\chapter{The ilu-\/preconditioned-\/solver program }
\hypertarget{ilu_preconditioned_solver}{}\label{ilu_preconditioned_solver}\index{The ilu-\/preconditioned-\/solver program@{The ilu-\/preconditioned-\/solver program}}
The ILU-\/preconditioned solver example.

This example depends on simple-\/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 example shows how to use incomplete factors generated via the Par\+ILU algorithm to generate an incomplete factorization (ILU) preconditioner, how to specify the sparse triangular solves in the ILU preconditioner application, and how to generate an ILU-\/preconditioned solver and apply it to a specific problem. \label{three_pt_stencil_solver_CommProg}%
\Hypertarget{three_pt_stencil_solver_CommProg}%
 \doxysection*{The commented program}


\begin{DoxyCode}{0}
\DoxyCodeLine{\textcolor{keyword}{const}\ \textcolor{keyword}{auto}\ executor\_string\ =\ argc\ >=\ 2\ ?\ argv[1]\ :\ \textcolor{stringliteral}{"{}reference"{}};}

\end{DoxyCode}


Figure out where to run the code


\begin{DoxyCode}{0}
\DoxyCodeLine{std::map<std::string,\ std::function<std::shared\_ptr<gko::Executor>()>>}
\DoxyCodeLine{\ \ \ \ exec\_map\{}
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\DoxyCodeLine{\ \ \ \ \ \ \ \ \{\textcolor{stringliteral}{"{}cuda"{}},}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ []\ \{}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \textcolor{keywordflow}{return}\ \doxymbox{\hyperlink{classgko_1_1CudaExecutor_a075a1957241de65c0cad59f9534430a2}{gko::CudaExecutor::create}}(0,}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \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}}

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Read data


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\DoxyCodeLine{\textcolor{keyword}{auto}\ A\ =\ \doxymbox{\hyperlink{namespacegko_ae99fdd8bfa5ac694adcb7297d432967e}{gko::share}}(\doxymbox{\hyperlink{namespacegko_abc58509ecdcb48399e12f9a081ed7545}{gko::read<mtx>}}(std::ifstream(\textcolor{stringliteral}{"{}data/A.mtx"{}}),\ exec));}
\DoxyCodeLine{\textcolor{keyword}{auto}\ b\ =\ \doxymbox{\hyperlink{namespacegko_abc58509ecdcb48399e12f9a081ed7545}{gko::read<vec>}}(std::ifstream(\textcolor{stringliteral}{"{}data/b.mtx"{}}),\ exec);}
\DoxyCodeLine{\textcolor{keyword}{auto}\ x\ =\ \doxymbox{\hyperlink{namespacegko_abc58509ecdcb48399e12f9a081ed7545}{gko::read<vec>}}(std::ifstream(\textcolor{stringliteral}{"{}data/x0.mtx"{}}),\ exec);}

\end{DoxyCode}


Generate incomplete factors using Par\+ILU


\begin{DoxyCode}{0}
\DoxyCodeLine{\textcolor{keyword}{auto}\ par\_ilu\_fact\ =}
\DoxyCodeLine{\ \ \ \ gko::factorization::ParIlu<ValueType,\ IndexType>::build().on(exec);}

\end{DoxyCode}


Generate concrete factorization for input matrix


\begin{DoxyCode}{0}
\DoxyCodeLine{\textcolor{keyword}{auto}\ par\_ilu\ =\ \doxymbox{\hyperlink{namespacegko_ae99fdd8bfa5ac694adcb7297d432967e}{gko::share}}(par\_ilu\_fact-\/>generate(A));}

\end{DoxyCode}


Generate an ILU preconditioner factory by setting lower and upper triangular solver -\/ in this case the exact triangular solves


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\DoxyCodeLine{\textcolor{keyword}{auto}\ ilu\_pre\_factory\ =}
\DoxyCodeLine{\ \ \ \ \doxymbox{\hyperlink{classgko_1_1preconditioner_1_1Ilu}{gko::preconditioner::Ilu<gko::solver::LowerTrs<ValueType,\ IndexType>}},}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \doxymbox{\hyperlink{classgko_1_1solver_1_1UpperTrs}{gko::solver::UpperTrs<ValueType,\ IndexType>}},}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \textcolor{keyword}{false}>::build()}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .on(exec);}

\end{DoxyCode}


Use incomplete factors to generate ILU preconditioner


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\DoxyCodeLine{\textcolor{keyword}{auto}\ ilu\_preconditioner\ =\ \doxymbox{\hyperlink{namespacegko_ae99fdd8bfa5ac694adcb7297d432967e}{gko::share}}(ilu\_pre\_factory-\/>generate(par\_ilu));}

\end{DoxyCode}


Use preconditioner inside GMRES solver factory Generating a solver factory tied to a specific preconditioner makes sense if there are several very similar systems to solve, and the same solver+preconditioner combination is expected to be effective.


\begin{DoxyCode}{0}
\DoxyCodeLine{\textcolor{keyword}{const}\ RealValueType\ reduction\_factor\{1e-\/7\};}
\DoxyCodeLine{\textcolor{keyword}{auto}\ ilu\_gmres\_factory\ =}
\DoxyCodeLine{\ \ \ \ gmres::build()}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .with\_criteria(gko::stop::Iteration::build().with\_max\_iters(1000u),}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ gko::stop::ResidualNorm<ValueType>::build()}
\DoxyCodeLine{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .with\_reduction\_factor(reduction\_factor))}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .with\_generated\_preconditioner(ilu\_preconditioner)}
\DoxyCodeLine{\ \ \ \ \ \ \ \ .on(exec);}

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Generate preconditioned solver for a specific target system


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\DoxyCodeLine{\textcolor{keyword}{auto}\ ilu\_gmres\ =\ ilu\_gmres\_factory-\/>generate(A);}

\end{DoxyCode}


Solve system


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\DoxyCodeLine{ilu\_gmres-\/>apply(b,\ x);}

\end{DoxyCode}


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}\ \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);}
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\DoxyCodeLine{\ \ \ \ std::cout\ <<\ \textcolor{stringliteral}{"{}Residual\ norm\ sqrt(r\string^T\ r):\(\backslash\)n"{}};}
\DoxyCodeLine{\ \ \ \ \doxymbox{\hyperlink{namespacegko_af82d8f7795fefcf5f38a38895e316c02}{write}}(std::cout,\ res);}
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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}
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\DoxyCodeLine{0.0384088}
\DoxyCodeLine{0.0396536}
\DoxyCodeLine{0.0402648}
\DoxyCodeLine{0.0338935}
\DoxyCodeLine{0.0193098}
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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{1.46249e-\/08}

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\label{three_pt_stencil_solver_Commentsaboutprogramminganddebugging}%
\Hypertarget{three_pt_stencil_solver_Commentsaboutprogramminganddebugging}%
\doxysubsubsection*{Comments about programming and debugging }

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


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\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ par\_ilu\_fact\ =}
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\DoxyCodeLine{\ \ \ \ \textcolor{keyword}{auto}\ ilu\_pre\_factory\ =}
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