hetrd (USM Version)
Reduces a complex Hermitian matrix to tridiagonal form. This routine
belongs to the
oneapi::mkl::lapack
namespace.Description
The routine reduces a complex Hermitian matrix
A
to Hermitian
tridiagonal form T
by a unitary similarity transformation:
A = Q*T*QH
. The unitary matrix Q
is not formed explicitly but
is represented as a product of n
-1 elementary reflectors.
Routines are provided to work with Q
in this representation.API
Syntax
namespace oneapi::mkl::lapack {
cl::sycl::event hetrd(cl::sycl::queue &queue,
mkl::uplo uplo,
std::int64_t n,
T *a,
std::int64_t lda,
T *d,
T *e,
T *tau,
T *scratchpad,
std::int64_t scratchpad_size,
const std::vector<cl::sycl::event> &events = {})
}
hetrd
(USM version) supports the following precisions and
devices:T | Devices supported |
---|---|
std::complex<float> | Host, CPU, and GPU |
std::complex<double> | Host, CPU, and GPU |
Input Parameters
- queue
- The device queue where calculations will be performed.
- uplo
- Must beuplo::upperoruplo::lower.Ifuplo = uplo::upper, a stores the upper triangular part ofA.Ifuplo = uplo::lower, a stores the lower triangular part ofA.
- n
- The order of the matricesA(0≤n).
- a
- Pointer to the matrixA, size(lda,*). Contains the upper or lower triangle as specified by uplo.
- lda
- The leading dimension of a; at leastmax(1, n)
- scratchpad
- Pointer to scratchpad memory to be used by the routine for storing intermediate results.
- scratchpad_size
- Size of scratchpad memory as a number of floating point elements of typeT. Size should not be less than the value returned by the hetrd_scratchpad_size function.
- events
- List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
- On exit,ifuplo = uplo::upper, the diagonal and first superdiagonal ofAare overwritten by the corresponding elements of the tridiagonal matrixT, and the elements above the first superdiagonal, with the buffer tau, represent the unitary matrixQas a product of elementary reflectors;ifuplo = uplo::lower, the diagonal and first subdiagonal ofAare overwritten by the corresponding elements of the tridiagonal matrixT, and the elements below the first subdiagonal, with the array tau, represent the unitary matrixQas a product of elementary reflectors.
- d
- Pointer to the diagonal elements of the matrixT. The dimension of d must be at leastmax(1, n).
- e
- Pointer to off diagonal elements of the matrixT. The dimension of e must be at leastmax(1, n-1).
- tau
- Pointer to memory array of size at leastmax(1, n). Stores(n-1)scalars that define elementary reflectors in decomposition of the unitary matrixQin a product ofn-1elementary reflectors. tau(n)is used as workspace.
Exceptions
Exception | Description |
---|---|
mkl::lapack::exception | This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If info = -i , the i -th parameter had an illegal value.If info is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object. |
Return Values
Output event to wait on to ensure computation is complete.