PDE-OPT/adv-diff-react/example_02.cpp

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/*! \file  example_02.cpp
    \brief Shows how to solve the stochastic advection-diffusion problem.
*/

#include "Teuchos_Comm.hpp"
#include "ROL_Stream.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"

#include "Tpetra_Core.hpp"
#include "Tpetra_Version.hpp"

#include <iostream>
#include <algorithm>
//#include <fenv.h>

#include "ROL_Bounds.hpp"
#include "ROL_Reduced_Objective_SimOpt.hpp"
#include "ROL_MonteCarloGenerator.hpp"
#include "ROL_OptimizationSolver.hpp"
#include "ROL_TpetraTeuchosBatchManager.hpp"

#include "../TOOLS/meshmanager.hpp"
#include "../TOOLS/pdeconstraint.hpp"
#include "../TOOLS/pdeobjective.hpp"
#include "../TOOLS/pdevector.hpp"
#include "../TOOLS/batchmanager.hpp"
#include "pde_stoch_adv_diff.hpp"
#include "obj_stoch_adv_diff.hpp"
#include "mesh_stoch_adv_diff.hpp"

typedef double RealT;

template<class Real>
Real random(const Teuchos::Comm<int> &comm,
            const Real a = -1, const Real b = 1) {
  Real val(0), u(0);
  if ( Teuchos::rank<int>(comm)==0 ) {
    u   = static_cast<Real>(rand())/static_cast<Real>(RAND_MAX);
    val = (b-a)*u + a;
  }
  Teuchos::broadcast<int,Real>(comm,0,1,&val);
  return val;
}

template<class Real>
void print(ROL::Objective<Real> &obj,
           const ROL::Vector<Real> &z,
           ROL::SampleGenerator<Real> &sampler,
           const ROL::Ptr<const Teuchos::Comm<int> > &comm,
           const std::string &filename) {
  Real tol(1e-8);
  int ngsamp = sampler.numGlobalSamples();
  // Build objective function distribution
  int nsamp = sampler.numMySamples();
  std::vector<Real> myvalues(nsamp), myzerovec(nsamp, 0);
  std::vector<double> gvalues(ngsamp), gzerovec(ngsamp, 0);
  std::vector<Real> sample = sampler.getMyPoint(0);
  int sdim = sample.size();
  std::vector<std::vector<Real> > mysamples(sdim, myzerovec);
  std::vector<std::vector<double> > gsamples(sdim, gzerovec);
  for (int i = 0; i < nsamp; ++i) {
    sample = sampler.getMyPoint(i);
    obj.setParameter(sample);
    myvalues[i] = static_cast<double>(obj.value(z,tol));
    for (int j = 0; j < sdim; ++j) {
      mysamples[j][i] = static_cast<double>(sample[j]);
    }
  }

  // Send data to root processor
#ifdef HAVE_MPI
  ROL::Ptr<const Teuchos::MpiComm<int> > mpicomm
    = ROL::dynamicPtrCast<const Teuchos::MpiComm<int> >(comm);
  int nproc = Teuchos::size<int>(*mpicomm);
  std::vector<int> sampleCounts(nproc, 0), sampleDispls(nproc, 0);
  MPI_Gather(&nsamp,1,MPI_INT,&sampleCounts[0],1,MPI_INT,0,*(mpicomm->getRawMpiComm())());
  for (int i = 1; i < nproc; ++i) {
    sampleDispls[i] = sampleDispls[i-1] + sampleCounts[i-1];
  }
  MPI_Gatherv(&myvalues[0],nsamp,MPI_DOUBLE,&gvalues[0],&sampleCounts[0],&sampleDispls[0],MPI_DOUBLE,0,*(mpicomm->getRawMpiComm())());
  for (int j = 0; j < sdim; ++j) {
    MPI_Gatherv(&mysamples[j][0],nsamp,MPI_DOUBLE,&gsamples[j][0],&sampleCounts[0],&sampleDispls[0],MPI_DOUBLE,0,*(mpicomm->getRawMpiComm())());
  }
#else
  gvalues.assign(myvalues.begin(),myvalues.end());
  for (int j = 0; j < sdim; ++j) {
    gsamples[j].assign(mysamples[j].begin(),mysamples[j].end());
  }
#endif

  // Print
  int rank  = Teuchos::rank<int>(*comm);
  if ( rank==0 ) {
    std::ofstream file;
    file.open(filename);
    file << std::scientific << std::setprecision(15);
    for (int i = 0; i < ngsamp; ++i) {
      for (int j = 0; j < sdim; ++j) {
        file << std::setw(25) << std::left << gsamples[j][i];
      }
      file << std::setw(25) << std::left << gvalues[i] << std::endl;
    }
    file.close();
  }
}

template<class Real>
void printSampler(ROL::SampleGenerator<Real> &sampler,
                  const ROL::Ptr<const Teuchos::Comm<int> > &comm,
                  const std::string &filename) {
  int ngsamp = sampler.numGlobalSamples();
  // Build objective function distribution
  int nsamp = sampler.numMySamples();
  std::vector<Real> myzerovec(nsamp, 0);
  std::vector<double> gzerovec(ngsamp, 0);
  std::vector<Real> sample = sampler.getMyPoint(0);
  int sdim = sample.size();
  std::vector<std::vector<Real> > mysamples(sdim, myzerovec);
  std::vector<std::vector<double> > gsamples(sdim, gzerovec);
  for (int i = 0; i < nsamp; ++i) {
    sample = sampler.getMyPoint(i);
    for (int j = 0; j < sdim; ++j) {
      mysamples[j][i] = static_cast<double>(sample[j]);
    }
  }

  // Send data to root processor
#ifdef HAVE_MPI
  ROL::Ptr<const Teuchos::MpiComm<int> > mpicomm
    = ROL::dynamicPtrCast<const Teuchos::MpiComm<int> >(comm);
  int nproc = Teuchos::size<int>(*mpicomm);
  std::vector<int> sampleCounts(nproc, 0), sampleDispls(nproc, 0);
  MPI_Gather(&nsamp,1,MPI_INT,&sampleCounts[0],1,MPI_INT,0,*(mpicomm->getRawMpiComm())());
  for (int i = 1; i < nproc; ++i) {
    sampleDispls[i] = sampleDispls[i-1] + sampleCounts[i-1];
  }
  for (int j = 0; j < sdim; ++j) {
    MPI_Gatherv(&mysamples[j][0],nsamp,MPI_DOUBLE,&gsamples[j][0],&sampleCounts[0],&sampleDispls[0],MPI_DOUBLE,0,*(mpicomm->getRawMpiComm())());
  }
#else
  for (int j = 0; j < sdim; ++j) {
    gsamples[j].assign(mysamples[j].begin(),mysamples[j].end());
  }
#endif

  // Print
  int rank  = Teuchos::rank<int>(*comm);
  if ( rank==0 ) {
    std::ofstream file;
    file.open(filename);
    file << std::scientific << std::setprecision(15);
    for (int i = 0; i < ngsamp; ++i) {
      for (int j = 0; j < sdim; ++j) {
        file << std::setw(25) << std::left << gsamples[j][i];
      }
      file << std::endl;
    }
    file.close();
  }
}

int main(int argc, char *argv[]) {
//  feenableexcept(FE_DIVBYZERO | FE_INVALID | FE_OVERFLOW);

  // This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
  int iprint     = argc - 1;
  ROL::Ptr<std::ostream> outStream;
  ROL::nullstream bhs; // outputs nothing

  /*** Initialize communicator. ***/
  Teuchos::GlobalMPISession mpiSession (&argc, &argv, &bhs);
  ROL::Ptr<const Teuchos::Comm<int> > comm
    = Tpetra::getDefaultComm();
  ROL::Ptr<const Teuchos::Comm<int> > serial_comm
    = ROL::makePtr<Teuchos::SerialComm<int>>();
  const int myRank = comm->getRank();
  if ((iprint > 0) && (myRank == 0)) {
    outStream = ROL::makePtrFromRef(std::cout);
  }
  else {
    outStream = ROL::makePtrFromRef(bhs);
  }
  int errorFlag  = 0;

  // *** Example body.
  try {

    /*** Read in XML input ***/
    std::string filename = "input.xml";
    Teuchos::RCP<Teuchos::ParameterList> parlist = Teuchos::rcp( new Teuchos::ParameterList() );
    Teuchos::updateParametersFromXmlFile( filename, parlist.ptr() );

    // Problem dimensions
    const int controlDim = 9, stochDim = 37;
    const RealT one(1);

    /*************************************************************************/
    /***************** BUILD GOVERNING PDE ***********************************/
    /*************************************************************************/
    /*** Initialize main data structure. ***/
    ROL::Ptr<MeshManager<RealT> > meshMgr
      = ROL::makePtr<MeshManager_stoch_adv_diff<RealT>>(*parlist);
    // Initialize PDE describing advection-diffusion equation
    ROL::Ptr<PDE_stoch_adv_diff<RealT> > pde
      = ROL::makePtr<PDE_stoch_adv_diff<RealT>>(*parlist);
    ROL::Ptr<ROL::Constraint_SimOpt<RealT> > con
      = ROL::makePtr<PDE_Constraint<RealT>>(pde,meshMgr,serial_comm,*parlist,*outStream);
    ROL::Ptr<PDE_Constraint<RealT> > pdeCon
      = ROL::dynamicPtrCast<PDE_Constraint<RealT> >(con);
    pdeCon->getAssembler()->printMeshData(*outStream);
    con->setSolveParameters(*parlist);

    /*************************************************************************/
    /***************** BUILD VECTORS *****************************************/
    /*************************************************************************/
    ROL::Ptr<Tpetra::MultiVector<> >  u_ptr = pdeCon->getAssembler()->createStateVector();
    ROL::Ptr<Tpetra::MultiVector<> >  p_ptr = pdeCon->getAssembler()->createStateVector();
    ROL::Ptr<Tpetra::MultiVector<> > du_ptr = pdeCon->getAssembler()->createStateVector();
    u_ptr->randomize();  //u_ptr->putScalar(static_cast<RealT>(1));
    p_ptr->randomize();  //p_ptr->putScalar(static_cast<RealT>(1));
    du_ptr->randomize(); //du_ptr->putScalar(static_cast<RealT>(0));
    ROL::Ptr<ROL::Vector<RealT> > up
      = ROL::makePtr<PDE_PrimalSimVector<RealT>>(u_ptr,pde,pdeCon->getAssembler());
    ROL::Ptr<ROL::Vector<RealT> > pp
      = ROL::makePtr<PDE_PrimalSimVector<RealT>>(p_ptr,pde,pdeCon->getAssembler());
    ROL::Ptr<ROL::Vector<RealT> > dup
      = ROL::makePtr<PDE_PrimalSimVector<RealT>>(du_ptr,pde,pdeCon->getAssembler());
    // Create residual vectors
    ROL::Ptr<Tpetra::MultiVector<> > r_ptr = pdeCon->getAssembler()->createResidualVector();
    r_ptr->randomize(); //r_ptr->putScalar(static_cast<RealT>(1));
    ROL::Ptr<ROL::Vector<RealT> > rp
      = ROL::makePtr<PDE_DualSimVector<RealT>>(r_ptr,pde,pdeCon->getAssembler());
    // Create control vector and set to ones
    ROL::Ptr<std::vector<RealT> >  z_ptr = ROL::makePtr<std::vector<RealT>>(controlDim);
    ROL::Ptr<std::vector<RealT> > dz_ptr = ROL::makePtr<std::vector<RealT>>(controlDim);
    ROL::Ptr<std::vector<RealT> > yz_ptr = ROL::makePtr<std::vector<RealT>>(controlDim);
    // Create control direction vector and set to random
    for (int i = 0; i < controlDim; ++i) {
      (*z_ptr)[i]  = random<RealT>(*comm);
      (*dz_ptr)[i] = random<RealT>(*comm);
      (*yz_ptr)[i] = random<RealT>(*comm);
    }
    ROL::Ptr<ROL::Vector<RealT> > zp
      = ROL::makePtr<PDE_OptVector<RealT>>(ROL::makePtr<ROL::StdVector<RealT>>(z_ptr));
    ROL::Ptr<ROL::Vector<RealT> > dzp
      = ROL::makePtr<PDE_OptVector<RealT>>(ROL::makePtr<ROL::StdVector<RealT>>(dz_ptr));
    ROL::Ptr<ROL::Vector<RealT> > yzp
      = ROL::makePtr<PDE_OptVector<RealT>>(ROL::makePtr<ROL::StdVector<RealT>>(yz_ptr));
    // Create ROL SimOpt vectors
    ROL::Vector_SimOpt<RealT> x(up,zp);
    ROL::Vector_SimOpt<RealT> d(dup,dzp);

    ROL::Ptr<Tpetra::MultiVector<> > dualu_ptr = pdeCon->getAssembler()->createStateVector();
    ROL::Ptr<ROL::Vector<RealT> > dualup
      = ROL::makePtr<PDE_DualSimVector<RealT>>(dualu_ptr,pde,pdeCon->getAssembler());

    /*************************************************************************/
    /***************** BUILD COST FUNCTIONAL *********************************/
    /*************************************************************************/
    std::vector<ROL::Ptr<QoI<RealT> > > qoi_vec(2,ROL::nullPtr);
    qoi_vec[0] = ROL::makePtr<QoI_State_Cost_stoch_adv_diff<RealT>>(pde->getFE());
    qoi_vec[1] = ROL::makePtr<QoI_Control_Cost_stoch_adv_diff<RealT>>();
    RealT stateCost   = parlist->sublist("Problem").get("State Cost",1.e5);
    RealT controlCost = parlist->sublist("Problem").get("Control Cost",1.e0);
    std::vector<RealT> wts = {stateCost, controlCost};
    ROL::Ptr<ROL::Objective_SimOpt<RealT> > obj
      = ROL::makePtr<PDE_Objective<RealT>>(qoi_vec,wts,pdeCon->getAssembler());
    bool storage = parlist->sublist("Problem").get("Use State and Adjoint Storage",true);
    ROL::Ptr<ROL::Reduced_Objective_SimOpt<RealT> > objReduced
      = ROL::makePtr<ROL::Reduced_Objective_SimOpt<RealT>>(obj, con, up, zp, pp, storage, false);

    /*************************************************************************/
    /***************** BUILD BOUND CONSTRAINT ********************************/
    /*************************************************************************/
    ROL::Ptr<std::vector<RealT> > zlo_ptr = ROL::makePtr<std::vector<RealT>>(controlDim,0);
    ROL::Ptr<std::vector<RealT> > zhi_ptr = ROL::makePtr<std::vector<RealT>>(controlDim,1);
    ROL::Ptr<ROL::Vector<RealT> > zlop
      = ROL::makePtr<PDE_OptVector<RealT>>(ROL::makePtr<ROL::StdVector<RealT>>(zlo_ptr));
    ROL::Ptr<ROL::Vector<RealT> > zhip
      = ROL::makePtr<PDE_OptVector<RealT>>(ROL::makePtr<ROL::StdVector<RealT>>(zhi_ptr));
    ROL::Ptr<ROL::BoundConstraint<RealT> > bnd
      = ROL::makePtr<ROL::Bounds<RealT>>(zlop,zhip);

    /*************************************************************************/
    /***************** BUILD SAMPLER *****************************************/
    /*************************************************************************/
    int nsamp = parlist->sublist("Problem").get("Number of Samples",100);
    std::vector<RealT> tmp = {-one,one};
    std::vector<std::vector<RealT> > bounds(stochDim,tmp);
    ROL::Ptr<ROL::BatchManager<RealT> > bman
      = ROL::makePtr<PDE_OptVector_BatchManager<RealT>>(comm);
    ROL::Ptr<ROL::SampleGenerator<RealT> > sampler
      = ROL::makePtr<ROL::MonteCarloGenerator<RealT>>(nsamp,bounds,bman);

    /*************************************************************************/
    /***************** BUILD STOCHASTIC PROBLEM ******************************/
    /*************************************************************************/
    ROL::OptimizationProblem<RealT> opt(objReduced,zp,bnd);
    parlist->sublist("SOL").set("Initial Statistic",one);
    opt.setStochasticObjective(*parlist,sampler);

    /*************************************************************************/
    /***************** RUN VECTOR AND DERIVATIVE CHECKS **********************/
    /*************************************************************************/
    bool checkDeriv = parlist->sublist("Problem").get("Check Derivatives",false);
    if ( checkDeriv ) {
      up->checkVector(*pp,*dup,true,*outStream);
      zp->checkVector(*yzp,*dzp,true,*outStream);
      std::vector<RealT> param(stochDim,0);
      objReduced->setParameter(param);
      *outStream << "\n\nCheck Gradient of Full Objective Function\n";
      obj->checkGradient(x,d,true,*outStream);
      *outStream << "\n\nCheck Hessian of Full Objective Function\n";
      obj->checkHessVec(x,d,true,*outStream);
      *outStream << "\n\nCheck Full Jacobian of PDE Constraint\n";
      con->checkApplyJacobian(x,d,*rp,true,*outStream);
      *outStream << "\n\nCheck Jacobian_1 of PDE Constraint\n";
      con->checkApplyJacobian_1(*up,*zp,*dup,*rp,true,*outStream);
      *outStream << "\n\nCheck Jacobian_2 of PDE Constraint\n";
      con->checkApplyJacobian_2(*up,*zp,*dzp,*rp,true,*outStream);
      *outStream << "\n\nCheck Full Hessian of PDE Constraint\n";
      con->checkApplyAdjointHessian(x,*pp,d,x,true,*outStream);
      *outStream << "\n\nCheck Hessian_11 of PDE Constraint\n";
      con->checkApplyAdjointHessian_11(*up,*zp,*pp,*dup,*dualup,true,*outStream);
      *outStream << "\n\nCheck Hessian_21 of PDE Constraint\n";
      con->checkApplyAdjointHessian_21(*up,*zp,*pp,*dzp,*dualup,true,*outStream);
      *outStream << "\n\nCheck Hessian_12 of PDE Constraint\n";
      con->checkApplyAdjointHessian_12(*up,*zp,*pp,*dup,*dzp,true,*outStream);
      *outStream << "\n\nCheck Hessian_22 of PDE Constraint\n";
      con->checkApplyAdjointHessian_22(*up,*zp,*pp,*dzp,*dzp,true,*outStream);
      *outStream << "\n";
      con->checkAdjointConsistencyJacobian(*dup,d,x,true,*outStream);
      *outStream << "\n";
      con->checkInverseJacobian_1(*up,*up,*up,*zp,true,*outStream);
      *outStream << "\n";
      *outStream << "\n\nCheck Gradient of Reduced Objective Function\n";
      objReduced->checkGradient(*zp,*dzp,true,*outStream);
      *outStream << "\n\nCheck Hessian of Reduced Objective Function\n";
      objReduced->checkHessVec(*zp,*dzp,true,*outStream);

      opt.check(*outStream);
    }

    /*************************************************************************/
    /***************** SOLVE OPTIMIZATION PROBLEM ****************************/
    /*************************************************************************/
    parlist->sublist("Step").set("Type","Trust Region");
    ROL::OptimizationSolver<RealT> solver(opt,*parlist);
    zp->zero();
    std::clock_t timer = std::clock();
    solver.solve(*outStream);
    *outStream << "Optimization time: "
               << static_cast<RealT>(std::clock()-timer)/static_cast<RealT>(CLOCKS_PER_SEC)
               << " seconds." << std::endl << std::endl;

    /*************************************************************************/
    /***************** OUTPUT RESULTS ****************************************/
    /*************************************************************************/
    std::clock_t timer_print = std::clock();
    // Output control to file
    if ( myRank == 0 ) {
      std::ofstream zfile;
      zfile.open("control.txt");
      for (int i = 0; i < controlDim; i++) {
        zfile << std::scientific << std::setprecision(15);
        zfile << (*z_ptr)[i] << std::endl;
      }
      zfile.close();
    }
    // Output statisitic to file
    std::vector<RealT> stat = opt.getObjectiveStatistic();
    if ( myRank == 0 && stat.size() > 0 ) {
      std::ofstream sfile;
      sfile.open("stat.txt");
      for (int i = 0; i < static_cast<int>(stat.size()); ++i) {
        sfile << std::scientific << std::setprecision(15);
        sfile << stat[i] << std::endl;
      }
    }
    // Output expected state and samples to file
    up->zero(); pp->zero(); dup->zero();
    RealT tol(1.e-8);
    ROL::Ptr<ROL::BatchManager<RealT> > bman_Eu
      = ROL::makePtr<ROL::TpetraTeuchosBatchManager<RealT>>(comm);
    std::vector<RealT> sample(stochDim);
    for (int i = 0; i < sampler->numMySamples(); ++i) {
      sample = sampler->getMyPoint(i);
      con->setParameter(sample);
      con->solve(*rp,*dup,*zp,tol);
      up->axpy(sampler->getMyWeight(i),*dup);
    }
    bman_Eu->sumAll(*up,*pp);
    pdeCon->getAssembler()->outputTpetraVector(p_ptr,"mean_state.txt");
    // Print samples
    printSampler<RealT>(*sampler,comm,"samples.txt");
    // Build objective function distribution
    int nsamp_dist = parlist->sublist("Problem").get("Number of Output Samples",100);
    ROL::Ptr<ROL::SampleGenerator<RealT> > sampler_dist
      = ROL::makePtr<ROL::MonteCarloGenerator<RealT>>(nsamp_dist,bounds,bman);
    print<RealT>(*objReduced,*zp,*sampler_dist,comm,"obj_samples.txt");
    *outStream << "Output time: "
               << static_cast<RealT>(std::clock()-timer_print)/static_cast<RealT>(CLOCKS_PER_SEC)
               << " seconds." << std::endl << std::endl;

    Teuchos::Array<RealT> res(1,0);
    pdeCon->solve(*rp,*up,*zp,tol);
    r_ptr->norm2(res.view(0,1));

    /*************************************************************************/
    /***************** CHECK RESIDUAL NORM ***********************************/
    /*************************************************************************/
    *outStream << "Residual Norm: " << res[0] << std::endl << std::endl;
    errorFlag += (res[0] > 1.e-6 ? 1 : 0);
  }
  catch (std::logic_error& err) {
    *outStream << err.what() << "\n";
    errorFlag = -1000;
  }; // end try

  if (errorFlag != 0)
    std::cout << "End Result: TEST FAILED\n";
  else
    std::cout << "End Result: TEST PASSED\n";

  return 0;
}