\chapter{The reordered-\/preconditioned-\/solver program }
\hypertarget{reordered_preconditioned_solver}{}\label{reordered_preconditioned_solver}\index{The reordered-\/preconditioned-\/solver program@{The reordered-\/preconditioned-\/solver program}}
The reordered preconditioned solver example.

This example depends on preconditioned-\/solver.

 \label{three_pt_stencil_solver_Intro}%
\Hypertarget{three_pt_stencil_solver_Intro}%
 \label{three_pt_stencil_solver_Introduction}%
\Hypertarget{three_pt_stencil_solver_Introduction}%
\doxysection*{Introduction}

\label{three_pt_stencil_solver_Abouttheexample}%
\Hypertarget{three_pt_stencil_solver_Abouttheexample}%
\doxysubsubsection*{About the example }

This uses an RCM reordering on an input matrix to construct a Par\+ILU preconditioned solver and solve a linear system. \label{three_pt_stencil_solver_CommProg}%
\Hypertarget{three_pt_stencil_solver_CommProg}%
 \doxysection*{The commented program}


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\DoxyCodeLine{\ \ \ \ std::cerr\ <<\ \textcolor{stringliteral}{"{}Usage:\ "{}}\ <<\ argv[0]\ <<\ \textcolor{stringliteral}{"{}\ [executor]"{}}\ <<\ std::endl;}
\DoxyCodeLine{\ \ \ \ std::exit(-\/1);}
\DoxyCodeLine{\}}

\end{DoxyCode}


Figure out where to run the code


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\DoxyCodeLine{std::map<std::string,\ std::function<std::shared\_ptr<gko::Executor>()>>}
\DoxyCodeLine{\ \ \ \ exec\_map\{}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \{\textcolor{stringliteral}{"{}omp"{}},\ []\ \{\ \textcolor{keywordflow}{return}\ \doxymbox{\hyperlink{classgko_1_1OmpExecutor_af977cb680e0427ca4eb71eb7b1266211}{gko::OmpExecutor::create}}();\ \}\},}
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executor where Ginkgo will perform the computation


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\DoxyCodeLine{\textcolor{keyword}{const}\ \textcolor{keyword}{auto}\ exec\ =\ exec\_map.at(executor\_string)();\ \ \textcolor{comment}{//\ throws\ if\ not\ valid}}

\end{DoxyCode}


Read data


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\DoxyCodeLine{\textcolor{keyword}{auto}\ b\ =\ \doxymbox{\hyperlink{namespacegko_abc58509ecdcb48399e12f9a081ed7545}{gko::read<vec>}}(std::ifstream(\textcolor{stringliteral}{"{}data/b.mtx"{}}),\ exec);}
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\DoxyCodeLine{\textcolor{keyword}{auto}\ reordering\ =}
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\DoxyCodeLine{\ \ \ \ \ \ \ \ A);}

\end{DoxyCode}


Permute matrix and vectors


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\DoxyCodeLine{\textcolor{keyword}{auto}\ A\_reordered\ =\ \doxymbox{\hyperlink{namespacegko_ae99fdd8bfa5ac694adcb7297d432967e}{share}}(A-\/>permute(reordering));}
\DoxyCodeLine{\textcolor{keyword}{auto}\ b\_reordered\ =\ b-\/>permute(reordering,\ \doxymbox{\hyperlink{namespacegko_1_1matrix_ade1f3cdbf05032c2d681fa151de02972adf347a373b8f92aa0ae3dd920a5ec2f6}{gko::matrix::permute\_mode::rows}});}

\end{DoxyCode}


this reordering is not necessary, but it maps the initial guess to the unreordered case


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\DoxyCodeLine{\textcolor{keyword}{auto}\ x\_reordered\ =\ x-\/>permute(reordering,\ \doxymbox{\hyperlink{namespacegko_1_1matrix_ade1f3cdbf05032c2d681fa151de02972adf347a373b8f92aa0ae3dd920a5ec2f6}{gko::matrix::permute\_mode::rows}});}
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\DoxyCodeLine{\textcolor{keyword}{const}\ RealValueType\ reduction\_factor\{1e-\/7\};}

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Create solver factory


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\DoxyCodeLine{\textcolor{keyword}{auto}\ solver\_gen\ =}
\DoxyCodeLine{\ \ \ \ cg::build()}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .with\_criteria(gko::stop::Iteration::build().with\_max\_iters(20u),}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ gko::stop::ResidualNorm<ValueType>::build()}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .with\_reduction\_factor(reduction\_factor))}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .with\_preconditioner(ilu::build())}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .on(exec);}

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Create solver


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\DoxyCodeLine{\textcolor{keyword}{auto}\ \doxymbox{\hyperlink{namespacegko_1_1log_a15f71654c6c4f4defc95f9359343fa27a7cbf673200498a0d1324f4330825202a}{solver}}\ =\ solver\_gen-\/>generate(A\_reordered);}

\end{DoxyCode}


Solve system


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\DoxyCodeLine{\doxymbox{\hyperlink{namespacegko_1_1log_a15f71654c6c4f4defc95f9359343fa27a7cbf673200498a0d1324f4330825202a}{solver}}-\/>apply(b\_reordered,\ x\_reordered);}

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Revert permutation to get the unpermuted solution


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\DoxyCodeLine{x\_reordered-\/>permute(reordering,\ x,}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \doxymbox{\hyperlink{namespacegko_1_1matrix_ade1f3cdbf05032c2d681fa151de02972ae984283c0e504f8717eda53ea45edfeb}{gko::matrix::permute\_mode::inverse\_rows}});}

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Print solution


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\DoxyCodeLine{std::cout\ <<\ \textcolor{stringliteral}{"{}Solution\ (x):\(\backslash\)n"{}};}
\DoxyCodeLine{\doxymbox{\hyperlink{namespacegko_af82d8f7795fefcf5f38a38895e316c02}{write}}(std::cout,\ x);}

\end{DoxyCode}


Calculate residual


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\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ neg\_one\ =\ \doxymbox{\hyperlink{group__LinOp_ga70851b4c3c9b01bb667b3a8e438fb6d2}{gko::initialize<vec>}}(\{-\/1.0\},\ exec);}
\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ res\ =\ \doxymbox{\hyperlink{group__LinOp_ga70851b4c3c9b01bb667b3a8e438fb6d2}{gko::initialize<real\_vec>}}(\{0.0\},\ exec);}
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 \label{three_pt_stencil_solver_Results}%
\Hypertarget{three_pt_stencil_solver_Results}%
\doxysection*{Results}

This is the expected output:\+


\begin{DoxyCode}{0}
\DoxyCodeLine{Solution\ (x):}
\DoxyCodeLine{\%\%MatrixMarket\ matrix\ \doxymbox{\hyperlink{namespacegko_ae749a5ea11a93c1bcc9158d9a6e9fb68af1f713c9e000f5d3f280adbd124df4f5}{array}}\ \doxymbox{\hyperlink{namespacegko_af21648097306adbabc6234b4609ce297}{real}}\ general}
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\DoxyCodeLine{0.252218}
\DoxyCodeLine{0.108645}
\DoxyCodeLine{0.0662811}
\DoxyCodeLine{0.0630433}
\DoxyCodeLine{0.0384088}
\DoxyCodeLine{0.0396536}
\DoxyCodeLine{0.0402648}
\DoxyCodeLine{0.0338935}
\DoxyCodeLine{0.0193098}
\DoxyCodeLine{0.0234653}
\DoxyCodeLine{0.0211499}
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\DoxyCodeLine{Residual\ norm\ sqrt(r\string^T\ r):}
\DoxyCodeLine{\%\%MatrixMarket\ matrix\ \doxymbox{\hyperlink{namespacegko_ae749a5ea11a93c1bcc9158d9a6e9fb68af1f713c9e000f5d3f280adbd124df4f5}{array}}\ \doxymbox{\hyperlink{namespacegko_af21648097306adbabc6234b4609ce297}{real}}\ general}
\DoxyCodeLine{1\ 1}
\DoxyCodeLine{4.82005e-\/08}

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 \label{three_pt_stencil_solver_PlainProg}%
\Hypertarget{three_pt_stencil_solver_PlainProg}%
 \doxysection*{The plain program}


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\DoxyCodeLine{\ \ \ \ x\_reordered-\/>permute(reordering,\ x,}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \doxymbox{\hyperlink{namespacegko_1_1matrix_ade1f3cdbf05032c2d681fa151de02972ae984283c0e504f8717eda53ea45edfeb}{gko::matrix::permute\_mode::inverse\_rows}});}
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\DoxyCodeLine{\ \ \ \ std::cout\ <<\ \textcolor{stringliteral}{"{}Solution\ (x):\(\backslash\)n"{}};}
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\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ \doxymbox{\hyperlink{namespacegko_a0059e27f8f4bc348ff65c1e60caf47c8}{one}}\ =\ \doxymbox{\hyperlink{group__LinOp_ga70851b4c3c9b01bb667b3a8e438fb6d2}{gko::initialize<vec>}}(\{1.0\},\ exec);}
\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ neg\_one\ =\ \doxymbox{\hyperlink{group__LinOp_ga70851b4c3c9b01bb667b3a8e438fb6d2}{gko::initialize<vec>}}(\{-\/1.0\},\ exec);}
\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ res\ =\ \doxymbox{\hyperlink{group__LinOp_ga70851b4c3c9b01bb667b3a8e438fb6d2}{gko::initialize<real\_vec>}}(\{0.0\},\ exec);}
\DoxyCodeLine{\ \ \ \ A-\/>apply(one,\ x,\ neg\_one,\ b);}
\DoxyCodeLine{\ \ \ \ b-\/>compute\_norm2(res);}
\DoxyCodeLine{}
\DoxyCodeLine{\ \ \ \ std::cout\ <<\ \textcolor{stringliteral}{"{}Residual\ norm\ sqrt(r\string^T\ r):\(\backslash\)n"{}};}
\DoxyCodeLine{\ \ \ \ \doxymbox{\hyperlink{namespacegko_af82d8f7795fefcf5f38a38895e316c02}{write}}(std::cout,\ res);}
\DoxyCodeLine{\}}

\end{DoxyCodeInclude}
 