.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_lapack_unmtr: unmtr ===== Multiplies a complex matrix by the complex unitary matrix Q determined by :ref:`onemath_lapack_hetrd`. .. container:: section .. rubric:: Description ``unmtr`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``std::complex`` * - ``std::complex`` The routine multiplies a complex matrix :math:`C` by :math:`Q` or :math:`Q^{H}`, where :math:`Q` is the 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`. Depending on the parameters ``side`` and ``trans``, the routine can form one of the matrix products :math:`QC`, :math:`Q^{H}C`, :math:`CQ`, or :math:`CQ^{H}` (overwriting the result on :math:`C`). unmtr (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { void unmtr(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`\ =\ :math:`m` - if ``side = side::left`` * - :math:`r`\ =\ :math:`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^{H}` is applied to :math:`C` from the left. If ``side=side::right``, :math:`Q` or :math:`Q^{H}` 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_hetrd`. trans Must be either ``transpose::nontrans`` or ``transpose::conjtrans``. If ``trans=transpose::nontrans``, the routine multiplies :math:`C` by :math:`Q`. If ``trans=transpose::conjtrans``, the routine multiplies :math:`C` by :math:`Q^{H}`. m The number of rows in the matrix :math:`C` (:math:`m \ge 0`). n The number of columns the matrix :math:`C` (:math:`n \ge 0`). k The number of elementary reflectors whose product defines the matrix :math:`Q` (:math:`0 \le k \le n`). a The buffer ``a`` as returned by :ref:`onemath_lapack_hetrd`. lda The leading dimension of ``a`` :math:`(\text{lda} \ge \max(1,r))`. tau The buffer ``tau`` as returned by :ref:`onemath_lapack_hetrd`. 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_unmtr_scratchpad_size` function. .. container:: section .. rubric:: Output Parameters c Overwritten by the product :math:`QC`, :math:`Q^{H}C`, :math:`CQ`, or :math:`CQ^{H}` (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:`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. unmtr (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { cl::sycl::event unmtr(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`\ =\ :math:`m` - if ``side = side::left`` * - :math:`r`\ =\ :math:`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^{H}` is applied to :math:`C` from the left. If ``side=side::right``, :math:`Q` or :math:`Q^{H}` 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_hetrd`. trans Must be either ``transpose::nontrans`` or ``transpose::conjtrans``. If ``trans=transpose::nontrans``, the routine multiplies :math:`C` by :math:`Q`. If ``trans=transpose::conjtrans``, the routine multiplies :math:`C` by :math:`Q^{H}`. m The number of rows in the matrix :math:`C` (:math:`m \ge 0`). n The number of columns the matrix :math:`C` (:math:`n \ge 0`). k The number of elementary reflectors whose product defines the matrix :math:`Q` (:math:`0 \le k \le n`). a The pointer to ``a`` as returned by :ref:`onemath_lapack_hetrd`. lda The leading dimension of ``a`` :math:`(\text{lda} \ge \max(1,r))`. tau The pointer to ``tau`` as returned by :ref:`onemath_lapack_hetrd`. The dimension of ``tau`` must be at least :math:`\max(1,r-1)`. c The array ``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_unmtr_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^{H}C`, :math:`CQ`, or :math:`CQ^{H}` (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:`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`