int LSmear::var_to_bisect(IntervalMatrix& J, const IntervalVector& box) const {
int lvar = -1;
//Linearization
LPSolver::Status_Sol stat = LPSolver::UNKNOWN;
Vector dual_solution(1);
if (lsmode==LSMEAR_MG) { //compute the Jacobian in the midpoint
IntervalMatrix J2(sys.f_ctrs.image_dim(), sys.nb_var);
IntervalVector box2(IntervalVector(box.mid()).inflate(1e-8));
// IntervalVector box2(IntervalVector(box.random()));
box2 &= box;
sys.f_ctrs.jacobian(box2,J2);
stat = getdual(J2, box, dual_solution);
} else if (lsmode==LSMEAR) {
stat = getdual(J, box, dual_solution);
}
if (stat == LPSolver::OPTIMAL) {
double max_Lmagn = 0.0;
int k=0;
for (int j=0; j<nbvars; j++) {
Interval lsmear=Interval(0.0);
if ((!too_small(box,j)) && (box[j].mag() <1 || box[j].diam()/ box[j].mag() >= prec(j))){
lsmear=dual_solution[j];
for (int i=0; i<sys.f_ctrs.image_dim(); i++){
lsmear += dual_solution[sys.nb_var+i] * J[i][j];
}
}
lsmear*=(box[j].diam());
if (lsmear.mag() > 1e-10 && (j!=goal_var() || mylinearsolver->get_obj_value().mid() > box[goal_var()].lb() )) {
k++;
if (lsmear.mag() > max_Lmagn) {
max_Lmagn = lsmear.mag();
lvar = j;
}
}
}
if (k==1 && lvar==goal_var()) { lvar=-1; }
}
if (lvar==-1) {
// std::cout << "ssr " << std::endl;
lvar=SmearSumRelative::var_to_bisect(J, box);
}
// std::cout << "lsmear " << lvar << std::endl;
return lvar;
}
// The main program
int main(int argc, char** argv)
{
// Initialize libMesh
LibMeshInit init(argc, argv);
// Parameters
GetPot infile("fem_system_params.in");
const Real global_tolerance = infile("global_tolerance", 0.);
const unsigned int nelem_target = infile("n_elements", 400);
const bool transient = infile("transient", true);
const Real deltat = infile("deltat", 0.005);
unsigned int n_timesteps = infile("n_timesteps", 1);
//const unsigned int coarsegridsize = infile("coarsegridsize", 1);
const unsigned int coarserefinements = infile("coarserefinements", 0);
const unsigned int max_adaptivesteps = infile("max_adaptivesteps", 10);
//const unsigned int dim = 2;
#ifdef LIBMESH_HAVE_EXODUS_API
const unsigned int write_interval = infile("write_interval", 5);
#endif
// Create a mesh, with dimension to be overridden later, distributed
// across the default MPI communicator.
Mesh mesh(init.comm());
GetPot infileForMesh("convdiff_mprime.in");
std::string find_mesh_here = infileForMesh("mesh","psiLF_mesh.xda");
mesh.read(find_mesh_here);
std::cout << "Read in mesh from: " << find_mesh_here << "\n\n";
// And an object to refine it
MeshRefinement mesh_refinement(mesh);
mesh_refinement.coarsen_by_parents() = true;
mesh_refinement.absolute_global_tolerance() = global_tolerance;
mesh_refinement.nelem_target() = nelem_target;
mesh_refinement.refine_fraction() = 0.3;
mesh_refinement.coarsen_fraction() = 0.3;
mesh_refinement.coarsen_threshold() = 0.1;
//mesh_refinement.uniformly_refine(coarserefinements);
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Name system
ConvDiff_MprimeSys & system =
equation_systems.add_system<ConvDiff_MprimeSys>("Diff_ConvDiff_MprimeSys");
// Steady-state problem
system.time_solver =
AutoPtr<TimeSolver>(new SteadySolver(system));
// Sanity check that we are indeed solving a steady problem
libmesh_assert_equal_to (n_timesteps, 1);
// Read in all the equation systems data from the LF solve (system, solutions, rhs, etc)
std::string find_psiLF_here = infileForMesh("psiLF_file","psiLF.xda");
std::cout << "Looking for psiLF at: " << find_psiLF_here << "\n\n";
equation_systems.read(find_psiLF_here, READ,
EquationSystems::READ_HEADER |
EquationSystems::READ_DATA |
EquationSystems::READ_ADDITIONAL_DATA);
// Check that the norm of the solution read in is what we expect it to be
Real readin_L2 = system.calculate_norm(*system.solution, 0, L2);
std::cout << "Read in solution norm: "<< readin_L2 << std::endl << std::endl;
//DEBUG
//equation_systems.write("right_back_out.xda", WRITE, EquationSystems::WRITE_DATA |
// EquationSystems::WRITE_ADDITIONAL_DATA);
#ifdef LIBMESH_HAVE_GMV
//GMVIO(equation_systems.get_mesh()).write_equation_systems(std::string("right_back_out.gmv"), equation_systems);
#endif
// Initialize the system
//equation_systems.init (); //already initialized by read-in
// And the nonlinear solver options
NewtonSolver *solver = new NewtonSolver(system);
system.time_solver->diff_solver() = AutoPtr<DiffSolver>(solver);
solver->quiet = infile("solver_quiet", true);
solver->verbose = !solver->quiet;
solver->max_nonlinear_iterations =
infile("max_nonlinear_iterations", 15);
solver->relative_step_tolerance =
infile("relative_step_tolerance", 1.e-3);
solver->relative_residual_tolerance =
infile("relative_residual_tolerance", 0.0);
solver->absolute_residual_tolerance =
infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver->max_linear_iterations =
infile("max_linear_iterations", 50000);
solver->initial_linear_tolerance =
infile("initial_linear_tolerance", 1.e-3);
// Print information about the system to the screen.
equation_systems.print_info();
// Now we begin the timestep loop to compute the time-accurate
// solution of the equations...not that this is transient, but eh, why not...
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
// A pretty update message
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
// Adaptively solve the timestep
unsigned int a_step = 0;
for (; a_step != max_adaptivesteps; ++a_step)
{ // VESTIGIAL for now ('vestigial' eh ? ;) )
std::cout << "\n\n I should be skipped what are you doing here lalalalalalala *!**!*!*!*!*!* \n\n";
system.solve();
system.postprocess();
ErrorVector error;
AutoPtr<ErrorEstimator> error_estimator;
// To solve to a tolerance in this problem we
// need a better estimator than Kelly
if (global_tolerance != 0.)
{
// We can't adapt to both a tolerance and a mesh
// size at once
libmesh_assert_equal_to (nelem_target, 0);
UniformRefinementEstimator *u =
new UniformRefinementEstimator;
// The lid-driven cavity problem isn't in H1, so
// lets estimate L2 error
u->error_norm = L2;
error_estimator.reset(u);
}
else
{
// If we aren't adapting to a tolerance we need a
// target mesh size
libmesh_assert_greater (nelem_target, 0);
// Kelly is a lousy estimator to use for a problem
// not in H1 - if we were doing more than a few
// timesteps we'd need to turn off or limit the
// maximum level of our adaptivity eventually
error_estimator.reset(new KellyErrorEstimator);
}
// Calculate error
std::vector<Real> weights(9,1.0); // based on u, v, p, c, their adjoints, and source parameter
// Keep the same default norm type.
std::vector<FEMNormType>
norms(1, error_estimator->error_norm.type(0));
error_estimator->error_norm = SystemNorm(norms, weights);
error_estimator->estimate_error(system, error);
// Print out status at each adaptive step.
Real global_error = error.l2_norm();
std::cout << "Adaptive step " << a_step << ": " << std::endl;
if (global_tolerance != 0.)
std::cout << "Global_error = " << global_error
<< std::endl;
if (global_tolerance != 0.)
std::cout << "Worst element error = " << error.maximum()
<< ", mean = " << error.mean() << std::endl;
if (global_tolerance != 0.)
{
// If we've reached our desired tolerance, we
// don't need any more adaptive steps
if (global_error < global_tolerance)
break;
mesh_refinement.flag_elements_by_error_tolerance(error);
}
else
{
// If flag_elements_by_nelem_target returns true, this
// should be our last adaptive step.
if (mesh_refinement.flag_elements_by_nelem_target(error))
{
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
a_step = max_adaptivesteps;
break;
}
}
// Carry out the adaptive mesh refinement/coarsening
mesh_refinement.refine_and_coarsen_elements();
equation_systems.reinit();
std::cout << "Refined mesh to "
<< mesh.n_active_elem()
<< " active elements and "
<< equation_systems.n_active_dofs()
<< " active dofs." << std::endl;
} // End loop over adaptive steps
// Do one last solve if necessary
if (a_step == max_adaptivesteps)
{
QoISet qois;
std::vector<unsigned int> qoi_indices;
qoi_indices.push_back(0);
qois.add_indices(qoi_indices);
qois.set_weight(0, 1.0);
system.assemble_qoi_sides = true; //QoI doesn't involve sides
std::cout << "\n~*~*~*~*~*~*~*~*~ adjoint solve start ~*~*~*~*~*~*~*~*~\n" << std::endl;
std::pair<unsigned int, Real> adjsolve = system.adjoint_solve();
std::cout << "number of iterations to solve adjoint: " << adjsolve.first << std::endl;
std::cout << "final residual of adjoint solve: " << adjsolve.second << std::endl;
std::cout << "\n~*~*~*~*~*~*~*~*~ adjoint solve end ~*~*~*~*~*~*~*~*~" << std::endl;
NumericVector<Number> &dual_solution = system.get_adjoint_solution(0);
NumericVector<Number> &primal_solution = *system.solution;
primal_solution.swap(dual_solution);
ExodusII_IO(mesh).write_timestep("super_adjoint.exo",
equation_systems,
1, /* This number indicates how many time steps
are being written to the file */
system.time);
primal_solution.swap(dual_solution);
system.assemble(); //overwrite residual read in from psiLF solve
// The total error estimate
system.postprocess(); //to compute M_HF(psiLF) and M_LF(psiLF) terms
Real QoI_error_estimate = (-0.5*(system.rhs)->dot(dual_solution)) + system.get_MHF_psiLF() - system.get_MLF_psiLF();
std::cout << "\n\n 0.5*M'_HF(psiLF)(superadj): " << std::setprecision(17) << 0.5*(system.rhs)->dot(dual_solution) << "\n";
std::cout << " M_HF(psiLF): " << std::setprecision(17) << system.get_MHF_psiLF() << "\n";
std::cout << " M_LF(psiLF): " << std::setprecision(17) << system.get_MLF_psiLF() << "\n";
std::cout << "\n\n Residual L2 norm: " << system.calculate_norm(*system.rhs, L2) << "\n";
std::cout << " Residual discrete L2 norm: " << system.calculate_norm(*system.rhs, DISCRETE_L2) << "\n";
std::cout << " Super-adjoint L2 norm: " << system.calculate_norm(dual_solution, L2) << "\n";
std::cout << " Super-adjoint discrete L2 norm: " << system.calculate_norm(dual_solution, DISCRETE_L2) << "\n";
std::cout << "\n\n QoI error estimate: " << std::setprecision(17) << QoI_error_estimate << "\n\n";
//DEBUG
std::cout << "\n------------ herp derp ------------" << std::endl;
//libMesh::out.precision(16);
//dual_solution.print();
//system.get_adjoint_rhs().print();
AutoPtr<NumericVector<Number> > adjresid = system.solution->clone();
(system.matrix)->vector_mult(*adjresid,system.get_adjoint_solution(0));
SparseMatrix<Number>& adjmat = *system.matrix;
(system.matrix)->get_transpose(adjmat);
adjmat.vector_mult(*adjresid,system.get_adjoint_solution(0));
//std::cout << "******************** matrix-superadj product (libmesh) ************************" << std::endl;
//adjresid->print();
adjresid->add(-1.0, system.get_adjoint_rhs(0));
//std::cout << "******************** superadjoint system residual (libmesh) ***********************" << std::endl;
//adjresid->print();
std::cout << "\n\nadjoint system residual (discrete L2): " << system.calculate_norm(*adjresid,DISCRETE_L2) << std::endl;
std::cout << "adjoint system residual (L2, all): " << system.calculate_norm(*adjresid,L2) << std::endl;
std::cout << "adjoint system residual (L2, 0): " << system.calculate_norm(*adjresid,0,L2) << std::endl;
std::cout << "adjoint system residual (L2, 1): " << system.calculate_norm(*adjresid,1,L2) << std::endl;
std::cout << "adjoint system residual (L2, 2): " << system.calculate_norm(*adjresid,2,L2) << std::endl;
std::cout << "adjoint system residual (L2, 3): " << system.calculate_norm(*adjresid,3,L2) << std::endl;
std::cout << "adjoint system residual (L2, 4): " << system.calculate_norm(*adjresid,4,L2) << std::endl;
std::cout << "adjoint system residual (L2, 5): " << system.calculate_norm(*adjresid,5,L2) << std::endl;
/*
AutoPtr<NumericVector<Number> > sadj_matlab = system.solution->clone();
AutoPtr<NumericVector<Number> > adjresid_matlab = system.solution->clone();
if(FILE *fp=fopen("superadj_matlab.txt","r")){
Real value;
int counter = 0;
int flag = 1;
while(flag != -1){
flag = fscanf(fp,"%lf",&value);
if(flag != -1){
sadj_matlab->set(counter, value);
counter += 1;
}
}
fclose(fp);
}
(system.matrix)->vector_mult(*adjresid_matlab,*sadj_matlab);
//std::cout << "******************** matrix-superadj product (matlab) ***********************" << std::endl;
//adjresid_matlab->print();
adjresid_matlab->add(-1.0, system.get_adjoint_rhs(0));
//std::cout << "******************** superadjoint system residual (matlab) ***********************" << std::endl;
//adjresid_matlab->print();
std::cout << "\n\nmatlab import adjoint system residual (discrete L2): " << system.calculate_norm(*adjresid_matlab,DISCRETE_L2) << "\n" << std::endl;
*/
/*
AutoPtr<NumericVector<Number> > sadj_fwd_hack = system.solution->clone();
AutoPtr<NumericVector<Number> > adjresid_fwd_hack = system.solution->clone();
if(FILE *fp=fopen("superadj_forward_hack.txt","r")){
Real value;
int counter = 0;
int flag = 1;
while(flag != -1){
flag = fscanf(fp,"%lf",&value);
if(flag != -1){
sadj_fwd_hack->set(counter, value);
counter += 1;
}
}
fclose(fp);
}
(system.matrix)->vector_mult(*adjresid_fwd_hack,*sadj_fwd_hack);
//std::cout << "******************** matrix-superadj product (fwd_hack) ***********************" << std::endl;
//adjresid_fwd_hack->print();
adjresid_fwd_hack->add(-1.0, system.get_adjoint_rhs(0));
//std::cout << "******************** superadjoint system residual (fwd_hack) ***********************" << std::endl;
//adjresid_fwd_hack->print();
std::cout << "\n\nfwd_hack import adjoint system residual (discrete L2): " << system.calculate_norm(*adjresid_fwd_hack,DISCRETE_L2) << "\n" << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 0): " << system.calculate_norm(*adjresid_fwd_hack,0,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 1): " << system.calculate_norm(*adjresid_fwd_hack,1,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 2): " << system.calculate_norm(*adjresid_fwd_hack,2,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 3): " << system.calculate_norm(*adjresid_fwd_hack,3,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 4): " << system.calculate_norm(*adjresid_fwd_hack,4,L2) << std::endl;
std::cout << "fwd_hack adjoint system residual (L2, 5): " << system.calculate_norm(*adjresid_fwd_hack,5,L2) << std::endl;
*/
//std::cout << "************************ system.matrix ***********************" << std::endl;
//system.matrix->print();
std::cout << "\n------------ herp derp ------------" << std::endl;
// The cell wise breakdown
ErrorVector cell_wise_error;
cell_wise_error.resize((system.rhs)->size());
for(unsigned int i = 0; i < (system.rhs)->size() ; i++)
{
if(i < system.get_mesh().n_elem())
cell_wise_error[i] = fabs(-0.5*((system.rhs)->el(i) * dual_solution(i))
+ system.get_MHF_psiLF(i) - system.get_MLF_psiLF(i));
else
cell_wise_error[i] = fabs(-0.5*((system.rhs)->el(i) * dual_solution(i)));
/*csv from 'save data' from gmv output gives a few values at each node point (value
for every element that shares that node), yet paraview display only seems to show one
of them -> the value in an element is given at each of the nodes that it has, hence the
repetition; what is displayed in paraview is each element's value; even though MHF_psiLF
and MLF_psiLF are stored by element this seems to give elemental contributions that
agree with if we had taken the superadj-residual dot product by integrating over elements*/
/*at higher mesh resolutions and lower k, weird-looking artifacts start to appear and
it no longer agrees with output from manual integration of superadj-residual...*/
}
// Plot it
std::ostringstream error_gmv;
error_gmv << "error.gmv";
cell_wise_error.plot_error(error_gmv.str(), equation_systems.get_mesh());
//alternate element-wise breakdown, outputed as values matched to element centroids; for matlab plotz
primal_solution.swap(dual_solution);
system.postprocess(1);
primal_solution.swap(dual_solution);
system.postprocess(2);
std::cout << "\n\n -0.5*M'_HF(psiLF)(superadj): " << std::setprecision(17) << system.get_half_adj_weighted_resid() << "\n";
primal_solution.swap(dual_solution);
std::string write_error_here = infileForMesh("error_est_output_file", "error_est_breakdown.dat");
std::ofstream output(write_error_here);
for(unsigned int i = 0 ; i < system.get_mesh().n_elem(); i++) {
Point elem_cent = system.get_mesh().elem(i)->centroid();
if(output.is_open()) {
output << elem_cent(0) << " " << elem_cent(1) << " "
<< fabs(system.get_half_adj_weighted_resid(i) + system.get_MHF_psiLF(i) - system.get_MLF_psiLF(i)) << "\n";
}
}
output.close();
} // End if at max adaptive steps
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out this timestep if we're requested to
if ((t_step+1)%write_interval == 0)
{
std::ostringstream file_name;
/*
// We write the file in the ExodusII format.
file_name << "out_"
<< std::setw(3)
<< std::setfill('0')
<< std::right
<< t_step+1
<< ".e";
//this should write out the primal which should be the same as what's read in...
ExodusII_IO(mesh).write_timestep(file_name.str(),
equation_systems,
1, //number of time steps written to file
system.time);
*/
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
}
// All done.
return 0;
} //end main
LinearSolver::Status_Sol CtcPolytopeHull::run_simplex(IntervalVector& box,
LinearSolver::Sense sense, int var, Interval& obj, double bound) {
int nvar=nb_var;
int nctr=mylinearsolver->getNbRows();
// the linear solver is always called in a minimization mode : in case of maximization of var , the opposite of var is minimized
if(sense==LinearSolver::MINIMIZE)
mylinearsolver->setVarObj(var, 1.0);
else
mylinearsolver->setVarObj(var, -1.0);
// mylinearsolver->writeFile("coucou.lp");
// system("cat coucou.lp");
LinearSolver::Status_Sol stat = mylinearsolver->solve();
// cout << " stat solver " << stat << endl;
if(stat == LinearSolver::OPTIMAL) {
if( ((sense==LinearSolver::MINIMIZE) && ( mylinearsolver->getObjValue() <=bound)) ||
((sense==LinearSolver::MAXIMIZE) && ((-mylinearsolver->getObjValue())>=bound))) {
stat = LinearSolver::UNKNOWN;
}
}
// Neumaier - Shcherbina postprocessing
if(stat == LinearSolver::OPTIMAL) {
// the dual solution : used to compute the bound
Vector dual_solution(mylinearsolver->getNbRows());
LinearSolver::Status stat_dual = mylinearsolver->getDualSol(dual_solution);
Matrix A_trans (nb_var,mylinearsolver->getNbRows()) ;
LinearSolver::Status stat_A = mylinearsolver->getCoefConstraint_trans(A_trans);
/* IntervalMatrix IA_trans (nb_var,mylinearsolver->getNbRows());
for (int i=0;i<nvar; i++){
for(int j=0; j<nctr; j++)
IA_trans[i][j]= A_trans[i][j];
}*/
IntervalVector B(mylinearsolver->getNbRows());
LinearSolver::Status stat_B = mylinearsolver->getB(B);
bool minimization=false;
if (sense==LinearSolver::MINIMIZE)
minimization=true;
// cout << "B " << B << endl;
// cout << "A_trans " << IA_trans << endl;
if ((stat_dual==LinearSolver::OK) && (stat_A==LinearSolver::OK) && (stat_B==LinearSolver::OK))
NeumaierShcherbina_postprocessing( mylinearsolver->getNbRows(), var, obj, box, A_trans, B, dual_solution, minimization);
else
stat = LinearSolver::UNKNOWN;
}
// infeasibility test cf Neumaier Shcherbina paper
if(stat == LinearSolver::INFEASIBLE_NOTPROVED) {
Vector infeasible_dir(mylinearsolver->getNbRows());
LinearSolver::Status stat1 = mylinearsolver->getInfeasibleDir(infeasible_dir);
Matrix A_trans (nb_var,mylinearsolver->getNbRows()) ;
LinearSolver::Status stat2 = mylinearsolver->getCoefConstraint_trans(A_trans);
IntervalVector B(mylinearsolver->getNbRows());
LinearSolver::Status stat3 = mylinearsolver->getB(B);
if ((stat1==LinearSolver::OK) && (stat2==LinearSolver::OK) && (stat3==LinearSolver::OK) &&
(NeumaierShcherbina_infeasibilitytest (mylinearsolver->getNbRows(), box, A_trans, B, infeasible_dir))) {
stat = LinearSolver::INFEASIBLE;
}
}
// Reset the objective of the LP solver
mylinearsolver->setVarObj(var, 0.0);
return stat;
}
