her2k¶

Performs a hermitian rank-2k update.

Description¶

The her2k routines perform a rank-2k update of an n x n hermitian matrix C by general matrices A and B. The operation is defined as:

If trans = transpose::nontrans,

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

where:

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

If trans = transpose::conjtrans,

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

where:

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

In both cases:

alpha is a complex scalar and beta is a real scalar
C is hermitian matrix, A and B are general matrices
The inner dimension of both matrix multiplications is k

her2k supports the following precisions:

T	T_real
`std::complex<float>`	`float`
`std::complex<double>`	`double`

her2k (Buffer Version)¶

Syntax¶

namespace oneapi::mkl::blas::column_major {
    void her2k(sycl::queue &queue,
               oneapi::mkl::uplo upper_lower,
               oneapi::mkl::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_real beta,
               sycl::buffer<T,1> &c,
               std::int64_t ldc)
}

namespace oneapi::mkl::blas::row_major {
    void her2k(sycl::queue &queue,
               oneapi::mkl::uplo upper_lower,
               oneapi::mkl::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_real 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 matrix C is upper or lower triangular. See Data Types for more details.

trans

Specifies the transposition operation applied as described above. Supported operations are transpose::nontrans and transpose::conjtrans.

n

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

k

Inner dimension of matrix multiplications. Must be at least zero.

alpha

Complex scaling factor for the rank-2k update.

a

Buffer holding input matrix A. See Matrix Storage for more details.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	`A` is `n` x `k` matrix. Size of array `a` must be at least `lda` * `k`	`A` is `k` x `n` matrix. Size of array `a` must be at least `lda` * `n`
Row major	`A` is `n` x `k` matrix. Size of array `a` must be at least `lda` * `n`	`A` is `k` x `n` matrix. Size of array `a` must be at least `lda` * `k`

lda

Leading dimension of matrix A. Must be positive.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	Must be at least `n`	Must be at least `k`
Row major	Must be at least `k`	Must be at least `n`

beta

Real scaling factor for matrix C.

b

Buffer holding input matrix B. See Matrix Storage for more details.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	`B` is `k` x `n` matrix. Size of array `b` must be at least `ldb` * `n`	`B` is `n` x `k` matrix. Size of array `b` must be at least `ldb` * `k`
Row major	`B` is `k` x `n` matrix. Size of array `b` must be at least `ldb` * `k`	`B` is `n` x `k` matrix. Size of array `b` must be at least `ldb` * `n`

ldb

Leading dimension of matrix B. Must be positive.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	Must be at least `k`	Must be at least `n`
Row major	Must be at least `n`	Must be at least `k`

c

Buffer holding input/output matrix C. Size of the buffer must be at least ldc * n. See Matrix Storage for more details.

ldc

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

Output Parameters¶

c: Output buffer overwritten by updated C matrix.

her2k (USM Version)¶

Syntax¶

namespace oneapi::mkl::blas::column_major {
    sycl::event her2k(sycl::queue &queue,
                      oneapi::mkl::uplo upper_lower,
                      oneapi::mkl::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_real beta,
                      T* c,
                      std::int64_t ldc,
                      const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
    sycl::event her2k(sycl::queue &queue,
                      oneapi::mkl::uplo upper_lower,
                      oneapi::mkl::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_real 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 matrix C is upper or lower triangular. See Data Types for more details.

trans

Specifies the transposition operation applied as described above. Supported operations are transpose::nontrans and transpose::conjtrans.

n

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

k

Inner dimension of matrix multiplications. Must be at least zero.

alpha

Complex scaling factor for the rank-2k update.

a

Pointer to input matrix A. See Matrix Storage for more details.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	`A` is `n` x `k` matrix. Size of array `a` must be at least `lda` * `k`	`A` is `k` x `n` matrix. Size of array `a` must be at least `lda` * `n`
Row major	`A` is `n` x `k` matrix. Size of array `a` must be at least `lda` * `n`	`A` is `k` x `n` matrix. Size of array `a` must be at least `lda` * `k`

lda

Leading dimension of matrix A. Must be positive.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	Must be at least `n`	Must be at least `k`
Row major	Must be at least `k`	Must be at least `n`

beta

Real scaling factor for matrix C.

b

Pointer to input matrix B. See Matrix Storage for more details.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	`B` is `k` x `n` matrix. Size of array `b` must be at least `ldb` * `n`	`B` is `n` x `k` matrix. Size of array `b` must be at least `ldb` * `k`
Row major	`B` is `k` x `n` matrix. Size of array `b` must be at least `ldb` * `k`	`B` is `n` x `k` matrix. Size of array `b` must be at least `ldb` * `n`

ldb

Leading dimension of matrix B. Must be positive.

	`trans` = `transpose::nontrans`	`trans` = `transpose::conjtrans`
Column major	Must be at least `k`	Must be at least `n`
Row major	Must be at least `n`	Must be at least `k`

c

Pointer to input/output matrix C. Size of the array must be at least ldc * n. See Matrix Storage for more details.

ldc

Leading dimension of matrix 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 output matrix overwritten by updated C matrix.

Return Values¶

Output event to wait on to ensure computation is complete.

hemm herk

oneAPI Math Kernel Library (oneMKL) documentation

her2k¶

Description¶

her2k (Buffer Version)¶

Syntax¶

Input Parameters¶

Output Parameters¶

her2k (USM Version)¶

Syntax¶

Input Parameters¶

Output Parameters¶

Return Values¶