/*! \file */ /* ************************************************************************ * Copyright (C) 2023-2026 Advanced Micro Devices, Inc. All rights Reserved. * * Permission is hereby granted, free of charge, to any person obtaining a copy * of this software and associated documentation files (the Software), to deal * in the Software without restriction, including without limitation the rights * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the Software is * furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED AS IS, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN * THE SOFTWARE. * * ************************************************************************ */ #ifndef ROCSPARSE_CSRIC0_H #define ROCSPARSE_CSRIC0_H #include "../../rocsparse-types.h" #include "rocsparse/rocsparse-export.h" #ifdef __cplusplus extern "C" { #endif /*! \ingroup precond_module * \details * \p rocsparse_csric_zero_pivot returns \ref rocsparse_status_zero_pivot if either a * structural or numerical zero has been found during \ref rocsparse_scsric0 "rocsparse_Xcsric0()" * computation. The first zero pivot \f$j\f$ at \f$A_{j,j}\f$ is stored in \p position, using * the same index base as the CSR matrix. * * \p position can be in host or device memory. If no zero pivot has been found, * \p position is set to -1 and \ref rocsparse_status_success is returned instead. * * \note \p rocsparse_csric0_zero_pivot is a blocking function. It might negatively influence * performance. * * \note * This routine does not support execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * info structure that holds the information collected during the analysis step. * @param[inout] * position pointer to zero pivot \f$j\f$, which can be in host or device memory. * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_pointer \p info or \p position pointer is * invalid. * \retval rocsparse_status_internal_error an internal error occurred. * \retval rocsparse_status_zero_pivot zero pivot has been found. */ ROCSPARSE_EXPORT rocsparse_status rocsparse_csric0_zero_pivot(rocsparse_handle handle, rocsparse_mat_info info, rocsparse_int* position); /*! \ingroup precond_module * \details * rocsparse_csric0_singular_pivot() returns the position of a * numerical singular pivot (where \f$|L_{j,j}| \leq \text{tolerance}\f$) * that has been found during \ref rocsparse_scsric0 "rocsparse_Xcsric0()" computation. * The first singular pivot \f$j\f$ at \f$L_{j,j}\f$ is stored in \p position, using the * same index base as the CSR matrix. * * \p position can be in host or device memory. If no singular pivot has been found, * \p position is set to -1. * * \note rocsparse_csric0_singular_pivot() is a blocking function. It might negatively influence * performance. * * \note * This routine does not support execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * info structure that holds the information collected during the analysis step. * @param[inout] * position pointer to singular pivot \f$k\f$, which can be in host or device memory. * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_pointer \p info or \p position pointer is * invalid. * \retval rocsparse_status_internal_error an internal error occurred. */ ROCSPARSE_EXPORT rocsparse_status rocsparse_csric0_singular_pivot(rocsparse_handle handle, rocsparse_mat_info info, rocsparse_int* position); /*! \ingroup precond_module * \details * rocsparse_csric0_set_tolerance() sets the numerical tolerance for detecting a * numerical singular pivot (where \f$|L_{j,j}| \leq \text{tolerance}\f$) * that might be found during \ref rocsparse_scsric0 "rocsparse_Xcsric0()" computation. * * * \note rocsparse_csric0_set_tolerance() is a blocking function. It might negatively influence * performance. * * \note * This routine does not support execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * info structure that holds the information collected during the analysis step. * @param[in] * tolerance tolerance for detecting singular pivot (\f$|L_{j,j}| \leq \text{tolerance}\f$). * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_pointer if \p info tolerance pointer is * invalid */ ROCSPARSE_EXPORT rocsparse_status rocsparse_csric0_set_tolerance(rocsparse_handle handle, rocsparse_mat_info info, double tolerance); /*! \ingroup precond_module * \details * rocsparse_csric0_get_tolerance() returns the numerical tolerance for detecting a * numerical singular pivot (where \f$|L_{j,j}| \leq \text{tolerance}\f$) * that might be found during \ref rocsparse_scsric0 "rocsparse_Xcsric0()" computation. * * * \note rocsparse_csric0_get_tolerance() is a blocking function. It might negatively influence * performance. * * \note * This routine does not support execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * info structure that holds the information collected during the analysis step. * @param[out] * tolerance obtain tolerance for detecting singular pivot (\f$|L_{j,j}| \leq \text{tolerance}\f$). * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_pointer if \p info or \p tolerance pointer is * invalid */ ROCSPARSE_EXPORT rocsparse_status rocsparse_csric0_get_tolerance(rocsparse_handle handle, rocsparse_mat_info info, double* tolerance); /*! \ingroup precond_module * \details * \p rocsparse_csric0_buffer_size returns the size of the temporary storage buffer * that is required by \ref rocsparse_scsric0_analysis "rocsparse_Xcsric0_analysis()". * The temporary storage buffer must be allocated by the user. The size of the temporary * storage buffer is identical to the size returned by * \ref rocsparse_scsrsv_buffer_size "rocsparse_Xcsrsv_buffer_size()" and * \ref rocsparse_scsrilu0_buffer_size "rocsparse_Xcsrilu0_buffer_size()" if the matrix * sparsity pattern is identical. The user-allocated buffer can therefore be shared between * subsequent calls to those functions. * * \note * This function is non-blocking and executed asynchronously with respect to the host. * It can return before the actual computation has finished. * * \note * This routine supports execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * m number of rows of the sparse CSR matrix. * @param[in] * nnz number of non-zero entries of the sparse CSR matrix. * @param[in] * descr descriptor of the sparse CSR matrix. * @param[in] * csr_val array of \p nnz elements of the sparse CSR matrix. * @param[in] * csr_row_ptr array of \p m+1 elements that point to the start of every row of the * sparse CSR matrix. * @param[in] * csr_col_ind array of \p nnz elements containing the column indices of the sparse * CSR matrix. * @param[out] * info structure that holds the information collected during the analysis step. * @param[out] * buffer_size number of bytes of the temporary storage buffer required by * \ref rocsparse_scsric0_analysis "rocsparse_Xcsric0_analysis()" and * \ref rocsparse_scsric0 "rocsparse_Xcsric0()". * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_size \p m or \p nnz is invalid. * \retval rocsparse_status_invalid_pointer \p descr, \p csr_val, \p csr_row_ptr, * \p csr_col_ind, \p info, or \p buffer_size pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. * \retval rocsparse_status_not_implemented * \ref rocsparse_matrix_type != \ref rocsparse_matrix_type_general. */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_scsric0_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const float* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_dcsric0_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const double* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_ccsric0_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const rocsparse_float_complex* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_zcsric0_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const rocsparse_double_complex* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, size_t* buffer_size); /**@}*/ /*! \ingroup precond_module * \details * \p rocsparse_csric0_analysis performs the analysis step for * \ref rocsparse_scsric0 "rocsparse_Xcsric0()". It is expected that this function will be * executed only once for a given matrix and particular operation type. The analysis metadata * can be cleared by \ref rocsparse_csric0_clear(). * * \p rocsparse_csric0_analysis can share its metadata with * \ref rocsparse_scsrilu0_analysis "rocsparse_Xcsrilu0_analysis()", * \ref rocsparse_scsrsv_analysis "rocsparse_Xcsrsv_analysis()", and * \ref rocsparse_scsrsm_analysis "rocsparse_Xcsrsm_analysis()". Selecting * \ref rocsparse_analysis_policy_reuse policy can greatly improve the computation * performance of metadata. However, the user needs to ensure that the sparsity * pattern remains unchanged. If this cannot be assured, * \ref rocsparse_analysis_policy_force has to be used. * * \note * If the matrix sparsity pattern changes, the gathered information will become invalid. * * \note * This function is blocking with respect to the host. * * \note * This routine does not support execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * m number of rows of the sparse CSR matrix. * @param[in] * nnz number of non-zero entries of the sparse CSR matrix. * @param[in] * descr descriptor of the sparse CSR matrix. * @param[in] * csr_val array of \p nnz elements of the sparse CSR matrix. * @param[in] * csr_row_ptr array of \p m+1 elements that point to the start of every row of the * sparse CSR matrix. * @param[in] * csr_col_ind array of \p nnz elements containing the column indices of the sparse * CSR matrix. * @param[out] * info structure that holds the information collected during * the analysis step. * @param[in] * analysis \ref rocsparse_analysis_policy_reuse or * \ref rocsparse_analysis_policy_force. * @param[in] * solve \ref rocsparse_solve_policy_auto. * @param[in] * temp_buffer temporary storage buffer allocated by the user. * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_size \p m or \p nnz is invalid. * \retval rocsparse_status_invalid_pointer \p descr, \p csr_val, \p csr_row_ptr, * \p csr_col_ind, \p info, or \p temp_buffer pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. * \retval rocsparse_status_not_implemented * \ref rocsparse_matrix_type != \ref rocsparse_matrix_type_general. */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_scsric0_analysis(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const float* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_analysis_policy analysis, rocsparse_solve_policy solve, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_dcsric0_analysis(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const double* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_analysis_policy analysis, rocsparse_solve_policy solve, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_ccsric0_analysis(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const rocsparse_float_complex* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_analysis_policy analysis, rocsparse_solve_policy solve, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_zcsric0_analysis(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, const rocsparse_double_complex* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_analysis_policy analysis, rocsparse_solve_policy solve, void* temp_buffer); /**@}*/ /*! \ingroup precond_module * \details * \p rocsparse_csric0_clear deallocates all memory that was allocated by * \ref rocsparse_scsric0_analysis "rocsparse_Xcsric0_analysis()". This is especially * useful if memory is an issue and the analysis data is not required for further * computation. * * \note * Calling \p rocsparse_csric0_clear is optional. All allocated resources will be * cleared when the opaque \ref rocsparse_mat_info struct is destroyed using * \ref rocsparse_destroy_mat_info(). * * \note * This routine does not support execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[inout] * info structure that holds the information collected during the analysis step. * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_pointer \p info pointer is invalid. * \retval rocsparse_status_memory_error the buffer holding the metadata could not * be deallocated. * \retval rocsparse_status_internal_error an internal error occurred. */ ROCSPARSE_EXPORT rocsparse_status rocsparse_csric0_clear(rocsparse_handle handle, rocsparse_mat_info info); /*! \ingroup precond_module * \brief Incomplete Cholesky factorization with 0 fill-ins and no pivoting using the CSR * storage format. * * \details * \p rocsparse_csric0 computes the incomplete Cholesky factorization with 0 fill-ins * and no pivoting of a sparse \f$m \times m\f$ CSR matrix \f$A\f$, such that * \f[ * A \approx LL^T * \f] * where the lower triangular matrix \f$L\f$ is computed using: * \f[ * L_{ij} = \left\{ * \begin{array}{ll} * \sqrt{A_{jj} - \sum_{k=0}^{j-1}(L_{jk})^{2}}, & \text{if i == j} \\ * \frac{1}{L_{jj}}(A_{ij} - \sum_{k=0}^{j-1}L_{ik} \times L_{jk}), & \text{if i > j} * \end{array} * \right. * \f] * for each entry found in the CSR matrix \f$A\f$. * * Computing the above incomplete Cholesky factorization requires three steps to complete. First, * determine the size of the required temporary storage buffer by calling * \ref rocsparse_scsric0_buffer_size "rocsparse_Xcsric0_buffer_size()". After this buffer size has been determined, * allocate the buffer and pass it to \ref rocsparse_scsric0_analysis "rocsparse_Xcsric0_analysis()". * This will perform analysis on the sparsity pattern of the matrix. Finally, call \p rocsparse_scsric0, * \p rocsparse_dcsric0, \p rocsparse_ccsric0, or \p rocsparse_zcsric0 to perform the actual factorization. The calculation * of the buffer size and the analysis of the sparse matrix only need to be performed once for a given sparsity pattern, * while the factorization can be repeatedly applied to multiple matrices having the same sparsity pattern. After all calls * to \ref rocsparse_scsric0 "rocsparse_Xcsric0()" are complete, the temporary buffer can be deallocated. * * When computing the Cholesky factorization, it is possible that \f$L_{jj} == 0\f$, which would result in a division by zero. * This could occur from either \f$A_{jj}\f$ not existing in the sparse CSR matrix (referred to as a structural zero) or because * \f$A_{jj} - \sum_{k=0}^{j-1}(L_{jk})^{2} == 0\f$ (referred to as a numerical zero). For example, running the Cholesky * factorization on the following matrix: * \f[ * \begin{bmatrix} * 2 & 1 & 0 \\ * 1 & 2 & 1 \\ * 0 & 1 & 2 * \end{bmatrix} * \f] * results in a successful Cholesky factorization, however running with the matrix: * \f[ * \begin{bmatrix} * 2 & 1 & 0 \\ * 1 & 1/2 & 1 \\ * 0 & 1 & 2 * \end{bmatrix} * \f] * results in a numerical zero because: * \f[ * \begin{array}{ll} * L_{00} &= \sqrt{2} \\ * L_{10} &= \frac{1}{\sqrt{2}} \\ * L_{11} &= \sqrt{\frac{1}{2} - (\frac{1}{\sqrt{2}})^2} * &= 0 * \end{array} * \f] * The user can detect the presence of a structural zero by calling \ref rocsparse_csric0_zero_pivot() after * \ref rocsparse_scsric0_analysis "rocsparse_Xcsric0_analysis()" and/or the presence of a structural or * numerical zero by calling \ref rocsparse_csric0_zero_pivot() after \ref rocsparse_scsric0 "rocsparse_Xcsric0()": * \code{.c} * rocsparse_dcsric0(handle, * m, * nnz, * descr_M, * csr_val, * csr_row_ptr, * csr_col_ind, * info, * rocsparse_solve_policy_auto, * temp_buffer); * * // Check for zero pivot * if(rocsparse_status_zero_pivot == rocsparse_csric0_zero_pivot(handle, * info, * &position)) * { * printf("L has structural and/or numerical zero at L(%d,%d)\n", position, position); * } * \endcode * In both cases, \ref rocsparse_csric0_zero_pivot() will report the first zero pivot (either numerical or structural) * found. See the full example below. The user can also set the diagonal type to be \f$1\f$ using \ref rocsparse_set_mat_diag_type(), * which will interpret the matrix \f$A\f$ as having ones on its diagonal (even if no non-zero exists in the sparsity pattern). * * \p rocsparse_csric0 computes the Cholesky factorization inplace, meaning that the values array \p csr_val of the \f$A\f$ * matrix is overwritten with the \f$L\f$ matrix stored in the lower triangular part of \f$A\f$: * * \f[ * \begin{align} * \begin{bmatrix} * a_{00} & a_{01} & a_{02} \\ * a_{10} & a_{11} & a_{12} \\ * a_{20} & a_{21} & a_{22} * \end{bmatrix} * \rightarrow * \begin{bmatrix} * l_{00} & a_{01} & a_{02} \\ * l_{10} & l_{11} & a_{12} \\ * l_{20} & l_{21} & l_{22} * \end{bmatrix} * \end{align} * \f] * The row pointer array \p csr_row_ptr and the column indices array \p csr_col_ind remain the same for \f$A\f$ and the output, as * the incomplete factorization does not generate new non-zeros in the output which do not already exist in \f$A\f$. * * The performance of computing the Cholesky factorization with rocSPARSE greatly depends on the sparsity pattern * of the matrix \f$A\f$, as this is what determines the amount of parallelism available. * * \note * The sparse CSR matrix has to be sorted. This can be achieved by calling * rocsparse_csrsort(). * * \note * This function is non-blocking and executed asynchronously with respect to the host. * It can return before the actual computation has finished. * * \note * This routine supports execution in a hipGraph context. * * @param[in] * handle handle to the rocSPARSE library context queue. * @param[in] * m number of rows of the sparse CSR matrix. * @param[in] * nnz number of non-zero entries of the sparse CSR matrix. * @param[in] * descr descriptor of the sparse CSR matrix. * @param[inout] * csr_val array of \p nnz elements of the sparse CSR matrix. * @param[in] * csr_row_ptr array of \p m+1 elements that point to the start * of every row of the sparse CSR matrix. * @param[in] * csr_col_ind array of \p nnz elements containing the column indices of the sparse * CSR matrix. * @param[in] * info structure that holds the information collected during the analysis step. * @param[in] * policy \ref rocsparse_solve_policy_auto. * @param[in] * temp_buffer temporary storage buffer allocated by the user. * * \retval rocsparse_status_success the operation completed successfully. * \retval rocsparse_status_invalid_handle the library context was not initialized. * \retval rocsparse_status_invalid_size \p m or \p nnz is invalid. * \retval rocsparse_status_invalid_pointer \p descr, \p csr_val, \p csr_row_ptr, * or \p csr_col_ind pointer is invalid. * \retval rocsparse_status_arch_mismatch the device is not supported. * \retval rocsparse_status_internal_error an internal error occurred. * \retval rocsparse_status_not_implemented * \ref rocsparse_matrix_type != \ref rocsparse_matrix_type_general. * * \par Example * Consider the sparse \f$m \times m\f$ matrix \f$A\f$, stored in the CSR * storage format. The following example computes the incomplete Cholesky factorization * \f$M \approx LL^T\f$ and solves the preconditioned system \f$My = x\f$. * \snippet example_rocsparse_csric0.cpp doc example */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_scsric0(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, float* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_solve_policy policy, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_dcsric0(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, double* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_solve_policy policy, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_ccsric0(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, rocsparse_float_complex* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_solve_policy policy, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_zcsric0(rocsparse_handle handle, rocsparse_int m, rocsparse_int nnz, const rocsparse_mat_descr descr, rocsparse_double_complex* csr_val, const rocsparse_int* csr_row_ptr, const rocsparse_int* csr_col_ind, rocsparse_mat_info info, rocsparse_solve_policy policy, void* temp_buffer); /**@}*/ #ifdef __cplusplus } #endif #endif /* ROCSPARSE_CSRIC0_H */