.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_potrf: potrf ===== Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix. .. container:: section .. rubric:: Description potrf supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double * - std::complex * - std::complex The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix :math:A: .. list-table:: :header-rows: 1 * - :math:A = :math:U^{T}U for real data, :math:A = U^{H}U for complex data - if upper_lower=\ oneapi::mkl::uplo::upper * - :math:A = :math:LL^{T} for real data, :math:A = LL^{H} for complex data - if upper_lower=\ oneapi::mkl::uplo::lower where :math:L is a lower triangular matrix and :math:U is upper triangular. potrf (Buffer Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void potrf(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 whether the upper or lower triangular part of :math:A is stored and how :math:A is factored: If upper_lower=\ oneapi::mkl::uplo::upper, the array a stores the upper triangular part of the matrix :math:A, and the strictly lower triangular part of the matrix is not referenced. If upper_lower=\ oneapi::mkl::uplo::lower, the array a stores the lower triangular part of the matrix :math:A, and the strictly upper triangular part of the matrix is not referenced. n Specifies the order of the matrix :math:A (:math:0 \le n). a Buffer holding input matrix :math:A. The buffer a contains either the upper or the lower triangular part of the matrix :math:A (see upper_lower). 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_potrf_scratchpad_size function. .. container:: section .. rubric:: Output Parameters a The buffer a is overwritten by the Cholesky factor :math:U or :math:L, as 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, and detail() returns 0, then the leading minor of order :math:i (and therefore the matrix :math:A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix :math:A. 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. potrf (USM Version) ---------------------- .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event potrf(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 whether the upper or lower triangular part of :math:A is stored and how :math:A is factored: If upper_lower=\ oneapi::mkl::uplo::upper, the array a stores the upper triangular part of the matrix :math:A, and the strictly lower triangular part of the matrix is not referenced. If upper_lower=\ oneapi::mkl::uplo::lower, the array a stores the lower triangular part of the matrix :math:A, and the strictly upper triangular part of the matrix is not referenced. n Specifies the order of the matrix :math:A (:math:0 \le n). a Pointer to input matrix :math:A. The array a contains either the upper or the lower triangular part of the matrix :math:A (see upper_lower). 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_potrf_scratchpad_size function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters a The memory pointer to by pointer a is overwritten by the Cholesky factor :math:U or :math:L, as 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, and detail() returns 0, then the leading minor of order :math:i (and therefore the matrix :math:A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix :math:A. 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