.. 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. .. 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. 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 std::vector &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:: 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