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