# syrk¶

Performs a symmetric rank-k update.

Description

The syrk routines perform a rank-k update of a symmetric matrix C by a general matrix A. The operation is defined as:

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

where:

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

alpha and beta are scalars,

C is a symmetric matrix and Ais a general matrix.

Here op(A) is n-by-k, and C is n-by-n.

syrk supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## syrk (Buffer Version)¶

Syntax

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

namespace oneapi::mkl::blas::row_major {
void syrk(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,
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 op(A), the transposition operation applied to A (See oneMKL Defined Datatypes for more details). 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

Number of columns in op(A).The value of k must be at least zero.

alpha

Scaling factor for the rank-k 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.

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 alpha*op(A)*op(A)T + beta*C.

## syrk (USM Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event syrk(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,
T beta,
T* c,
std::int64_t ldc,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event syrk(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,
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 op(A), the transposition operation applied to A (See oneMKL Defined Datatypes for more details). 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

Number of columns in op(A). The value of k must be at least zero.

alpha

Scaling factor for the rank-k 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.

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.

Output Parameters

c

Pointer to the output matrix, overwritten by alpha*op(A)*op(A)T + beta*C.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: BLAS Level 3 Routines