.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_ormrq: ormrq ===== Multiplies a real matrix by the orthogonal matrix :math:Q of the RQ factorization formed by :ref:onemkl_lapack_gerqf. .. container:: section .. rubric:: Description ormrq supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double The routine multiplies a rectangular real :math:m \times n matrix :math:C by :math:Q or :math:Q^T, where :math:Q is the complex unitary matrix defined as a product of :math:k elementary reflectors :math:H(i) of order :math:n: :math:Q = H(1)^TH(2)^T ... H(k)^T as returned by the RQ factorization routine :ref:onemkl_lapack_gerqf. 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 over :math:C). ormrq (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void ormrq(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t k, 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 queue The queue where the routine should be executed. side If side = oneapi::mkl::side::left, :math:Q or :math:Q^{T} is applied to :math:C from the left. If side = oneapi::mkl::side::right, :math:Q or :math:Q^{T} is applied to :math:C from the right. trans If trans = oneapi::mkl::transpose::nontrans, the routine multiplies :math:C by :math:Q. If trans = oneapi::mkl::transpose::trans, the routine multiplies :math:C by :math:Q^{T}. m The number of rows in the matrix :math:C (:math:0 \le m). n The number of columns in the matrix :math:C (:math:0 \le n). k The number of elementary reflectors whose product defines the matrix :math:Q If side = oneapi::mkl::side::left, :math:0 \le k \le m If side = oneapi::mkl::side::right, :math:0 \le k \le n a The buffer a as returned by :ref:onemkl_lapack_gerqf. The second dimension of a must be at least :math:\max(1,k). lda The leading dimension of a. tau The buffer tau as returned by :ref:onemkl_lapack_gerqf. 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. 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 the :ref:onemkl_lapack_ormrq_scratchpad_size function. .. container:: section .. rubric:: Output Parameters c Overwritten by the product :math:QC, :math:Q^{T}C, :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. ormrq (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event ormrq(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, std::int64_t k, 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 queue The queue where the routine should be executed. side If side = oneapi::mkl::side::left, :math:Q or :math:Q^{T} is applied to :math:C from the left. If side = oneapi::mkl::side::right, :math:Q or :math:Q^{T} is applied to :math:C from the right. trans If trans = oneapi::mkl::transpose::nontrans, the routine multiplies :math:C by :math:Q. If trans = oneapi::mkl::transpose::trans, the routine multiplies :math:C by :math:Q^{T}. m The number of rows in the matrix :math:C (:math:0 \le m). n The number of columns in the matrix :math:C (:math:0 \le n). k The number of elementary reflectors whose product defines the matrix :math:Q If side = oneapi::mkl::side::left, :math:0 \le k \le m If side = oneapi::mkl::side::right, :math:0 \le k \le n a The pointer to a as returned by :ref:onemkl_lapack_gerqf. The second dimension of a must be at least :math:\max(1,k). lda The leading dimension of a. tau The pointer to tau as returned by :ref:onemkl_lapack_gerqf. c The pointer c points to the matrix :math:C. The second dimension of c must be at least :math:\max(1,n). ldc The leading dimension of c. 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 the :ref:onemkl_lapack_ormrq_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^{T}C, :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-linear-equation-routines