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151 lines
4.2 KiB
ReStructuredText
151 lines
4.2 KiB
ReStructuredText
.. meta::
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:description: rocSOLVER refactorization and direct solvers API documentation
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:keywords: rocSOLVER, ROCm, API, documentation, refactorization, direct solvers
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.. _refactor:
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**********************************************
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rocSOLVER refactorization and direct solvers
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**********************************************
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These functions implement direct solvers for sparse systems with
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different coefficient matrices that share the same sparsity pattern.
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The refactorization functions are divided into the following categories:
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* :ref:`rfinit`: Basic functions to initialize and destroy meta data.
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* :ref:`rfrefact`: Refactorization of new matrices given a known sparsity pattern.
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* :ref:`rfsolver`: Based on triangular refactorization.
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.. note::
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The API descriptions use the following notations:
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* ``i``, ``j``, and ``k`` are used as general purpose indices. In some legacy LAPACK APIs, ``k`` can be
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a parameter indicating some problem or matrix dimension.
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* Depending on the context, when it is necessary to index rows, columns, and blocks or submatrices,
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``i`` is assigned to rows, ``j`` to columns, and ``k`` to blocks. ``l`` is always used to index
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matrices or problems in a batch.
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* ``x[i]`` stands for the i-th element of vector x, while ``A[i,j]`` represents the element
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in the i-th row and j-th column of matrix ``A``. Indices are 1-based, for instance, ``x[1]`` is the first
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element of ``x``.
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* To identify a block in a matrix or a matrix in the batch, ``k`` and ``l`` are used as sub-indices
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* ``x_i`` :math:`=x_i`. Both notations are used, :math:`x_i` when displaying mathematical
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equations and ``x_i`` in the text describing the function parameters.
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* If ``X`` is a real vector or matrix, :math:`X^T` indicates its transpose. If ``X`` is complex, then
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:math:`X^H` represents its conjugate transpose. When ``X`` could be real or complex, the descriptions use ``X'`` to
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indicate ``X`` transposed or ``X`` conjugate transposed, accordingly.
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* When a matrix ``A`` is formed as the product of several matrices, the following notation is used:
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``A=M(1)M(2)...M(t)``.
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.. _rfinit:
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Initialization and meta data
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==================================
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.. contents:: List of initialization functions
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:local:
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:backlinks: top
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.. _rfinfocreate:
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rocsolver_create_rfinfo()
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---------------------------------------
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.. doxygenfunction:: rocsolver_create_rfinfo
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.. _rfinfodestroy:
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rocsolver_destroy_rfinfo()
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---------------------------------------
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.. doxygenfunction:: rocsolver_destroy_rfinfo
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.. _rfinfoset:
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rocsolver_set_rfinfo_mode()
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---------------------------------------
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.. doxygenfunction:: rocsolver_set_rfinfo_mode
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.. _rfinfoget:
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rocsolver_get_rfinfo_mode()
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---------------------------------------
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.. doxygenfunction:: rocsolver_get_rfinfo_mode
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.. _rfanalysis:
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rocsolver_csrrf_analysis()
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--------------------------------------
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.. doxygenfunction:: rocsolver_dcsrrf_analysis
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:outline:
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.. doxygenfunction:: rocsolver_scsrrf_analysis
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.. _rfrefact:
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Triangular refactorization
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==================================
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.. contents:: List of refactorization functions
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:local:
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:backlinks: top
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.. _rfsumlu:
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rocsolver_<type>csrrf_sumlu()
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----------------------------------
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.. doxygenfunction:: rocsolver_dcsrrf_sumlu
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:outline:
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.. doxygenfunction:: rocsolver_scsrrf_sumlu
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.. _rfsplitlu:
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rocsolver_<type>csrrf_splitlu()
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------------------------------------
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.. doxygenfunction:: rocsolver_dcsrrf_splitlu
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:outline:
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.. doxygenfunction:: rocsolver_scsrrf_splitlu
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.. _rfrefactlu:
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rocsolver_<type>csrrf_refactlu()
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------------------------------------
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.. doxygenfunction:: rocsolver_dcsrrf_refactlu
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:outline:
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.. doxygenfunction:: rocsolver_scsrrf_refactlu
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.. _rfrefactchol:
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rocsolver_<type>csrrf_refactchol()
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------------------------------------
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.. doxygenfunction:: rocsolver_dcsrrf_refactchol
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:outline:
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.. doxygenfunction:: rocsolver_scsrrf_refactchol
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.. _rfsolver:
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Direct sparse solvers
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==================================
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.. contents:: List of direct solvers
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:local:
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:backlinks: top
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.. _rfsolve:
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rocsolver_<type>csrrf_solve()
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----------------------------------
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.. doxygenfunction:: rocsolver_dcsrrf_solve
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:outline:
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.. doxygenfunction:: rocsolver_scsrrf_solve
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