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.

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

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

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

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

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

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 a Hermitian matrix and A , B are general matrices.

The inner dimension of both matrix multiplications is k.

her2k supports the following precisions:

T

Treal

std::complex<float>

float

std::complex<double>

double

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

her2k (Buffer Version)#

Syntax

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

namespace oneapi::math::blas::row_major {
    void her2k(sycl::queue &queue,
               oneapi::math::uplo upper_lower,
               oneapi::math::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,
               Treal 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 oneMath defined datatypes for more details.

trans

Specifies the operation to apply, as described above. Supported operations are transpose::nontrans and transpose::conjtrans.

n

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

k

The inner dimension of matrix multiplications. The value of k must be at least equal to zero.

alpha

Complex 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

Real 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.

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::math::invalid_argument

oneapi::math::unsupported_device

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

her2k (USM Version)#

Syntax

namespace oneapi::math::blas::column_major {
    sycl::event her2k(sycl::queue &queue,
                      oneapi::math::uplo upper_lower,
                      oneapi::math::transpose trans,
                      std::int64_t n,
                      std::int64_t k,
                      value_or_pointer<T> alpha,
                      const T *a,
                      std::int64_t lda,
                      const T *b,
                      std::int64_t ldb,
                      value_or_pointer<Treal> beta,
                      T *c,
                      std::int64_t ldc,
                      const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::math::blas::row_major {
    sycl::event her2k(sycl::queue &queue,
                      oneapi::math::uplo upper_lower,
                      oneapi::math::transpose trans,
                      std::int64_t n,
                      std::int64_t k,
                      value_or_pointer<T> alpha,
                      const T *a,
                      std::int64_t lda,
                      const T *b,
                      std::int64_t ldb,
                      value_or_pointer<Treal> 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 oneMath defined datatypes for more details.

trans

Specifies the operation to apply, as described above. Supported operations are transpose::nontrans and transpose::conjtrans.

n

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

k

The inner dimension of matrix multiplications. The value of k must be at least equal to zero.

alpha

Complex scaling factor for the rank-2k update. See Scalar Arguments in BLAS for more details.

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`.