.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_lapack_ormtr: ormtr ===== Multiplies a real matrix by the real orthogonal matrix :math:`Q` determined by :ref:`onemath_lapack_sytrd`. .. container:: section .. rubric:: Description ``ormtr`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``float`` * - ``double`` The routine multiplies a real matrix :math:`C` by :math:`Q` or :math:`Q^{T}`, where :math:`Q` is the orthogonal matrix :math:`Q` formed by:ref:`onemath_lapack_sytrd` when reducing a real symmetric matrix :math:`A` to tridiagonal form: :math:`A = QTQ^T`. Use this routine after a call to :ref:`onemath_lapack_sytrd`. Depending on the parameters side and trans, the routine can form one of the matrix products :math:`QC`, :math:`Q^TC`, :math:`CQ`, or :math:`CQ^T` (overwriting the result on :math:`C`). ormtr (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { void ormtr(cl::sycl::queue &queue, oneapi::math::side side, oneapi::math::uplo upper_lower, oneapi::math::transpose trans, std::int64_t m, std::int64_t n, cl::sycl::buffer &a, std::int64_t lda, cl::sycl::buffer &tau, cl::sycl::buffer &c, std::int64_t ldc, cl::sycl::buffer &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters In the descriptions below, ``r`` denotes the order of :math:`Q`: .. container:: tablenoborder .. list-table:: :header-rows: 0 * - :math:`r = m` - if ``side = side::left`` * - :math:`r = n` - if ``side = side::right`` queue The queue where the routine should be executed. side Must be either ``side::left`` or ``side::right``. If ``side = side::left``, :math:`Q` or :math:`Q^{T}` is applied to :math:`C` from the left. If ``side = side::right``, :math:`Q` or :math:`Q^{T}` is applied to :math:`C` from the right. upper_lower Must be either ``uplo::upper`` or ``uplo::lower``. Uses the same ``upper_lower`` as supplied to :ref:`onemath_lapack_sytrd`. trans Must be either ``transpose::nontrans`` or ``transpose::trans``. If ``trans = transpose::nontrans``, the routine multiplies :math:`C` by :math:`Q`. If ``trans = transpose::trans``, the routine multiplies :math:`C` by :math:`Q^{T}`. m The number of rows in the matrix :math:`C` :math:`(m \ge 0)`. n The number of columns in the matrix :math:`C` :math:`(n \ge 0)`. a The buffer ``a`` as returned by :ref:`onemath_lapack_sytrd`. lda The leading dimension of ``a`` :math:`(\text{lda} \ge \max(1, r))`. tau The buffer ``tau`` as returned by a :ref:`onemath_lapack_sytrd`. The dimension of ``tau`` must be at least :math:`\max(1, r-1)`. c The buffer ``c`` contains the matrix :math:`C`. The second dimension of ``c`` must be at least :math:`\max(1, n)`. ldc The leading dimension of ``c`` :math:`(\text{ldc} \ge \max(1, m))`. 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_ormtr_scratchpad_size` function. .. container:: section .. rubric:: Output Parameters c Overwritten by the product :math:`QC`, :math:`Q^TC`, :math:`CQ`, or :math:`CQ^T` (as specified by ``side`` and ``trans``). 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. ormtr (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { cl::sycl::event ormtr(cl::sycl::queue &queue, oneapi::math::side side, oneapi::math::uplo upper_lower, oneapi::math::transpose trans, std::int64_t m, std::int64_t n, const T *a, std::int64_t lda, const T *tau, T *c, std::int64_t ldc, T *scratchpad, std::int64_t scratchpad_size, const std::vector &events = {}) } .. container:: section .. rubric:: Input Parameters In the descriptions below, ``r`` denotes the order of :math:`Q`: .. container:: tablenoborder .. list-table:: :header-rows: 0 * - :math:`r = m` - if ``side = side::left`` * - :math:`r = n` - if ``side = side::right`` queue The queue where the routine should be executed. side Must be either ``side::left`` or ``side::right``. If ``side = side::left``, :math:`Q` or :math:`Q^{T}` is applied to :math:`C` from the left. If ``side = side::right``, :math:`Q` or :math:`Q^{T}` is applied to :math:`C` from the right. upper_lower Must be either ``uplo::upper`` or ``uplo::lower``. Uses the same ``upper_lower`` as supplied to :ref:`onemath_lapack_sytrd`. trans Must be either ``transpose::nontrans`` or ``transpose::trans``. If ``trans = transpose::nontrans``, the routine multiplies :math:`C` by :math:`Q`. If ``trans = transpose::trans``, the routine multiplies :math:`C` by :math:`Q^{T}`. m The number of rows in the matrix :math:`C` :math:`(m \ge 0)`. n The number of columns in the matrix :math:`C` :math:`(n \ge 0)`. a The pointer to ``a`` as returned by :ref:`onemath_lapack_sytrd`. lda The leading dimension of ``a`` :math:`(\text{lda} \ge \max(1, r))`. tau The buffer ``tau`` as returned by :ref:`onemath_lapack_sytrd`. The dimension of ``tau`` must be at least :math:`\max(1, r-1)`. c The pointer to memory containing the matrix :math:`C`. The second dimension of ``c`` must be at least :math:`\max(1, n)`. ldc The leading dimension of ``c`` :math:`(\text{ldc} \ge \max(1, m))`. 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_ormtr_scratchpad_size` function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters c Overwritten by the product :math:`QC`, :math:`Q^TC`, :math:`CQ`, or :math:`CQ^T` (as specified by ``side`` and ``trans``). 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`