Ejemplo n.º 1
0
void drawCRSpline(IplImage* img,CvPoint* p,int num,int thickness=1)
{
    for (float t=0;t<1;t=t+.001)
    {
        double x=0;
        double y=0;
        for (int i=0;i<num;i++)
        {
            x+=Lagrangian(num,i,t)*p[i].x;
            y+=Lagrangian(num,i,t)*p[i].y;


        }
        cvCircle(img, cvPoint(x,y), thickness, cvScalar(0,0,0), 1);
    }
}
void NonlinearPDEConstrainedObj::initEquations(
  const Array<Expr>& stateVars,
  const Array<Expr>& adjointVars,
  const Array<Array<Expr> >& fixedVarsInStateEqns,
  const Array<Array<Expr> >& fixedVarsInStateEqnsVals,
  const Array<Array<Expr> >& fixedVarsInAdjointEqns,
  const Array<Array<Expr> >& fixedVarsInAdjointEqnsVals
  )
{
  Tabs tab(0);
  PLAYA_MSG2(verb(), tab << "setting up nonlinear equations");
  
  for (int i=0; i<stateVars.size(); i++)
  {
    Tabs tab1;
    PLAYA_MSG3(verb(), tab1 << "setting up state equation #" << i);
    Expr fixedVars = new ListExpr(fixedVarsInStateEqns[i]);
    Expr fixedVarVals = new ListExpr(fixedVarsInStateEqnsVals[i]);
    PLAYA_MSG3(verb(), tab1 << "Fixed vars are: " << fixedVars);
    NonlinearProblem stateProb 
      = Lagrangian().nonlinearVariationalProb(adjointVars[i], 
        adjointVarVals(i),
        stateVars[i], stateVarVals(i),
        fixedVars, fixedVarVals);
                                   
    stateProbs_.append(stateProb);
  }

  for (int i=0; i<adjointVars.size(); i++)
  {
    Tabs tab1;
    PLAYA_MSG3(verb(), tab1 << "setting up adjoint equation #" << i);
    Expr fixedVars = new ListExpr(fixedVarsInAdjointEqns[i]);
    Expr fixedVarVals = new ListExpr(fixedVarsInAdjointEqnsVals[i]);
    PLAYA_MSG3(verb(), tab1 << "Fixed vars are: " << fixedVars);
    LinearProblem adjointProb 
      = Lagrangian().linearVariationalProb(stateVars[i], stateVarVals(i),
        adjointVars[i],
        fixedVars, fixedVarVals);
                                   
    adjointProbs_.append(adjointProb);
  }

  PLAYA_MSG2(verb(), tab << "done setting up nonlinear equations");
}
Ejemplo n.º 3
0
int main(int argc, char** argv)
{
  try
		{
			Sundance::init(&argc, &argv);
      int np = MPIComm::world().getNProc();
      
      int nx = 48;
      int ny = 48;
      int npx = -1;
      int npy = -1;
      PartitionedRectangleMesher::balanceXY(np, &npx, &npy);
      TEUCHOS_TEST_FOR_EXCEPT(npx < 1);
      TEUCHOS_TEST_FOR_EXCEPT(npy < 1);
      TEUCHOS_TEST_FOR_EXCEPT(npx * npy != np);
      MeshType meshType = new BasicSimplicialMeshType();
      MeshSource mesher = new PartitionedRectangleMesher(0.0, 1.0, nx, npx, 
        0.0,  1.0, ny, npy, meshType);

      Mesh mesh = mesher.getMesh();
      CellFilter interior = new MaximalCellFilter();
      CellFilter bdry = new BoundaryCellFilter();
      
      /* Create a vector space factory, used to 
       * specify the low-level linear algebra representation */
      VectorType<double> vecType = new EpetraVectorType();
  
      /* create a discrete space on the mesh */
      DiscreteSpace discreteSpace(mesh, new Lagrange(1), vecType);

      /* initialize the design, state, and multiplier vectors */
      Expr alpha0 = new DiscreteFunction(discreteSpace, 1.0, "alpha0");
      Expr u0 = new DiscreteFunction(discreteSpace, 1.0, "u0");
      Expr lambda0 = new DiscreteFunction(discreteSpace, 1.0, "lambda0");

      /* create symbolic objects for test and unknown functions */
      Expr u = new UnknownFunction(new Lagrange(1), "u");
      Expr lambda = new UnknownFunction(new Lagrange(1), "lambda");
      Expr alpha = new UnknownFunction(new Lagrange(1), "alpha");

      /* create symbolic differential operators */
      Expr dx = new Derivative(0);
      Expr dy = new Derivative(1);
      Expr grad = List(dx, dy);

      /* create symbolic coordinate functions */
      Expr x = new CoordExpr(0);
      Expr y = new CoordExpr(1);

      /* create target function */
      const double pi = 4.0*atan(1.0);
      Expr uStar = sin(pi*x)*sin(pi*y);
      
      /* create quadrature rules of different orders */
      QuadratureFamily q1 = new GaussianQuadrature(1);
      QuadratureFamily q2 = new GaussianQuadrature(2);
      QuadratureFamily q4 = new GaussianQuadrature(4);

      /* Regularization weight */
      double R = 0.001;
      double U0 = 1.0/(1.0 + 4.0*pow(pi,4.0)*R);
      double A0 = -2.0*pi*pi*U0;

      /* Form objective function */
      Expr reg = Integral(interior, 0.5 * R * alpha*alpha, q2);
      Expr fit = Integral(interior, 0.5 * pow(u-uStar, 2.0), q4);

      Expr constraintEqn = Integral(interior, 
        (grad*lambda)*(grad*u) + lambda*alpha, q2);
      Expr L = reg + fit + constraintEqn;

      Expr constraintBC = EssentialBC(bdry, lambda*u, q2);
      Functional Lagrangian(mesh, L, constraintBC, vecType);
      
      LinearSolver<double> solver 
        = LinearSolverBuilder::createSolver("amesos.xml");

      RCP<ObjectiveBase> obj = rcp(new LinearPDEConstrainedObj(
        Lagrangian, u, u0, lambda, lambda0, alpha, alpha0,
        solver));

      Vector<double> xInit = obj->getInit();

      bool doFDCheck = false;
      if (doFDCheck)
      {
        Out::root() << "Doing FD check of gradient..." << endl;
        bool fdOK = obj->fdCheck(xInit, 1.0e-6, 2);
        if (fdOK) 
        {
          Out::root() << "FD check OK" << endl;
        }
        else
        {
          Out::root() << "FD check FAILED" << endl;
        }
      }

      RCP<UnconstrainedOptimizerBase> opt 
          = OptBuilder::createOptimizer("basicLMBFGS.xml");
      opt->setVerb(2);

      OptState state = opt->run(obj, xInit);

      bool ok = true;
      if (state.status() != Opt_Converged)
      {
        Out::root()<< "optimization failed: " << state.status() << endl;
        TEUCHOS_TEST_FOR_EXCEPT(state.status() != Opt_Converged);
      }

      Out::root() << "opt converged: " << state.iter() << " iterations"
                  << endl;
      Out::root() << "exact solution: U0=" << U0 << " A0=" << A0 << endl;
      FieldWriter w = new VTKWriter("PoissonSourceInversion");
      w.addMesh(mesh);
      w.addField("u", new ExprFieldWrapper(u0));
      w.addField("alpha", new ExprFieldWrapper(alpha0));
      w.addField("lambda", new ExprFieldWrapper(lambda0));
      w.write();
      
      
      double uErr = L2Norm(mesh, interior, u0-U0*uStar, q4);
      double aErr = L2Norm(mesh, interior, alpha0-A0*uStar, q4);
      Out::root() << "error in u = " << uErr << endl;
      Out::root() << "error in alpha = " << aErr << endl;

      double tol = 0.01;
      Sundance::passFailTest(uErr + aErr, tol);
    }
	catch(std::exception& e)
		{
      cerr << "main() caught exception: " << e.what() << endl;
		}
	Sundance::finalize();
  return Sundance::testStatus(); 
}
Ejemplo n.º 4
0
int main(int argc, char** argv)
{
  try
		{
			Sundance::init(&argc, &argv);
      int np = MPIComm::world().getNProc();
      
      int nx = 64;
      const double pi = 4.0*atan(1.0);
      MeshType meshType = new BasicSimplicialMeshType();
      MeshSource mesher = new PartitionedLineMesher(0.0, pi, nx, meshType);

      Mesh mesh = mesher.getMesh();
      CellFilter interior = new MaximalCellFilter();
      CellFilter bdry = new BoundaryCellFilter();
      
      /* Create a vector space factory, used to 
       * specify the low-level linear algebra representation */
      VectorType<double> vecType = new EpetraVectorType();

      /* create symbolic coordinate functions */
      Expr x = new CoordExpr(0);

      /* create target function */
      double R = 0.01;
      Expr sx = sin(x);
      Expr cx = cos(x);
      Expr ssx = sin(sx);
      Expr sx2 = sx*sx;
      Expr cx2 = cx*cx;
      Expr f = sx2 - sx - ssx;
      Expr uStar = 2.0*R*(sx2-cx2) + R*sx2*ssx + sx;

      /* Form exact solution */
      Expr uEx = sx;
      Expr lambdaEx = R*sx2;
      Expr alphaEx = -lambdaEx/R;
      

      /* create a discrete space on the mesh */
      BasisFamily bas = new Lagrange(1);
      DiscreteSpace discreteSpace(mesh, bas, vecType);

      /* initialize the design, state, and multiplier vectors to constants */
      Expr alpha0 = new DiscreteFunction(discreteSpace, 0.25, "alpha0");
      Expr u0 = new DiscreteFunction(discreteSpace, 0.5, "u0");
      Expr lambda0 = new DiscreteFunction(discreteSpace, 0.25, "lambda0");

      /* create symbolic objects for test and unknown functions */
      Expr u = new UnknownFunction(bas, "u");
      Expr lambda = new UnknownFunction(bas, "lambda");
      Expr alpha = new UnknownFunction(bas, "alpha");

      /* create symbolic differential operators */
      Expr dx = new Derivative(0);
      Expr grad = dx;

      /* create quadrature rules of different orders */
      QuadratureFamily q1 = new GaussianQuadrature(1);
      QuadratureFamily q2 = new GaussianQuadrature(2);
      QuadratureFamily q4 = new GaussianQuadrature(4);

      /* Form objective function */
      Expr reg = Integral(interior, 0.5 * R * alpha*alpha, q2);
      Expr fit = Integral(interior, 0.5 * pow(u-uStar, 2.0), q4);

      Expr constraintEqn = Integral(interior, 
        (grad*lambda)*(grad*u) + lambda*(alpha + sin(u) + f), q4);
      Expr L = reg + fit + constraintEqn;

      Expr constraintBC = EssentialBC(bdry, lambda*u, q2);

      Functional Lagrangian(mesh, L, constraintBC, vecType);
      
      LinearSolver<double> adjSolver 
        = LinearSolverBuilder::createSolver("amesos.xml");
      ParameterXMLFileReader reader("nox-amesos.xml");
      ParameterList noxParams = reader.getParameters();
      NOXSolver nonlinSolver(noxParams);

      RCP<PDEConstrainedObjBase> obj = rcp(new NonlinearPDEConstrainedObj(
        Lagrangian, u, u0, lambda, lambda0, alpha, alpha0,
        nonlinSolver, adjSolver));

      Vector<double> xInit = obj->getInit();

      bool doFDCheck = true;
      if (doFDCheck)
      {
        Out::root() << "Doing FD check of gradient..." << endl;
        bool fdOK = obj->fdCheck(xInit, 1.0e-6, 0);
        if (fdOK) 
        {
          Out::root() << "FD check OK" << endl;
        }
        else
        {
          Out::root() << "FD check FAILED" << endl;
          TEUCHOS_TEST_FOR_EXCEPT(!fdOK);
        }
      }

      RCP<UnconstrainedOptimizerBase> opt 
          = OptBuilder::createOptimizer("basicLMBFGS.xml");
      opt->setVerb(3);

      OptState state = opt->run(obj, xInit);

      if (state.status() != Opt_Converged)
      {
        Out::root()<< "optimization failed: " << state.status() << endl;
        TEUCHOS_TEST_FOR_EXCEPT(state.status() != Opt_Converged);
      }
      else
      {
        Out::root() << "opt converged: " << state.iter() << " iterations"
                    << endl;
      }
      FieldWriter w = new MatlabWriter("NonlinControl1D");
      w.addMesh(mesh);
      w.addField("u", new ExprFieldWrapper(u0));
      w.addField("alpha", new ExprFieldWrapper(alpha0));
      w.addField("lambda", new ExprFieldWrapper(lambda0));
      w.write();

      double uErr = L2Norm(mesh, interior, u0-uEx, q4);
      double lamErr = L2Norm(mesh, interior, lambda0-lambdaEx, q4);
      double aErr = L2Norm(mesh, interior, alpha0-alphaEx, q4);
      Out::root() << "error in u = " << uErr << endl;
      Out::root() << "error in lambda = " << lamErr << endl;
      Out::root() << "error in alpha = " << aErr << endl;

      double tol = 0.05;
      Sundance::passFailTest(uErr + lamErr + aErr, tol);
    }
	catch(exception& e)
		{
      cerr << "main() caught exception: " << e.what() << endl;
		}
	Sundance::finalize();
  return Sundance::testStatus(); 
}
void LinearPDEConstrainedObj
::solveStateAndAdjoint(const Vector<double>& x) const
{
  Tabs tab(0);
  PLAYA_MSG2(verb(), tab << "solving state and adjoint"); 
  PLAYA_MSG3(verb(), tab << "|x|=" << x.norm2()); 
  PLAYA_MSG5(verb(), tab << "x=" << endl << tab << x.norm2()); 

  Tabs tab1;
  setDiscreteFunctionVector(designVarVal(), x);

  PLAYA_MSG3(verb(), tab1 << "solving state eqns");
  /* solve the state equations in order */
  for (int i=0; i<stateProbs_.size(); i++)
  {
    SolverState<double> status 
      = stateProbs_[i].solve(solvers_[i], stateVarVals(i));

    /* if the solve failed, write out the design var and known state
     * variables */
    if (status.finalState() != SolveConverged)
    {
      FieldWriter w = new VTKWriter("badSolve");
      w.addMesh(Lagrangian().mesh());
      w.addField("designVar", new ExprFieldWrapper(designVarVal()));
      for (int j=0; j<i; j++)
      {
        Expr tmp = stateVarVals(j).flatten();
        for (int k=0; k<tmp.size(); k++)
        {
          w.addField("stateVar-"+Teuchos::toString(j)+"-"+Teuchos::toString(k),
            new ExprFieldWrapper(tmp[k]));
        }
      }
      w.write();
    }
    TEUCHOS_TEST_FOR_EXCEPTION(status.finalState() != SolveConverged,
      std::runtime_error,
      "state equation " << i 
      << " could not be solved: status="
      << status.stateDescription());
  }

  PLAYA_MSG3(verb(), tab1 << "done solving state eqns");

  /* do postprocessing */
  statePostprocCallback();

  PLAYA_MSG3(verb(), tab1 << "solving adjoint eqns");

  /* solve the adjoint equations in reverse order */
  for (int i=adjointProbs_.size()-1; i>=0; i--)
  {
    SolverState<double> status 
      = adjointProbs_[i].solve(solvers_[i], adjointVarVals(i));

    /* if the solve failed, write out the design var and known state
     * and adjoint variables */
    if (status.finalState() != SolveConverged)
    {
      FieldWriter w = new VTKWriter("badSolve");
      w.addMesh(Lagrangian().mesh());
      w.addField("designVar", new ExprFieldWrapper(designVarVal()));
      for (int j=0; j<stateProbs_.size(); j++)
      {
        Expr tmp = stateVarVals(j).flatten();
        for (int k=0; k<tmp.size(); k++)
        {
          w.addField("stateVar-"+Teuchos::toString(j)+"-"+Teuchos::toString(k),
            new ExprFieldWrapper(tmp[k]));
        }
      }
      for (int j=adjointProbs_.size()-1; j>i; j--)
      {
        Expr tmp = adjointVarVals(j).flatten();
        for (int k=0; k<tmp.size(); k++)
        {
          w.addField("adjointVar-"+Teuchos::toString(j)+"-"+Teuchos::toString(k),
            new ExprFieldWrapper(tmp[k]));
        }

      }
      w.write();

    }
    TEUCHOS_TEST_FOR_EXCEPTION(status.finalState() != SolveConverged,
      std::runtime_error,
      "adjoint equation " << i 
      << " could not be solved: status="
      << status.stateDescription());
  }
  PLAYA_MSG3(verb(), tab1 << "done solving adjoint eqns");
  PLAYA_MSG2(verb(), tab1 << "done solving state and adjoint eqns");
}