.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_getrf: getrf ===== Computes the LU factorization of a general :math:m \times n matrix. .. container:: section .. rubric:: Description getrf supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double * - std::complex * - std::complex The routine computes the LU factorization of a general :math:m \times n matrix :math:A as :math:A = PLU, where :math:P is a permutation matrix, :math:L is lower triangular with unit diagonal elements (lower trapezoidal if :math:m > n) and :math:U is upper triangular (upper trapezoidal if :math:m < n). The routine uses partial pivoting, with row interchanges. getrf (BUFFER Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void getrf(sycl::queue &queue, std::int64_t m, std::int64_t n, sycl::buffer &a, std::int64_t lda, sycl::buffer &ipiv, 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 :math:A (:math:0 \le n). a Buffer holding input matrix :math:A. The buffer a contains the matrix :math:A. The second dimension of a must be at least :math:\max(1, n). 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_getrf_scratchpad_size function. .. container:: section .. rubric:: Output Parameters a Overwritten by :math:L and :math:U. The unit diagonal elements of :math:L are not stored. ipiv Array, size at least :math:\max(1,\min(m, n)). Contains the pivot indices; for :math:1 \le i \le \min(m, n), row :math:i was interchanged with row :math:\text{ipiv}(i). scratchpad Buffer holding scratchpad memory to be used by routine for storing intermediate results. getrf (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { sycl::event getrf(sycl::queue &queue, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, std::int64_t *ipiv, 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 :math:A (:math:0 \le n). a Pointer to array holding input matrix :math:A. The second dimension of a must be at least :math:\max(1, n). 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_getrf_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:L and :math:U. The unit diagonal elements of :math:L are not stored. ipiv Array, size at least :math:\max(1,\min(m, n)). Contains the pivot indices; for :math:1 \le i \le \min(m, n), row :math:i was interchanged with row :math:\text{ipiv}(i). 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