```// @HEADER
// ***********************************************************************
//
//                      Didasko Tutorial Package
//                 Copyright (2005) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
//
// Questions about Didasko? Contact Marzio Sala (marzio.sala _AT_ gmail.com)
//
// ***********************************************************************

// Trilinos Tutorial
// -----------------
// Simple nonlinear problem.
// This file shows how to solve the nonlinear problem
//
// x(0)^2 + x(1)^2 -1 = 0
//      x(1) - x(0)^2 = 0
//
// using NOX. Due to the very small dimension of the problem,
// it should be run with one process.

#include <iostream>
#include "Epetra_ConfigDefs.h"
#ifdef HAVE_MPI
#include "mpi.h"
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_Map.h"
#include "Epetra_Vector.h"
#include "Epetra_RowMatrix.h"
#include "Epetra_CrsMatrix.h"
#include "NOX.H"
#include "NOX_Epetra_Interface_Required.H"
#include "NOX_Epetra_Interface_Jacobian.H"
#include "NOX_Epetra_LinearSystem_AztecOO.H"
#include "NOX_Epetra_Group.H"

class SimpleProblemInterface : public NOX::Epetra::Interface::Required,
public NOX::Epetra::Interface::Jacobian
{

public:

SimpleProblemInterface( Epetra_Vector & InitialGuess,
Epetra_Vector & ExactSolution )
{
InitialGuess_ = new Epetra_Vector(InitialGuess);
ExactSolution_ = new Epetra_Vector(ExactSolution);
};

~SimpleProblemInterface()
{
};

bool computeF(const Epetra_Vector & x, Epetra_Vector & f,
NOX::Epetra::Interface::Required::FillType F )
{
f[0] = x[0]*x[0] + x[1]*x[1] - 1.0;
f[1] = x[1] - x[0]*x[0];
return true;
};

bool computeJacobian(const Epetra_Vector & x, Epetra_Operator & Jac)
{

Epetra_CrsMatrix * J;
J = dynamic_cast<Epetra_CrsMatrix*>(&Jac);
if (J == NULL) {
cout << "*ERR* Problem_Interface::computeJacobian() - The supplied" << endl;
cout << "*ERR* Epetra_Operator is NOT an Epetra_CrsMatrix!" << endl;
throw;
}

std::vector<int> indices(2);
std::vector<double> values(2);

indices[0] = 0;
indices[1] = 1;

// Row 0
values[0] = 2.0 * x[0];
values[1] = 2.0 * x[1];
J->ReplaceGlobalValues(0, 2, &values[0], &indices[0]);

// Row 1
values[0] = - 2.0 * x[0];
values[1] = 1.0;
J->ReplaceGlobalValues(1, 2, &values[0], &indices[0]);

return true;
}

bool computePrecMatrix(const Epetra_Vector & x, Epetra_RowMatrix & M)
{
cout << "*ERR* SimpleProblem::preconditionVector()\n";
cout << "*ERR* don't use explicit preconditioning" << endl;
exit( 0 );
throw 1;
}

bool computePreconditioner(const Epetra_Vector & x, Epetra_Operator & O)
{
cout << "*ERR* SimpleProblem::preconditionVector()\n";
cout << "*ERR* don't use explicit preconditioning" << endl;
exit( 0 );
throw 1;
}

private:
Epetra_Vector * InitialGuess_;
Epetra_Vector * ExactSolution_;

};

// =========== //
// main driver //
// =========== //

int main( int argc, char **argv )
{

#ifdef HAVE_MPI
MPI_Init(&argc, &argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif

if (Comm.NumProc() != 1) {
if (Comm.MyPID() == 0)
cerr << "Please run this test with one process only!" << endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
exit(EXIT_SUCCESS);
}

// linear map for the 2 global elements
Epetra_Map Map(2,0,Comm);

// build up initial guess and exact solution
Epetra_Vector ExactSolution(Map);
ExactSolution[0] = sqrt(0.5*(sqrt(5.0)-1));
ExactSolution[1] = 0.5*(sqrt(5.0)-1);

Epetra_Vector InitialGuess(Map);
InitialGuess[0] = 0.5;
InitialGuess[1] = 0.5;

// Set up the problem interface
Teuchos::RCP<SimpleProblemInterface> interface =
Teuchos::rcp(new SimpleProblemInterface(InitialGuess,ExactSolution) );

// Create the top level parameter list
Teuchos::RCP<Teuchos::ParameterList> nlParamsPtr =
Teuchos::rcp(new Teuchos::ParameterList);
Teuchos::ParameterList& nlParams = *(nlParamsPtr.get());

// Set the nonlinear solver method
nlParams.set("Nonlinear Solver", "Line Search Based");

// Set the printing parameters in the "Printing" sublist
Teuchos::ParameterList& printParams = nlParams.sublist("Printing");
printParams.set("MyPID", Comm.MyPID());
printParams.set("Output Precision", 3);
printParams.set("Output Processor", 0);
printParams.set("Output Information",
NOX::Utils::OuterIteration +
NOX::Utils::OuterIterationStatusTest +
NOX::Utils::InnerIteration +
NOX::Utils::Parameters +
NOX::Utils::Details +
NOX::Utils::Warning);

// start definition of nonlinear solver parameters
// Sublist for line search
Teuchos::ParameterList& searchParams = nlParams.sublist("Line Search");
searchParams.set("Method", "Full Step");

// Sublist for direction
Teuchos::ParameterList& dirParams = nlParams.sublist("Direction");
dirParams.set("Method", "Newton");

Teuchos::ParameterList& newtonParams = dirParams.sublist("Newton");
newtonParams.set("Forcing Term Method", "Constant");

// Sublist for linear solver for the Newton method
Teuchos::ParameterList& lsParams = newtonParams.sublist("Linear Solver");
lsParams.set("Aztec Solver", "GMRES");
lsParams.set("Max Iterations", 800);
lsParams.set("Tolerance", 1e-4);
lsParams.set("Output Frequency", 50);
lsParams.set("Aztec Preconditioner", "ilu");

// Build the Jacobian matrix
Teuchos::RCP<Epetra_CrsMatrix> A =
Teuchos::rcp(new Epetra_CrsMatrix(Copy,Map,2));
{
std::vector<int> indices(2);
std::vector<double> values(2);
indices[0]=0;
indices[1]=1;

values[0] = 2.0 * InitialGuess[0];
values[1] = 2.0 * InitialGuess[1];
A.get()->InsertGlobalValues(0, 2, &values[0], &indices[0]);
values[0] = - 2.0 * InitialGuess[0];
values[1] = 1.0;
A.get()->InsertGlobalValues(1, 2, &values[0], &indices[0]);

A.get()->FillComplete();
}

Teuchos::RCP<NOX::Epetra::Interface::Required> iReq = interface;
Teuchos::RCP<NOX::Epetra::Interface::Jacobian> iJac = interface;
Teuchos::RCP<NOX::Epetra::LinearSystemAztecOO> linSys =
Teuchos::rcp(new NOX::Epetra::LinearSystemAztecOO(printParams, lsParams,
iReq,
iJac, A,
InitialGuess));

// Need a NOX::Epetra::Vector for constructor
NOX::Epetra::Vector noxInitGuess(InitialGuess, NOX::DeepCopy);
Teuchos::RCP<NOX::Epetra::Group> grpPtr =
Teuchos::rcp(new NOX::Epetra::Group(printParams,
iReq,
noxInitGuess,
linSys));

// Set up the status tests
Teuchos::RCP<NOX::StatusTest::NormF> testNormF =
Teuchos::rcp(new NOX::StatusTest::NormF(1.0e-4));
Teuchos::RCP<NOX::StatusTest::MaxIters> testMaxIters =
Teuchos::rcp(new NOX::StatusTest::MaxIters(20));
// this will be the convergence test to be used
Teuchos::RCP<NOX::StatusTest::Combo> combo =
Teuchos::rcp(new NOX::StatusTest::Combo(NOX::StatusTest::Combo::OR,
testNormF, testMaxIters));

// Create the solver
Teuchos::RCP<NOX::Solver::Generic> solver =
NOX::Solver::buildSolver(grpPtr, combo, nlParamsPtr);

// Solve the nonlinesar system
NOX::StatusTest::StatusType status = solver->solve();

if( NOX::StatusTest::Converged  == status )
cout << "\n" << "-- NOX solver converged --" << "\n";
else
cout << "\n" << "-- NOX solver did not converge --" << "\n";

// Print the answer
cout << "\n" << "-- Parameter List From Solver --" << "\n";
solver->getList().print(cout);

// Get the Epetra_Vector with the final solution from the solver
const NOX::Epetra::Group & finalGroup =
dynamic_cast<const NOX::Epetra::Group&>(solver->getSolutionGroup());
const Epetra_Vector & finalSolution =
(dynamic_cast<const NOX::Epetra::Vector&>(finalGroup.getX())).getEpetraVector();

if( Comm.MyPID() == 0 ) cout << "Computed solution : " << endl;
cout << finalSolution;

if( Comm.MyPID() == 0 ) cout << "Exact solution : " << endl;
cout << ExactSolution;

#ifdef HAVE_MPI
MPI_Finalize();
#endif
return(EXIT_SUCCESS);
}

#else

#include <stdlib.h>
#include <stdio.h>
#ifdef HAVE_MPI
#include "mpi.h"
#endif

int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
#endif