.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_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:onemkl_lapack_potrf to factorize :math:A. potri (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void potri(cl::sycl::queue &queue, oneapi::mkl::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::mkl::uplo::upper, the upper triangle of :math:A is stored. If upper_lower = oneapi::mkl::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:onemkl_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:onemkl_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::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, 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::mkl::lapack { cl::sycl::event potri(cl::sycl::queue &queue, oneapi::mkl::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::mkl::uplo::upper, the upper triangle of :math:A is stored. If upper_lower = oneapi::mkl::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:onemkl_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:onemkl_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::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, 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:onemkl_lapack-linear-equation-routines