi::mkl::blas::row_major {
void syr2k(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,
sycl::buffer<T,1> &b,
std::int64_t ldb,
T beta,
sycl::buffer<T,1> &c,
std::int64_t ldc)
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A’s data is stored in its upper or lower triangle. See oneMKL Defined Datatypes for more details.

trans

Specifies the operation to apply, as described above. Conjugation is never performed, even if trans = transpose::conjtrans.

n

Number of rows and columns in C.The value of n must be at least zero.

k

Inner dimension of matrix multiplications.The value of k must be at least zero.

alpha

Scaling factor for the rank-2k update.

a

Buffer holding input matrix A.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

Column major

A is an n-by-k matrix so the array a must have size at least lda*k.

A is an k-by-n matrix so the array a must have size at least lda*n

Row major

A is an n-by-k matrix so the array a must have size at least lda*n.

A is an k-by-n matrix so the array a must have size at least lda*k.

See Matrix Storage for more details.

lda

The leading dimension of A. It must be positive.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

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.

b

Buffer holding input matrix B.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

Column major

B is an k-by-n matrix so the array b must have size at least ldb*n.

B is an n-by-k matrix so the array b must have size at least ldb*k

Row major

B is an k-by-n matrix so the array b must have size at least ldb*k.

B is an n-by-k matrix so the array b must have size at least ldb*n.

See Matrix Storage for more details.

ldb

The leading dimension of B. It must be positive.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

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.

beta

Scaling factor for matrix C.

c

Buffer holding input/output matrix C. Must have size at least ldc*n. See Matrix Storage for more details

ldc

Leading dimension of C. Must be positive and at least n.

Output Parameters

c

Output buffer, overwritten by the updated C matrix.

## syr2k (USM Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event syr2k(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
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,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event syr2k(sycl::queue &queue,
onemkl::uplo upper_lower,
onemkl::transpose trans,
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,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A’s data is stored in its upper or lower triangle. See oneMKL Defined Datatypes for more details.

trans

Specifies the operation to apply, as described above. Conjugation is never performed, even if trans = transpose::conjtrans.

n

Number of rows and columns in C. The value of n must be at least zero.

k

Inner dimension of matrix multiplications.The value of k must be at least zero.

alpha

Scaling factor for the rank-2k update.

a

Pointer to input matrix A.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

Column major

A is an n-by-k matrix so the array a must have size at least lda*k.

A is an k-by-n matrix so the array a must have size at least lda*n

Row major

A is an n-by-k matrix so the array a must have size at least lda*n.

A is an k-by-n matrix so the array a must have size at least lda*k.

See Matrix Storage for more details.

lda

The leading dimension of A. It must be positive.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

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.

b

Pointer to input matrix B.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

Column major

B is an k-by-n matrix so the array b must have size at least ldb*n.

B is an n-by-k matrix so the array b must have size at least ldb*k

Row major

B is an k-by-n matrix so the array b must have size at least ldb*k.

B is an n-by-k matrix so the array b must have size at least ldb*n.

See Matrix Storage for more details.

ldb

The leading dimension of B. It must be positive.

trans = transpose::nontrans

trans = transpose::trans or transpose::conjtrans

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.

beta

Scaling factor for matrix C.

c

Pointer to input/output matrix C. Must have size at least ldc*n. See Matrix Storage for more details

ldc

Leading dimension of C. Must be positive and at least n.

dependencies

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

Output Parameters

c

Pointer to the output matrix, overwritten by the updated C matrix.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: BLAS Level 3 Routines