.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack-linear-equation-routines: LAPACK Linear Equation Routines =============================== .. container:: LAPACK Linear Equation routines are used for factoring a matrix, solving a system of linear equations, solving linear least squares problems, and inverting a matrix. The following table lists the LAPACK Linear Equation routine groups. .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Routines - Scratchpad Size Routines - Description * - :ref:`onemkl_lapack_geqrf` - :ref:`onemkl_lapack_geqrf_scratchpad_size` - Computes the QR factorization of a general m-by-n matrix. * - :ref:`onemkl_lapack_gerqf` - :ref:`onemkl_lapack_gerqf_scratchpad_size` - Computes the RQ factorization of a general m-by-n matrix. * - :ref:`onemkl_lapack_getrf` - :ref:`onemkl_lapack_getrf_scratchpad_size` - Computes the LU factorization of a general m-by-n matrix. * - :ref:`onemkl_lapack_getri` - :ref:`onemkl_lapack_getri_scratchpad_size` - Computes the inverse of an LU-factored general matrix. * - :ref:`onemkl_lapack_getrs` - :ref:`onemkl_lapack_getrs_scratchpad_size` - Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides. * - :ref:`onemkl_lapack_hetrf` - :ref:`onemkl_lapack_hetrf_scratchpad_size` - Computes the Bunch-Kaufman factorization of a complex Hermitian matrix. * - :ref:`onemkl_lapack_orgqr` - :ref:`onemkl_lapack_orgqr_scratchpad_size` - Generates the real orthogonal matrix :math:`Q` of the QR factorization formed by geqrf. * - :ref:`onemkl_lapack_ormqr` - :ref:`onemkl_lapack_ormqr_scratchpad_size` - Multiplies a real matrix by the orthogonal matrix :math:`Q` of the QR factorization formed by geqrf. * - :ref:`onemkl_lapack_ormrq` - :ref:`onemkl_lapack_ormrq_scratchpad_size` - Multiplies a real matrix by the orthogonal matrix :math:`Q` of the RQ factorization formed by gerqf. * - :ref:`onemkl_lapack_potrf` - :ref:`onemkl_lapack_potrf_scratchpad_size` - Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix. * - :ref:`onemkl_lapack_potri` - :ref:`onemkl_lapack_potri_scratchpad_size` - Computes the inverse of a Cholesky-factored symmetric (Hermitian) positive-definite matrix. * - :ref:`onemkl_lapack_potrs` - :ref:`onemkl_lapack_potrs_scratchpad_size` - Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix, with multiple right-hand sides. * - :ref:`onemkl_lapack_sytrf` - :ref:`onemkl_lapack_sytrf_scratchpad_size` - Computes the Bunch-Kaufman factorization of a symmetric matrix. * - :ref:`onemkl_lapack_trtrs` - :ref:`onemkl_lapack_trtrs_scratchpad_size` - Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides. * - :ref:`onemkl_lapack_ungqr` - :ref:`onemkl_lapack_ungqr_scratchpad_size` - Generates the complex unitary matrix :math:`Q` of the QR factorization formed by geqrf. * - :ref:`onemkl_lapack_unmqr` - :ref:`onemkl_lapack_unmqr_scratchpad_size` - Multiplies a complex matrix by the unitary matrix :math:`Q` of the QR factorization formed by geqrf. * - :ref:`onemkl_lapack_unmrq` - :ref:`onemkl_lapack_unmrq_scratchpad_size` - Multiplies a complex matrix by the unitary matrix :math:`Q` of the RQ factorization formed by gerqf. .. toctree:: :hidden: geqrf geqrf_scratchpad_size gerqf gerqf_scratchpad_size getrf getrf_scratchpad_size getri getri_scratchpad_size getrs getrs_scratchpad_size hetrf hetrf_scratchpad_size orgqr orgqr_scratchpad_size ormqr ormqr_scratchpad_size ormrq ormrq_scratchpad_size potrf potrf_scratchpad_size potri potri_scratchpad_size potrs potrs_scratchpad_size sytrf sytrf_scratchpad_size trtrs trtrs_scratchpad_size ungqr ungqr_scratchpad_size unmqr unmqr_scratchpad_size unmrq unmrq_scratchpad_size