.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_lapack_orgbr: orgbr ===== Generates the real orthogonal matrix :math:`Q` or :math:`P^{T}` determined by :ref:`onemath_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:`onemath_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::math::lapack { void orgbr(cl::sycl::queue &queue, oneapi::math::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:`onemath_lapack_gebrd`. If ``gen = generate::p``, the number of rows in the original :math:`k \times n` matrix reduced by :ref:`onemath_lapack_gebrd`. a The buffer ``a`` as returned by :ref:`onemath_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:`onemath_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:`onemath_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::math::host_bad_alloc` :ref:`oneapi::math::device_bad_alloc` :ref:`oneapi::math::unimplemented` :ref:`oneapi::math::unsupported_device` :ref:`oneapi::math::lapack::invalid_argument` :ref:`oneapi::math::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::math::lapack { cl::sycl::event orgbr(cl::sycl::queue &queue, oneapi::math::generate gen, std::int64_t m, std::int64_t n, std::int64_t k, T *a, std::int64_t lda, const 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:`onemath_lapack_gebrd`. If ``gen = generate::p``, the number of rows in the original :math:`k \times n` matrix reduced by :ref:`onemath_lapack_gebrd`. a Pointer to array ``a`` as returned by :ref:`onemath_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:`onemath_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:`onemath_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::math::host_bad_alloc` :ref:`oneapi::math::device_bad_alloc` :ref:`oneapi::math::unimplemented` :ref:`oneapi::math::unsupported_device` :ref:`oneapi::math::lapack::invalid_argument` :ref:`oneapi::math::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:`onemath_lapack-singular-value-eigenvalue-routines`