.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_orgbr: orgbr ===== Generates the real orthogonal matrix :math:Q or :math:P^{T} determined by :ref:onemkl_lapack_gebrd. orgbr supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double .. container:: section .. rubric:: Description The routine generates the whole or part of the orthogonal matrices :math:Q and :math:P^{T} formed by the routines :ref:onemkl_lapack_gebrd. All valid combinations of arguments are described in *Input parameters*. In most cases you need the following: To compute the whole :math:m \times m matrix :math:Q: :: orgbr(queue, generate::q, m, m, n, a, ...) (note that the array a must have at least :math:m columns). To form the :math:n leading columns of :math:Q if :math:m > n: :: orgbr(queue, generate::q, m, n, n, a, ...) To compute the whole :math:n \times n matrix :math:P^{T}: :: orgbr(queue, generate::p, n, n, m, a, ...) (note that the array a must have at least :math:n rows). To form the :math:m leading rows of :math:P^{T} if :math:m < n: :: orgbr(queue, generate::p, m, n, m, a, ...) orgbr (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void orgbr(cl::sycl::queue &queue, oneapi::mkl::generate gen, 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 &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. gen Must be generate::q or generate::p. If gen = generate::q, the routine generates the matrix :math:Q. If gen = generate::p, the routine generates the matrix :math:P^{T}. m The number of rows in the matrix :math:Q or :math:P^{T} to be returned :math:(0 \le m). If gen = generate::q, :math:m \le n \le \min(m, k). If gen = generate::p, :math:n \le m \le \min(n, k). n The number of rows in the matrix :math:Q or :math:P^{T} to be returned :math:(0 \le n). See m for constraints. k If gen = generate::q, the number of columns in the original :math:m \times k matrix reduced by :ref:onemkl_lapack_gebrd. If gen = generate::p, the number of rows in the original :math:k \times n matrix reduced by :ref:onemkl_lapack_gebrd. a The buffer a as returned by :ref:onemkl_lapack_gebrd. lda The leading dimension of a. tau Buffer, size :math:\min(m,k) if gen = generate::q, size :math:\min(n,k) if gen = generate::p. Scalar factor of the elementary reflectors, as returned by :ref:onemkl_lapack_gebrd in the array tauq or taup. 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_orgbr_scratchpad_size function. .. container:: section .. rubric:: Output Parameters a Overwritten by n leading columns of the :math:m \times m orthogonal matrix :math:Q or :math:P^{T} (or the leading rows or columns thereof) as specified by gen, m, and n. scratchpad Buffer holding scratchpad memory to be used by routine for storing intermediate results. orgbr (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event orgbr(cl::sycl::queue &queue, oneapi::mkl::generate gen, 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 cl::sycl::vector_class &events = {}) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. gen Must be generate::q or generate::p. If gen = generate::q, the routine generates the matrix :math:Q. If gen = generate::p, the routine generates the matrix :math:P^{T}. m The number of rows in the matrix :math:Q or :math:P^{T} to be returned :math:(0 \le m). If gen = generate::q, :math:m \le n \le \min(m, k). If gen = generate::p, :math:n \le m \le \min(n, k). n The number of rows in the matrix :math:Q or :math:P^{T} to be returned :math:(0 \le n). See m for constraints. k If gen = generate::q, the number of columns in the original :math:m \times k matrix reduced by :ref:onemkl_lapack_gebrd. If gen = generate::p, the number of rows in the original :math:k \times n matrix reduced by :ref:onemkl_lapack_gebrd. a Pointer to array a as returned by :ref:onemkl_lapack_gebrd. lda The leading dimension of a. tau Pointer to array of size :math:\min(m,k) if gen = generate::q, size :math:\min(n,k) if gen = generate::p. Scalar factor of the elementary reflectors, as returned by :ref:onemkl_lapack_gebrd in the array tauq or taup. 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_orgbr_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 n leading columns of the :math:m \times m orthogonal matrix :math:Q or :math:P^{T} (or the leading rows or columns thereof) as specified by gen, m, and n. 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-singular-value-eigenvalue-routines