/*! \file */ /* ************************************************************************ * Copyright (C) 2023-2025 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_GTSV_H #define ROCSPARSE_GTSV_H #include "../../rocsparse-types.h" #include "rocsparse/rocsparse-export.h" #ifdef __cplusplus extern "C" { #endif /*! \ingroup precond_module * \details * \p rocsparse_gtsv_buffer_size returns the size of the temporary storage buffer * that is required by \ref rocsparse_sgtsv "rocsparse_Xgtsv()". The temporary * storage buffer must be allocated by the user. * * \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 size of the tri-diagonal linear system (must be >= 2). * @param[in] * n number of columns in the dense matrix B. * @param[in] * dl lower diagonal of tri-diagonal system. The first entry must be zero. * @param[in] * d main diagonal of tri-diagonal system. * @param[in] * du upper diagonal of tri-diagonal system. The last entry must be zero. * @param[in] * B dense matrix of size ( \p ldb, \p n ). * @param[in] * ldb leading dimension of B. Must satisfy \p ldb >= max(1, m). * @param[out] * buffer_size number of bytes of the temporary storage buffer required by * rocsparse_sgtsv(), rocsparse_dgtsv(), rocsparse_cgtsv(), * and rocsparse_zgtsv(). * * \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, \p n, or \p ldb is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, \p du, * \p B, or \p buffer_size pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const float* dl, const float* d, const float* du, const float* B, rocsparse_int ldb, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const double* dl, const double* d, const double* du, const double* B, rocsparse_int ldb, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, const rocsparse_float_complex* B, rocsparse_int ldb, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, const rocsparse_double_complex* B, rocsparse_int ldb, size_t* buffer_size); /**@}*/ /*! \ingroup precond_module * \brief Tridiagonal solver with pivoting * * \details * \p rocsparse_gtsv solves a tridiagonal system for multiple right-hand sides using pivoting * \f[ * T*B = B * \f] * where \f$T\f$ is a sparse tridiagonal matrix and \f$B\f$ is a dense \f$ldb \times n\f$ matrix storing the * right-hand side vectors in column order. The tridiagonal matrix \f$T\f$ is defined by three vectors: \p dl * for the lower diagonal, \p d for the main diagonal, and \p du for the upper diagonal. * * Solving the tridiagonal system involves two steps. First, call * \ref rocsparse_sgtsv_buffer_size "rocsparse_Xgtsv_buffer_size()" to determine the size of the required * temporary storage buffer. After this is determined, allocate this buffer and pass it to * \ref rocsparse_sgtsv "rocsparse_Xgtsv()" to perform the actual solve. The \f$B\f$ dense matrix, which initially * stores the \p n right-hand side vectors, is overwritten with the \p n solution vectors after the call to * \ref rocsparse_sgtsv "rocsparse_Xgtsv()". * * \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 size of the tri-diagonal linear system (must be >= 2). * @param[in] * n number of columns in the dense matrix B. * @param[in] * dl lower diagonal of tri-diagonal system. The first entry must be zero. * @param[in] * d main diagonal of tri-diagonal system. * @param[in] * du upper diagonal of tri-diagonal system. The last entry must be zero. * @param[inout] * B dense matrix of size ( \p ldb, \p n ). * @param[in] * ldb leading dimension of B. Must satisfy \p ldb >= max(1, m). * @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, \p n, or \p ldb is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, * \p du, \p B, or \p temp_buffer pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. * * \par Example * \snippet example_rocsparse_gtsv.cpp doc example */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const float* dl, const float* d, const float* du, float* B, rocsparse_int ldb, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const double* dl, const double* d, const double* du, double* B, rocsparse_int ldb, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, rocsparse_float_complex* B, rocsparse_int ldb, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, rocsparse_double_complex* B, rocsparse_int ldb, void* temp_buffer); /**@}*/ /*! \ingroup precond_module * \details * \p rocsparse_gtsv_no_pivot_buffer_size returns the size of the temporary storage buffer * that is required by \ref rocsparse_sgtsv_no_pivot "rocsparse_Xgtsv_no_pivot()". The temporary * storage buffer must be allocated by the user. * * \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 size of the tri-diagonal linear system (must be >= 2). * @param[in] * n number of columns in the dense matrix B. * @param[in] * dl lower diagonal of tri-diagonal system. The first entry must be zero. * @param[in] * d main diagonal of tri-diagonal system. * @param[in] * du upper diagonal of tri-diagonal system. The last entry must be zero. * @param[in] * B dense matrix of size ( \p ldb, \p n ). * @param[in] * ldb leading dimension of B. Must satisfy \p ldb >= max(1, m). * @param[out] * buffer_size number of bytes of the temporary storage buffer required by * rocsparse_sgtsv_no_pivot(), rocsparse_dgtsv_no_pivot(), rocsparse_cgtsv_no_pivot(), * and rocsparse_zgtsv_no_pivot(). * * \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, \p n, or \p ldb is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, \p du, * \p B, or \p buffer_size pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_no_pivot_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const float* dl, const float* d, const float* du, const float* B, rocsparse_int ldb, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_no_pivot_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const double* dl, const double* d, const double* du, const double* B, rocsparse_int ldb, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_no_pivot_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, const rocsparse_float_complex* B, rocsparse_int ldb, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_no_pivot_buffer_size(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, const rocsparse_double_complex* B, rocsparse_int ldb, size_t* buffer_size); /**@}*/ /*! \ingroup precond_module * \brief Tridiagonal solver (no pivoting) * * \details * \p rocsparse_gtsv_no_pivot solves a tridiagonal linear system for multiple right-hand sides without pivoting * \f[ * T*B = B * \f] * where \f$T\f$ is a sparse tridiagonal matrix and \f$B\f$ is a dense \f$ldb \times n\f$ matrix storing the * right-hand side vectors in column order. The tridiagonal matrix \f$T\f$ is defined by three vectors: \p dl * for the lower diagonal, \p d for the main diagonal, and \p du for the upper diagonal. * * Solving the tridiagonal system with multiple right-hand sides without pivoting involves two steps. First, * call \ref rocsparse_sgtsv_no_pivot_buffer_size "rocsparse_Xgtsv_no_pivot_buffer_size()" * to determine the size of the required temporary storage buffer. After this is determined, allocate the * buffer and pass it to \ref rocsparse_sgtsv_no_pivot "rocsparse_Xgtsv_no_pivot()" to perform the actual * solve. The \f$B\f$ dense matrix, which initially stores the \p n right-hand side vectors, is overwritten * with the \p n solution vectors after the call to \ref rocsparse_sgtsv_no_pivot "rocsparse_Xgtsv_no_pivot()". * * \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 size of the tri-diagonal linear system (must be >= 2). * @param[in] * n number of columns in the dense matrix B. * @param[in] * dl lower diagonal of tri-diagonal system. The first entry must be zero. * @param[in] * d main diagonal of tri-diagonal system. * @param[in] * du upper diagonal of tri-diagonal system. The last entry must be zero. * @param[inout] * B dense matrix of size ( \p ldb, \p n ). * @param[in] * ldb leading dimension of B. Must satisfy \p ldb >= max(1, m). * @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, \p n, or \p ldb is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, * \p du, \p B, or \p temp_buffer pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. * * \par Example * \snippet example_rocsparse_gtsv_no_pivot.cpp doc example */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_no_pivot(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const float* dl, const float* d, const float* du, float* B, rocsparse_int ldb, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_no_pivot(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const double* dl, const double* d, const double* du, double* B, rocsparse_int ldb, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_no_pivot(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, rocsparse_float_complex* B, rocsparse_int ldb, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_no_pivot(rocsparse_handle handle, rocsparse_int m, rocsparse_int n, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, rocsparse_double_complex* B, rocsparse_int ldb, void* temp_buffer); /**@}*/ /*! \ingroup precond_module * \details * \p rocsparse_gtsv_no_pivot_strided_batch_buffer_size returns the size of the temporary storage buffer * that is required by \ref rocsparse_sgtsv_no_pivot_strided_batch "rocsparse_Xgtsv_no_pivot_strided_batch()". * The temporary storage buffer must be allocated by the user. * * \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 size of the tri-diagonal linear system. * @param[in] * dl lower diagonal of tri-diagonal system, where the ith system lower diagonal starts at \p dl+batch_stride*i. * @param[in] * d main diagonal of tri-diagonal system, where the ith system diagonal starts at \p d+batch_stride*i. * @param[in] * du upper diagonal of tri-diagonal system, where the ith system upper diagonal starts at \p du+batch_stride*i. * @param[inout] * x dense array of righthand-sides where the ith righthand-side starts at \p x+batch_stride*i. * @param[in] * batch_count the number of systems to solve. * @param[in] * batch_stride the number of elements that separate each system. Must satisfy \p batch_stride >= \p m. * @param[out] * buffer_size number of bytes of the temporary storage buffer required by * \ref rocsparse_sgtsv_no_pivot_strided_batch "rocsparse_Xgtsv_no_pivot_strided_batch()". * * \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, \p batch_count, or \p batch_stride is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, \p du, * \p x, or \p buffer_size pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_no_pivot_strided_batch_buffer_size(rocsparse_handle handle, rocsparse_int m, const float* dl, const float* d, const float* du, const float* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_no_pivot_strided_batch_buffer_size(rocsparse_handle handle, rocsparse_int m, const double* dl, const double* d, const double* du, const double* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_no_pivot_strided_batch_buffer_size(rocsparse_handle handle, rocsparse_int m, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, const rocsparse_float_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_no_pivot_strided_batch_buffer_size(rocsparse_handle handle, rocsparse_int m, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, const rocsparse_double_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); /**@}*/ /*! \ingroup precond_module * \brief Strided Batch tridiagonal solver (no pivoting) * * \details * \p rocsparse_gtsv_no_pivot_strided_batch solves a batched tridiagonal linear system * \f[ * T^{i}*x^{i} = x^{i} * \f] * where for each batch \f$i=0\ldots\f$ \p batch_count, \f$T^{i}\f$ is a sparse tridiagonal matrix and * \f$x^{i}\f$ is a dense right-hand side vector. All of the tridiagonal matrices, \f$T^{i}\f$, are * packed one after the other into three vectors: \p dl for the lower diagonals, \p d for the main * diagonals, and \p du for the upper diagonals. See below for a description of what this strided * memory pattern looks like. * * Solving the batched tridiagonal system involves two steps. First, call * \ref rocsparse_sgtsv_no_pivot_strided_batch_buffer_size "rocsparse_Xgtsv_no_pivot_strided_batch_buffer_size()" * to determine the size of the required temporary storage buffer. After this is determined, allocate * the buffer and pass it to \ref rocsparse_sgtsv_no_pivot_strided_batch "rocsparse_Xgtsv_no_pivot_strided_batch()" * to perform the actual solve. The \f$x^{i}\f$ vectors, which initially stores the right-hand side values, are * overwritten with the solution after the call to * \ref rocsparse_sgtsv_no_pivot_strided_batch "rocsparse_Xgtsv_no_pivot_strided_batch()". * * The strided batch routines write each batch matrix one after the other in memory. For example, consider * the following batch matrices: * * \f[ * \begin{bmatrix} * t^{0}_{00} & t^{0}_{01} & 0 \\ * t^{0}_{10} & t^{0}_{11} & t^{0}_{12} \\ * 0 & t^{0}_{21} & t^{0}_{22} * \end{bmatrix} * \begin{bmatrix} * t^{1}_{00} & t^{1}_{01} & 0 \\ * t^{1}_{10} & t^{1}_{11} & t^{1}_{12} \\ * 0 & t^{1}_{21} & t^{1}_{22} * \end{bmatrix} * \begin{bmatrix} * t^{2}_{00} & t^{2}_{01} & 0 \\ * t^{2}_{10} & t^{2}_{11} & t^{2}_{12} \\ * 0 & t^{2}_{21} & t^{2}_{22} * \end{bmatrix} * \f] * * In strided format, the upper, lower, and diagonal arrays would look like: * \f[ * \begin{align} * \text{lower} &= \begin{bmatrix} 0 & t^{0}_{10} & t^{0}_{21} & 0 & t^{1}_{10} & t^{1}_{21} & 0 & t^{2}_{10} & t^{2}_{21} \end{bmatrix} \\ * \text{diagonal} &= \begin{bmatrix} t^{0}_{00} & t^{0}_{11} & t^{0}_{22} & t^{1}_{00} & t^{1}_{11} & t^{1}_{22} & t^{2}_{00} & t^{2}_{11} & t^{2}_{22} \end{bmatrix} \\ * \text{upper} &= \begin{bmatrix} t^{0}_{01} & t^{0}_{12} & 0 & t^{1}_{01} & t^{1}_{12} & 0 & t^{2}_{01} & t^{2}_{12} & 0 \end{bmatrix} \\ * \end{align} * \f] * For the lower array, for each batch \p i, the \p i*batch_stride entries are zero, and for the upper array, the * \p i*batch_stride+batch_stride-1 entries are zero. * * \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 size of the tri-diagonal linear system (must be >= 2). * @param[in] * dl lower diagonal of tri-diagonal system. The first entry must be zero. * @param[in] * d main diagonal of tri-diagonal system. * @param[in] * du upper diagonal of tri-diagonal system. The last entry must be zero. * @param[inout] * x dense array of righthand-sides, where the ith right-hand side starts at \p x+batch_stride*i. * @param[in] * batch_count the number of systems to solve. * @param[in] * batch_stride the number of elements that separate each system. Must satisfy \p batch_stride >= \p m. * @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, \p batch_count, or \p batch_stride is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, * \p du, \p x, or \p temp_buffer pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. * * \par Example * \snippet example_rocsparse_gtsv_no_pivot_strided_batch.cpp doc example */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_no_pivot_strided_batch(rocsparse_handle handle, rocsparse_int m, const float* dl, const float* d, const float* du, float* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_no_pivot_strided_batch(rocsparse_handle handle, rocsparse_int m, const double* dl, const double* d, const double* du, double* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_no_pivot_strided_batch(rocsparse_handle handle, rocsparse_int m, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, rocsparse_float_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_no_pivot_strided_batch(rocsparse_handle handle, rocsparse_int m, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, rocsparse_double_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); /**@}*/ /*! \ingroup precond_module * \details * \p rocsparse_gtsv_interleaved_batch_buffer_size returns the size of the temporary storage buffer * that is required by \ref rocsparse_sgtsv_interleaved_batch "rocsparse_Xgtsv_interleaved_batch()". * The temporary storage buffer must be allocated by the user. * * \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] * alg algorithm to use when solving tridiagonal systems. Options are Thomas ( \ref rocsparse_gtsv_interleaved_alg_thomas ), * LU ( \ref rocsparse_gtsv_interleaved_alg_lu ), or QR ( \ref rocsparse_gtsv_interleaved_alg_qr ). Passing * \ref rocsparse_gtsv_interleaved_alg_default defaults to using the QR algorithm. The Thomas algorithm is the fastest but is not * stable, while LU and QR are slower but are stable. * @param[in] * m size of the tri-diagonal linear system. * @param[in] * dl lower diagonal of tri-diagonal system. The first element of the lower diagonal must be zero. * @param[in] * d main diagonal of tri-diagonal system. * @param[in] * du upper diagonal of tri-diagonal system. The last element of the upper diagonal must be zero. * @param[inout] * x dense array of right-hand sides with dimension \p batch_stride by \p m. * @param[in] * batch_count the number of systems to solve. * @param[in] * batch_stride the number of elements that separate consecutive elements in a system. Must satisfy \p batch_stride >= \p batch_count. * @param[out] * buffer_size number of bytes of the temporary storage buffer required by * \ref rocsparse_sgtsv_interleaved_batch "rocsparse_Xgtsv_interleaved_batch()". * * \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, \p batch_count, \p batch_stride is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, \p du, * \p x, or \p buffer_size pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_interleaved_batch_buffer_size(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, const float* dl, const float* d, const float* du, const float* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_interleaved_batch_buffer_size(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, const double* dl, const double* d, const double* du, const double* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_interleaved_batch_buffer_size(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, const rocsparse_float_complex* dl, const rocsparse_float_complex* d, const rocsparse_float_complex* du, const rocsparse_float_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_interleaved_batch_buffer_size(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, const rocsparse_double_complex* dl, const rocsparse_double_complex* d, const rocsparse_double_complex* du, const rocsparse_double_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, size_t* buffer_size); /**@}*/ /*! \ingroup precond_module * \brief Interleaved batch tridiagonal solver. * * \details * \p rocsparse_gtsv_interleaved_batch solves a batched tridiagonal linear system * \f[ * T^{i}*x^{i} = x^{i} * \f] * where for each batch \f$i=0\ldots\f$ \p batch_count, \f$T^{i}\f$ is a sparse tridiagonal matrix and * \f$x^{i}\f$ is a dense right-hand side vector. All of the tridiagonal matrices, \f$T^{i}\f$, are * packed in an interleaved fashion into three vectors: \p dl for the lower diagonals, \p d for the main * diagonals, and \p du for the upper diagonals. See below for a description of what this interleaved * memory pattern looks like. * * Solving the batched tridiagonal system involves two steps. First, call * \ref rocsparse_sgtsv_interleaved_batch_buffer_size "rocsparse_Xgtsv_interleaved_batch_buffer_size()" * to determine the size of the required temporary storage buffer. After this is determined, allocate * the buffer and pass it to \ref rocsparse_sgtsv_interleaved_batch "rocsparse_Xgtsv_interleaved_batch()" * to perform the actual solve. The \f$x^{i}\f$ vectors, which initially stores the right-hand side values, are * overwritten with the solution after the call to * \ref rocsparse_sgtsv_interleaved_batch "rocsparse_Xgtsv_interleaved_batch()". * * The user can specify different algorithms for \p rocsparse_gtsv_interleaved_batch * to use. Options are Thomas ( \ref rocsparse_gtsv_interleaved_alg_thomas ), * LU ( \ref rocsparse_gtsv_interleaved_alg_lu ), or QR ( \ref rocsparse_gtsv_interleaved_alg_qr ). * Passing \ref rocsparse_gtsv_interleaved_alg_default defaults to using the QR algorithm. * * Unlike the strided batch routines, which write each batch matrix one after the other in memory, the interleaved * routines write the batch matrices such that each element from each matrix is written consecutively one after * the other. For example, consider the following batch matrices: * * \f[ * \begin{bmatrix} * t^{0}_{00} & t^{0}_{01} & 0 \\ * t^{0}_{10} & t^{0}_{11} & t^{0}_{12} \\ * 0 & t^{0}_{21} & t^{0}_{22} * \end{bmatrix} * \begin{bmatrix} * t^{1}_{00} & t^{1}_{01} & 0 \\ * t^{1}_{10} & t^{1}_{11} & t^{1}_{12} \\ * 0 & t^{1}_{21} & t^{1}_{22} * \end{bmatrix} * \begin{bmatrix} * t^{2}_{00} & t^{2}_{01} & 0 \\ * t^{2}_{10} & t^{2}_{11} & t^{2}_{12} \\ * 0 & t^{2}_{21} & t^{2}_{22} * \end{bmatrix} * \f] * * In interleaved format, the upper, lower, and diagonal arrays would look like: * \f[ * \begin{align} * \text{lower} &= \begin{bmatrix} 0 & 0 & 0 & t^{0}_{10} & t^{1}_{10} & t^{1}_{10} & t^{0}_{21} & t^{1}_{21} & t^{2}_{21} \end{bmatrix} \\ * \text{diagonal} &= \begin{bmatrix} t^{0}_{00} & t^{1}_{00} & t^{2}_{00} & t^{0}_{11} & t^{1}_{11} & t^{2}_{11} & t^{0}_{22} & t^{1}_{22} & t^{2}_{22} \end{bmatrix} \\ * \text{upper} &= \begin{bmatrix} t^{0}_{01} & t^{1}_{01} & t^{2}_{01} & t^{0}_{12} & t^{1}_{12} & t^{2}_{12} & 0 & 0 & 0 \end{bmatrix} \\ * \end{align} * \f] * For the lower array, the first \p batch_count entries are zero, and for the upper array, the last \p batch_count * entries are zero. * * \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] * alg algorithm to use when solving tridiagonal systems. Options are Thomas ( \ref rocsparse_gtsv_interleaved_alg_thomas ), * LU ( \ref rocsparse_gtsv_interleaved_alg_lu ), or QR ( \ref rocsparse_gtsv_interleaved_alg_qr ). Passing * \ref rocsparse_gtsv_interleaved_alg_default defaults to using the QR algorithm. The Thomas algorithm is the fastest but is not * stable, while LU and QR are slower but are stable. * @param[in] * m size of the tri-diagonal linear system. * @param[inout] * dl lower diagonal of tri-diagonal system. The first element of the lower diagonal must be zero. * @param[inout] * d main diagonal of tri-diagonal system. * @param[inout] * du upper diagonal of tri-diagonal system. The last element of the upper diagonal must be zero. * @param[inout] * x dense array of right-hand sides, with dimension \p batch_stride by \p m. * @param[in] * batch_count the number of systems to solve. * @param[in] * batch_stride the number of elements that separate consecutive elements in a system. Must satisfy \p batch_stride >= \p batch_count. * @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 batch_count, or \p batch_stride is invalid. * \retval rocsparse_status_invalid_pointer \p dl, \p d, * \p du, \p x, or \p temp_buffer pointer is invalid. * \retval rocsparse_status_internal_error an internal error occurred. * * \par Example * \snippet example_rocsparse_gtsv_interleaved_batch.cpp doc example */ /**@{*/ ROCSPARSE_EXPORT rocsparse_status rocsparse_sgtsv_interleaved_batch(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, float* dl, float* d, float* du, float* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_dgtsv_interleaved_batch(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, double* dl, double* d, double* du, double* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_cgtsv_interleaved_batch(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, rocsparse_float_complex* dl, rocsparse_float_complex* d, rocsparse_float_complex* du, rocsparse_float_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); ROCSPARSE_EXPORT rocsparse_status rocsparse_zgtsv_interleaved_batch(rocsparse_handle handle, rocsparse_gtsv_interleaved_alg alg, rocsparse_int m, rocsparse_double_complex* dl, rocsparse_double_complex* d, rocsparse_double_complex* du, rocsparse_double_complex* x, rocsparse_int batch_count, rocsparse_int batch_stride, void* temp_buffer); /**@}*/ #ifdef __cplusplus } #endif #endif /* ROCSPARSE_GTSV_H */