.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_lapack_potri: potri ===== Computes the inverse of a symmetric (Hermitian) positive-definite matrix using the Cholesky factorization. .. container:: section .. rubric:: Description ``potri`` supports the following precisions. .. list-table:: :header-rows: 1 * - T * - ``float`` * - ``double`` * - ``std::complex`` * - ``std::complex`` The routine computes the inverse :math:`A^{-1}` of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix :math:`A`. Before calling this routine, call :ref:`onemath_lapack_potrf` to factorize :math:`A`. potri (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { void potri(cl::sycl::queue &queue, oneapi::math::uplo upper_lower, std::int64_t n, cl::sycl::buffer &a, std::int64_t lda, cl::sycl::buffer &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters queue The queue where the routine should be executed. upper_lower Indicates how the input matrix :math:`A` has been factored: If ``upper_lower = oneapi::math::uplo::upper``, the upper triangle of :math:`A` is stored. If ``upper_lower = oneapi::math::uplo::lower``, the lower triangle of :math:`A` is stored. n Specifies the order of the matrix :math:`A` (:math:`0 \le n`). a Contains the factorization of the matrix :math:`A`, as returned by :ref:`onemath_lapack_potrf`. 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:`onemath_lapack_potri_scratchpad_size` function. .. container:: section .. rubric:: Output Parameters a Overwritten by the upper or lower triangle of the inverse of :math:`A`. Specified by ``upper_lower``. 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 :math:`\text{info}=i`, the :math:`i`-th diagonal element of the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed. 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. potri (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::math::lapack { cl::sycl::event potri(cl::sycl::queue &queue, oneapi::math::uplo upper_lower, std::int64_t n, T *a, std::int64_t lda, 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. upper_lower Indicates how the input matrix :math:`A` has been factored: If ``upper_lower = oneapi::math::uplo::upper``, the upper triangle of :math:`A` is stored. If ``upper_lower = oneapi::math::uplo::lower``, the lower triangle of :math:`A` is stored. n Specifies the order of the matrix :math:`A` (:math:`0 \le n`). a Contains the factorization of the matrix :math:`A`, as returned by :ref:`onemath_lapack_potrf`. 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:`onemath_lapack_potri_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 the upper or lower triangle of the inverse of :math:`A`. Specified by ``upper_lower``. 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 :math:`\text{info}=i`, the :math:`i`-th diagonal element of the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed. 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-linear-equation-routines`