.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_orgqr: orgqr ===== Generates the real orthogonal matrix :math:Q of the QR factorization formed by :ref:onemkl_lapack_geqrf. .. container:: section .. rubric:: Description orgqr supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double The routine generates the whole or part of :math:m \times m orthogonal matrix :math:Q of the QR factorization formed by the routine :ref:onemkl_lapack_geqrf. Usually :math:Q is determined from the QR factorization of an m by p matrix :math:A with :math:m \ge p. To compute the whole matrix :math:Q, use: :: oneapi::mkl::lapack::orgqr(queue, m, m, p, a, lda, tau, scratchpad, scratchpad_size) To compute the leading :math:p columns of :math:Q (which form an orthonormal basis in the space spanned by the columns of :math:A): :: oneapi::mkl::lapack::orgqr(queue, m, p, p, a, lda, tau, scratchpad, scratchpad_size) To compute the matrix :math:Q^{k} of the QR factorization of leading :math:k columns of the matrix :math:A: :: oneapi::mkl::lapack::orgqr(queue, m, m, k, a, lda, tau, scratchpad, scratchpad_size) To compute the leading :math:k columns of :math:Q^{k} (which form an orthonormal basis in the space spanned by leading :math:k columns of the matrix :math:A): :: oneapi::mkl::lapack::orgqr(queue, m, k, k, a, lda, tau, scratchpad, scratchpad_size) orgqr (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void orgqr(sycl::queue &queue, std::int64_t m, std::int64_t n, std::int64_t k, sycl::buffer &a, std::int64_t lda, sycl::buffer &tau, sycl::buffer &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. m The number of rows in the matrix :math:A (:math:0 \le m). n The number of columns in the matrix :math:A (:math:0 \le n). 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:onemkl_lapack_geqrf. lda The leading dimension of a (:math:\text{lda} \le m). tau The buffer tau as returned by :ref:onemkl_lapack_geqrf. 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_orgqr_scratchpad_size function. .. container:: section .. rubric:: Output Parameters a Overwritten by :math:n leading columns of the :math:m \times m orthogonal matrix :math:Q. scratchpad Buffer holding scratchpad memory to be used by routine for storing intermediate results. orgqr (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { sycl::event orgqr(sycl::queue &queue, std::int64_t m, std::int64_t n, std::int64_t k, T *a, std::int64_t lda, 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. m The number of rows in the matrix :math:A (:math:0 \le m). n The number of columns in the matrix :math:A (:math:0 \le n). 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:onemkl_lapack_geqrf. lda The leading dimension of a (:math:\text{lda} \le m). tau The pointer to tau as returned by :ref:onemkl_lapack_geqrf. 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_orgqr_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 :math:n leading columns of the :math:m \times m orthogonal matrix :math:Q. scratchpad Pointer to scratchpad memory to be used by routine for storing intermediate results. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. **Parent topic:** :ref:onemkl_lapack-linear-equation-routines