.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_lapack_ungtr: ungtr ===== Generates the complex unitary matrix :math:`Q` determined by :ref:`onemath_lapack_hetrd`. .. container:: section .. rubric:: Description ``ungtr`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``std::complex`` * - ``std::complex`` The routine explicitly generates the :math:`n \times n` unitary matrix :math:`Q` formed by :ref:`onemath_lapack_hetrd` when reducing a complex Hermitian matrix :math:`A` to tridiagonal form: :math:`A = QTQ^H`. Use this routine after a call to :ref:`onemath_lapack_hetrd`. ungtr (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { void ungtr(cl::sycl::queue &queue, oneapi::math::uplo upper_lower, std::int64_t n, cl::sycl::buffer &a, std::int64_t lda, cl::sycl::buffer &tau, cl::sycl::buffer &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. upper_lower Must be ``uplo::upper`` or ``uplo::lower``. Uses the same ``upper_lower`` as supplied to :ref:`onemath_lapack_hetrd`. n The order of the matrix :math:`Q` :math:`(0 \le n)`. a The buffer ``a`` as returned by :ref:`onemath_lapack_hetrd`. The second dimension of ``a`` must be at least :math:`\max(1, n)`. lda The leading dimension of ``a`` :math:`(n \le \text{lda})`. tau The buffer ``tau`` as returned by :ref:`onemath_lapack_hetrd`. The dimension of ``tau`` must be at least :math:`\max(1, n-1)`. scratchpad_size Size of scratchpad memory as a number of floating point elements of type ``T``. Size should not be less than the value returned by :ref:`onemath_lapack_ungtr_scratchpad_size` function. .. container:: section .. rubric:: Output Parameters a Overwritten by the unitary matrix :math:`Q`. scratchpad Buffer holding scratchpad memory to be used by routine for storing intermediate results. .. container:: section .. rubric:: 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. :ref:`oneapi::math::host_bad_alloc` :ref:`oneapi::math::device_bad_alloc` :ref:`oneapi::math::unimplemented` :ref:`oneapi::math::unsupported_device` :ref:`oneapi::math::lapack::invalid_argument` :ref:`oneapi::math::lapack::computation_error` Exception is thrown in case of problems during calculations. The ``info`` code of the problem can be obtained by `info()` method of exception object: If :math:`\text{info}=-i`, the :math:`i`-th parameter had an illegal value. If ``info`` equals to value passed as scratchpad size, and `detail()` returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by `detail()` method of exception object. ungtr (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { cl::sycl::event ungtr(cl::sycl::queue &queue, oneapi::math::uplo upper_lower, std::int64_t n, T *a, std::int64_t lda, const T *tau, T *scratchpad, std::int64_t scratchpad_size, const std::vector &events = {}) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. upper_lower Must be ``uplo::upper`` or ``uplo::lower``. Uses the same ``upper_lower`` as supplied to :ref:`onemath_lapack_hetrd`. n The order of the matrix :math:`Q` :math:`(0 \le n)`. a The pointer to ``a`` as returned by :ref:`onemath_lapack_hetrd`. The second dimension of ``a`` must be at least :math:`\max(1, n)`. lda The leading dimension of ``a`` :math:`(n \le \text{lda})`. tau The pointer to ``tau`` as returned by :ref:`onemath_lapack_hetrd`. The dimension of ``tau`` must be at least :math:`\max(1, n-1)`. scratchpad_size Size of scratchpad memory as a number of floating point elements of type ``T``. Size should not be less than the value returned by :ref:`onemath_lapack_ungtr_scratchpad_size` function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters a Overwritten by the unitary matrix :math:`Q`. scratchpad Pointer to scratchpad memory to be used by routine for storing intermediate results. .. container:: section .. rubric:: 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. :ref:`oneapi::math::host_bad_alloc` :ref:`oneapi::math::device_bad_alloc` :ref:`oneapi::math::unimplemented` :ref:`oneapi::math::unsupported_device` :ref:`oneapi::math::lapack::invalid_argument` :ref:`oneapi::math::lapack::computation_error` Exception is thrown in case of problems during calculations. The ``info`` code of the problem can be obtained by `info()` method of exception object: If :math:`\text{info}=-i`, the :math:`i`-th parameter had an illegal value. If ``info`` equals to value passed as scratchpad size, and `detail()` returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by `detail()` method of exception object. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:`onemath_lapack-singular-value-eigenvalue-routines`