.. 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(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, cl::sycl::buffer &a, std::int64_t lda, cl::sycl::buffer &ipiv, 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 :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. .. 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 :math:`\text{info}=i`, :math:`u_{ii}` is 0. The factorization has been completed, but :math:`U` is exactly singular. Division by 0 will occur if you use the factor :math:`U` for solving a system of linear equations. If :math:`\text{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. getrf (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event getrf(cl::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:: 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 :math:`\text{info}=i`, :math:`u_{ii}` is 0. The factorization has been completed, but :math:`U` is exactly singular. Division by 0 will occur if you use the factor :math:`U` for solving a system of linear equations. If :math:`\text{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-linear-equation-routines`