.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_gebrd: gebrd ===== Reduces a general matrix to bidiagonal form. .. container:: section .. rubric:: Description gebrd supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double * - std::complex * - std::complex The routine reduces a general :math:m \times n matrix :math:A to a bidiagonal matrix :math:B by an orthogonal (unitary) transformation. If :math:m \ge n, the reduction is given by :math:A=QBP^H=\begin{pmatrix}B_1\\0\end{pmatrix}P^H=Q_1B_1P_H where :math:B_{1} is an :math:n \times n upper diagonal matrix, :math:Q and :math:P are orthogonal or, for a complex :math:A, unitary matrices; :math:Q_{1} consists of the first :math:n columns of :math:Q. If :math:m < n, the reduction is given by :math:A = QBP^H = Q\begin{pmatrix}B_1\\0\end{pmatrix}P^H = Q_1B_1P_1^H, where :math:B_{1} is an :math:m \times m lower diagonal matrix, :math:Q and :math:P are orthogonal or, for a complex :math:A, unitary matrices; :math:P_{1} consists of the first :math:m columns of :math:P. The routine does not form the matrices :math:Q and :math:P explicitly, but represents them as products of elementary reflectors. Routines are provided to work with the matrices :math:Q and :math:P in this representation: If the matrix :math:A is real, - to compute :math:Q and :math:P explicitly, call :ref:onemkl_lapack_orgbr. If the matrix :math:A is complex, - to compute :math:Q and :math:P explicitly, call :ref:onemkl_lapack_ungbr gebrd (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void gebrd(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, cl::sycl::buffer &a, std::int64_t lda, cl::sycl::buffer &d, cl::sycl::buffer &e, cl::sycl::buffer &tauq, cl::sycl::buffer &taup, cl::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). a The buffer :math:a, size (lda,*). The buffer a contains the matrix :math:A. The second dimension of a must be at least :math:\max(1, m). lda The leading dimension of :math:a. 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_gebrd_scratchpad_size function. .. container:: section .. rubric:: Output Parameters a If :math:m \ge n, the diagonal and first super-diagonal of a are overwritten by the upper bidiagonal matrix :math:B. The elements below the diagonal, with the buffer tauq, represent the orthogonal matrix :math:Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the buffer taup, represent the orthogonal matrix :math:P as a product of elementary reflectors. If :math:m :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 info=-i, the 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. gebrd (USM Version) ------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event gebrd(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, RealT *d, RealT *e, T *tauq, T *taup, 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). a Pointer to matrix :math:A. The second dimension of a must be at least :math:\max(1, m). lda The leading dimension of a. 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_gebrd_scratchpad_size function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters a If :math:m \ge n, the diagonal and first super-diagonal of a are overwritten by the upper bidiagonal matrix :math:B. The elements below the diagonal, with the array tauq, represent the orthogonal matrix :math:Q as a product of elementary reflectors, and the elements above the first superdiagonal, with the array taup, represent the orthogonal matrix :math:P as a product of elementary reflectors. If :math:m :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 info=-i, the 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