.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_ormtr: ormtr ===== Multiplies a real matrix by the real orthogonal matrix :math:Q determined by :ref:onemkl_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:onemkl_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:onemkl_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::mkl::lapack { void ormtr(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::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: 1 * - :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:onemkl_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:onemkl_lapack_sytrd. lda The leading dimension of a :math:(\max(1, r) \le \text{lda}). tau The buffer tau as returned bya :ref:onemkl_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:(\max(1, n) \le \text{ldc}). 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:onemkl_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::mkl::host_bad_alloc :ref:oneapi::mkl::device_bad_alloc :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument :ref:oneapi::mkl::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::mkl::lapack { cl::sycl::event ormtr(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, 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: 1 * - :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:onemkl_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:onemkl_lapack_sytrd. lda The leading dimension of a :math:(\max(1, r) \le \text{lda}). tau The buffer tau as returned by :ref:onemkl_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:(\max(1, n) \le \text{ldc}). 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:onemkl_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::mkl::host_bad_alloc :ref:oneapi::mkl::device_bad_alloc :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument :ref:oneapi::mkl::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:onemkl_lapack-singular-value-eigenvalue-routines