.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack_potrs_batch: potrs_batch =========== Computes the LU factorizations of a batch of general matrices. .. container:: section .. rubric:: Description potrs_batch supports the following precisions. .. list-table:: :header-rows: 1 * - T * - float * - double * - std::complex * - std::complex .. _onemkl_lapack_potrs_batch_buffer: potrs_batch (Buffer Version) ---------------------------- .. container:: section .. rubric:: Description The buffer version of potrs_batch supports only the strided API. **Strided API** | The routine solves for :math:X_i the systems of linear equations :math:A_iX_i = B_i with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices :math:A_i, given the Cholesky factorization of :math:A_i, :math:i \in \{1...batch\_size\}: | :math:A_i = U_i^TU_i for real data, :math:A_i = U_i^HU_i for complex data if uplo = mkl::uplo::upper, | :math:A_i = L_iL_i^T for real data, :math:A_i = L_iL_i^H for complex data if uplo = mkl::uplo::lower, | where :math:L_i is a lower triangular matrix and :math:U_i is upper triangular. | The systems are solved with multiple right-hand sides stored in the columns of the matrices :math:B_i. | Before calling this routine, matrices :math:A_i should be factorized by call to the Strided API of the :ref:onemkl_lapack_potrf_batch_buffer function. .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { void potrs_batch(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer &a, std::int64_t lda, std::int64_t stride_a, cl::sycl::buffer &b, std::int64_t ldb, std::int64_t stride_b, std::int64_t batch_size, cl::sycl::buffer &scratchpad, std::int64_t scratchpad_size) } .. container:: section .. rubric:: Input Parameters queue Device queue where calculations will be performed. uplo | Indicates how the input matrices have been factored: | If uplo = mkl::uplo::upper, the upper triangle :math:U_i of :math:A_i is stored, where :math:A_i = U_i^TU_i for real data, :math:A_i = U_i^HU_i for complex data. | If uplo = mkl::uplo::lower, the upper triangle :math:L_i of :math:A_i is stored, where :math:A_i = L_iL_i^T for real data, :math:A_i = L_iL_i^H for complex data. n The order of matrices :math:A_i (:math:0 \le n). nrhs The number of right-hand sides (:math:0 \le \text{nrhs}). a Array containing batch of factorizations of the matrices :math:A_i, as returned by the Strided API of the :ref:onemkl_lapack_potrf_batch_buffer function. lda Leading dimension of :math:A_i. stride_a Stride between the beginnings of matrices inside the batch array a. b Array containing batch of matrices :math:B_i whose columns are the right-hand sides for the systems of equations. ldb Leading dimension of :math:B_i. stride_b Stride between the beginnings of matrices :math:B_i inside the batch array b. batch_size Number of problems in a batch. scratchpad Scratchpad memory to be used by routine for storing intermediate results. scratchpad_size Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by the Strided API of the :ref:onemkl_lapack_potrs_batch_scratchpad_size function. .. container:: section .. rubric:: Output Parameters b Solution matrices :math:X_i. .. 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::lapack::batch_error :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument The info code of the problem can be obtained by info() method of exception object: If info = -n, the :math:n-th parameter had an illegal value. 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 be not less then value returned by detail() method of exception object. If info is not zero and detail() returns zero, then there were some errors for some of the problems in the supplied batch and info code contains the number of failed calculations in a batch. If info is zero, then for some of the matrices diagonal element of the Cholesky factor is zero, and the solve could not be completed. The indices of such matrices in the batch can be obtained with ids() method of the exception object. The indices of first zero diagonal elements in these matrices can be obtained by exceptions() method of exception object. .. _onemkl_lapack_potrs_batch_usm: potrs_batch (USM Version) ------------------------- .. container:: section .. rubric:: Description The USM version of potrs_batch supports the group API and strided API. **Group API** .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event potrs_batch(cl::sycl::queue &queue, mkl::uplo *uplo, std::int64_t *n, std::int64_t *nrhs, T **a, std::int64_t *lda, T **b, std::int64_t *ldb, std::int64_t group_count, std::int64_t *group_sizes, T *scratchpad, std::int64_t scratchpad_size, const std::vector &events = {}) } .. container:: section .. rubric:: Input Parameters queue Device queue where calculations will be performed. uplo | Array of group_count :math:\text{uplo}_g parameters. | Each of :math:\text{uplo}_g indicates whether the upper or lower triangular parts of the input matrices are provided: | If :math:\text{uplo}_g is mkl::uplo::upper, input matrices from array a belonging to group :math:g store the upper triangular parts, | If :math:\text{uplo}_g is mkl::uplo::lower, input matrices from array a belonging to group :math:g store the lower triangular parts. n | Array of group_count :math:n_g parameters. | Each :math:n_g specifies the order of the input matrices from array a belonging to group :math:g. nrhs | Array of group_count :math:\text{nrhs}_g parameters. | Each :math:\text{nrhs}_g specifies the number of right-hand sides supplied for group :math:g in corresponding part of array b. a Array of batch_size pointers to Cholesky factored matrices :math:A_i as returned by the Group API of the :ref:onemkl_lapack_potrf_batch_usm function. lda | Array of group_count :math:\text{lda}_g parameters. | Each :math:\text{lda}_g specifies the leading dimensions of the matrices from a belonging to group :math:g. b Array of batch_size pointers to right-hand side matrices :math:B_i, each of size :math:\text{ldb}_g \cdot \text{nrhs}_g, where :math:g is an index of group corresponding to :math:B_i. ldb | Array of group_count :math:\text{ldb}_g parameters. | Each :math:\text{ldb}_g specifies the leading dimensions of the matrices from b belonging to group :math:g. group_count Number of groups of parameters. Must be at least 0. group_sizes Array of group_count integers. Array element with index :math:g specifies the number of problems to solve for each of the groups of parameters :math:g. So the total number of problems to solve, batch_size, is a sum of all parameter group sizes. scratchpad Scratchpad memory to be used by routine for storing intermediate results. scratchpad_size Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by the Group API of the :ref:onemkl_lapack_potrs_batch_scratchpad_size function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters b Solution matrices :math:X_i. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. .. 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::lapack::batch_error :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument The info code of the problem can be obtained by info() method of exception object: If info = -n, the n-th parameter had an illegal value. 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 be not less then value returned by detail() method of exception object. If info is not zero and detail() returns zero, then there were some errors for some of the problems in the supplied batch and info code contains the number of failed calculations in a batch. If info is zero, then for some of the matrices diagonal element of the Cholesky factor is zero, and the solve could not be completed. The indices of such matrices in the batch can be obtained with ids() method of the exception object. The indices of first zero diagonal elements in these matrices can be obtained by exceptions() method of exception object. **Strided API** | The routine solves for :math:X_i the systems of linear equations :math:A_iX_i = B_i with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices :math:A_i, given the Cholesky factorization of :math:A_i, :math:i \in \{1...batch\_size\}: | :math:A_i = U_i^TU_i for real data, :math:A_i = U_i^HU_i for complex data if uplo = mkl::uplo::upper, | :math:A_i = L_iL_i^T for real data, :math:A_i = L_iL_i^H for complex data if uplo = mkl::uplo::lower, | where :math:L_i is a lower triangular matrix and :math:U_i is upper triangular. | The systems are solved with multiple right-hand sides stored in the columns of the matrices :math:B_i. | Before calling this routine, matrices :math:A_i should be factorized by call to the Strided API of the :ref:onemkl_lapack_potrf_batch_usm function. .. container:: section .. rubric:: Syntax .. code-block:: cpp namespace oneapi::mkl::lapack { cl::sycl::event potrs_batch(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t stride_a, T *b, std::int64_t ldb, std::int64_t stride_b, std::int64_t batch_size, T *scratchpad, std::int64_t scratchpad_size, const std::vector &events = {}) }; .. container:: section .. rubric:: Input Parameters queue Device queue where calculations will be performed. uplo | Indicates how the input matrices have been factored: | If uplo = mkl::uplo::upper, the upper triangle :math:U_i of :math:A_i is stored, where :math:A_i = U_i^TU_i for real data, :math:A_i = U_i^HU_i for complex data. | If uplo = mkl::uplo::lower, the upper triangle :math:L_i of :math:A_i is stored, where :math:A_i = L_iL_i^T for real data, :math:A_i = L_iL_i^H for complex data. n The order of matrices :math:A_i (:math:0 \le n). nrhs The number of right-hand sides (:math:0 \le nrhs). a Array containing batch of factorizations of the matrices :math:A_i, as returned by the Strided API of the :ref:onemkl_lapack_potrf_batch_usm function. lda Leading dimension of :math:A_i. stride_a Stride between the beginnings of matrices inside the batch array a. b Array containing batch of matrices :math:B_i whose columns are the right-hand sides for the systems of equations. ldb Leading dimension of :math:B_i. stride_b Stride between the beginnings of matrices :math:B_i inside the batch array b. batch_size Number of problems in a batch. scratchpad Scratchpad memory to be used by routine for storing intermediate results. scratchpad_size Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by the Strided API of the :ref:onemkl_lapack_potrs_batch_scratchpad_size function. events List of events to wait for before starting computation. Defaults to empty list. .. container:: section .. rubric:: Output Parameters b Solution matrices :math:X_i. .. container:: section .. rubric:: Return Values Output event to wait on to ensure computation is complete. .. 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::lapack::batch_error :ref:oneapi::mkl::unimplemented :ref:oneapi::mkl::unsupported_device :ref:oneapi::mkl::lapack::invalid_argument 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 info = -n, the :math:n-th parameter had an illegal value. 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 be not less then value returned by detail() method of exception object. If info is not zero and detail() returns zero, then there were some errors for some of the problems in the supplied batch and info code contains the number of failed calculations in a batch. If info is zero, then for some of the matrices diagonal element of the Cholesky factor is zero, and the solve could not be completed. The indices of such matrices in the batch can be obtained with ids() method of the exception object. The indices of first zero diagonal elements in these matrices can be obtained by exceptions() method of exception object. **Parent topic:** :ref:onemkl_lapack-like-extensions-routines