void generate_minop_mesh(TriMesh & mesh,
const string & filename,
double edge_length){
double angle = 0.125;
cout << "Initial meshing..."<< endl;
mesh.build_box_boundary({{-1.1,1.1},{-1.1,1.1}});
mesh.build_circle(zeros<vec>(2),50,1.0);
mesh.build_circle(zeros<vec>(2),30,1.0/sqrt(2.0));
mesh.build_circle(zeros<vec>(2),25,0.25);
cout << "Refining based on (" << angle
<< "," << edge_length << ") criterion ..."<< endl;
mesh.refine(angle,edge_length);
//cout << "Optimizing (25 rounds of Lloyd)..."<< endl;
//mesh.lloyd(15);
mesh.freeze();
// Write initial mesh to file
cout << "Writing:"
<< "\n\t" << (filename + ".node") << " (Shewchuk node file)"
<< "\n\t" << (filename + ".ele") << " (Shewchuk element file)"
<< "\n\t" << (filename + ".tri") << " (CGAL mesh file)" << endl;
mesh.write_shewchuk(filename);
mesh.write_cgal(filename + ".tri");
}
////////////////////////////////////////////////////////////
// MAIN FUNCTION ///////////////////////////////////////////
////////////////////////////////////////////////////////////
int main(int argc, char** argv)
{
po::variables_map var_map = read_command_line(argc,argv);
arma_rng::set_seed_random();
// Read in the CGAL mesh
TriMesh mesh;
string file_base = var_map["outfile_base"].as<string>();
double edge_length = var_map["edge_length"].as<double>();
generate_minop_mesh(mesh,file_base,edge_length);
mesh.freeze();
// Stats
uint N = mesh.number_of_vertices();
uint F = mesh.number_of_faces();
cout << "Mesh stats:"
<< "\n\tNumber of vertices: " << N
<< "\n\tNumber of faces: " << F
<< endl;
// Build value basis
uint num_value_basis = 25;
uint num_flow_basis = 10;
Points points = mesh.get_spatial_nodes();
cout << "Generating Radial Fourier basis for value..." << endl;
mat value_basis = make_radial_fourier_basis(points,
num_value_basis,
(double)num_value_basis);
cout << "\tOrthogonalizing..." << endl;
value_basis = orth(value_basis);
cout << "Generating Voronoi basis for flow..." << endl;
sp_mat sp_value_basis = sp_mat(value_basis);
Points centers = 2 * randu(10,2) - 1;
mat flow_basis = make_voronoi_basis(points,
centers);
cout << "\tOrthogonalizing..." << endl;
flow_basis = orth(flow_basis);
sp_mat sp_flow_basis = sp_mat(flow_basis);
cout << "Building LCP..." << endl;
vec ref_weights = ones<vec>(N) / (double)N;
LCP ref_lcp;
vec ans;
build_minop_lcp(mesh,ref_weights,ref_lcp,ans);
assert(N == ans.n_elem);
cout << "Building PLCP..." << endl;
block_sp_vec D = {sp_value_basis,
sp_flow_basis,
sp_flow_basis};
sp_mat P = block_diag(D);
double regularizer = 1e-12;
sp_mat U = P.t() * (ref_lcp.M + regularizer*speye(size(ref_lcp.M)));
vec q = P *(P.t() * ref_lcp.q);
assert(3*N == P.n_rows);
assert(3*N == q.n_rows);
bvec free_vars = zeros<bvec>(3*N);
free_vars.head(N).fill(1);
PLCP ref_plcp = PLCP(P,U,q,free_vars);
ref_plcp.write(file_base + ".plcp");
ProjectiveSolver psolver;
psolver.comp_thresh = 1e-12;
psolver.max_iter = 250;
psolver.aug_rel_scale = 5;
psolver.verbose = false;
psolver.initial_sigma = 0.3;
cout << "Starting reference solve..." << endl;
SolverResult ref_sol = psolver.aug_solve(ref_plcp);
cout << "\tDone." << endl;
cout << "Reference solution error: "
<< norm(ans - ref_sol.p.head(N)) << endl;
assert(ALMOST_ZERO > norm(ref_sol.d.head(N))); // Essentially zero
ref_sol.write(file_base + ".sol");
psolver.comp_thresh = 1e-8;
// Exactish
vec twiddle = vec(N);
for(uint i = 0; i < N; i++){
cout << "Component: " << i << endl;
LCP twiddle_lcp;
vec et = zeros<vec>(N);
et(i) += 1.0 / (double) N;
assert(size(ref_weights) == size(et));
build_minop_lcp(mesh,ref_weights + et,twiddle_lcp,ans);
vec twiddle_q = P *(P.t() * twiddle_lcp.q);
PLCP twiddle_plcp = PLCP(P,U,twiddle_q,free_vars);
SolverResult twiddle_sol = psolver.aug_solve(twiddle_plcp);
twiddle(i) = twiddle_sol.p(i) - ref_sol.p(i);
}
uint R = 75;
mat jitter = mat(N,R);
mat noise = mat(N,R);
for(uint i = 0; i < R; i++){
cout << "Jitter round: " << i << endl;
LCP jitter_lcp;
noise.col(i) = max(1e-4*ones<vec>(N), 0.075 * randn<vec>(N));
build_minop_lcp(mesh,ref_weights + noise.col(i),jitter_lcp,ans);
vec jitter_q = P *(P.t() * jitter_lcp.q);
PLCP jitter_plcp = PLCP(P,U,jitter_q,free_vars);
SolverResult jitter_sol = psolver.aug_solve(jitter_plcp);
jitter.col(i) = (jitter_sol.p.head(N) - ref_sol.p.head(N));
}
Archiver arch;
arch.add_vec("p",ref_sol.p.head(N));
arch.add_vec("twiddle",twiddle);
arch.add_mat("jitter",jitter);
arch.add_mat("noise",noise);
arch.add_sp_mat("flow_basis",sp_flow_basis);
arch.write(file_base + ".exp_res");
}
int main(int argc, char** argv)
{
po::variables_map var_map = read_command_line(argc,argv);
string mesh_file = var_map["infile_base"].as<string>() + ".tri";
// Read in the CGAL mesh
TriMesh mesh;
cout << "Reading in cgal mesh file [" << mesh_file << ']' << endl;
mesh.read_cgal(mesh_file);
mesh.freeze();
uint V = mesh.number_of_vertices();
uint N = mesh.number_of_all_nodes();
assert(N == V+1);
uint F = mesh.number_of_faces();
cout << "Mesh stats:"
<< "\n\tNumber of vertices: " << V
<< "\n\tNumber of faces: " << F
<< endl;
Points centers = mesh.get_cell_centers();
// Find boundary from the mesh and create the simulator object
mat bbox = mesh.find_bounding_box();
vec lb = bbox.col(0);
vec ub = bbox.col(1);
cout << "\tLower bound:" << lb.t()
<< "\tUpper bound:" << ub.t();
// Read in solution information
string soln_file = var_map["infile_base"].as<string>() + ".sol";
cout << "Reading in LCP solution file [" << soln_file << ']' << endl;
Unarchiver sol_unarch(soln_file);
vec p = sol_unarch.load_vec("p");
string lcp_file = var_map["infile_base"].as<string>() + ".lcp";
Unarchiver lcp_unarch(lcp_file);
vec q = lcp_unarch.load_vec("q");
Archiver arch;
// Make sure that the primal information makes sense
assert(0 == p.n_elem % V);
uint A = p.n_elem / V;
assert(A == 3);
cout << "Blocking primal solution..."
<< "\n\tLength of primal solution: " << p.n_elem
<< "\n\tRatio of primal length to vertex number: " << A << endl;
mat P = reshape(p,size(V,A));
P = join_vert(P,datum::inf * ones<rowvec>(3)); // Pad
vec value = P.col(0);
mat flows = P.tail_cols(2);
mat Q = reshape(q,size(V,A));
Q = join_vert(Q,datum::inf * ones<rowvec>(3)); // Pad
vec recon_b = mesh.interpolate(centers,
conv_to<vec>::from(Q.col(1)));
vec recon_c = mesh.interpolate(centers,
conv_to<vec>::from(Q.col(2)));
arch.add_vec("recon_b",recon_b);
arch.add_vec("recon_c",recon_c);
vec area = mesh.cell_area();
arch.add_vec("area",area);
// True values
vec sq_dist = sum(pow(centers,2),1);
vec b = sq_dist;
vec c = max(zeros<vec>(F),1 - sq_dist);
vec x = arma::min(b,c);
assert(all(x >= 0));
assert(F == x.n_elem);
uvec pi = arma::index_min(join_horiz(b,c),1);
assert(F == pi.n_elem);
arch.add_uvec("pi",pi);
// Approx policy
assert(2 == flows.n_cols);
mat interp_flows = mesh.interpolate(centers,flows);
uvec flow_pi = arma::index_max(interp_flows,1);
arch.add_uvec("flow_pi",flow_pi);
assert(F == flow_pi.n_elem);
uvec diff = zeros<uvec>(F);
diff(find(flow_pi != pi)).fill(1);
arch.add_uvec("policy_diff",diff);
// Approx value
vec interp_value = mesh.interpolate(centers,value);
assert(F == interp_value.n_elem);
vec res = abs(x - interp_value);
arch.add_vec("residual",res);
vec heuristic = res;
heuristic(find(flow_pi != pi)) *= 4;
arch.add_vec("heuristic",heuristic);
double quant = 0.9;
cout << "Quantile:" << quant << endl;
double cutoff = quantile(heuristic,quant);
cout << "\t Cutoff: " << cutoff
<< "\n\t Max:" << max(heuristic)
<< "\n\t Min:" << min(heuristic) << endl;
// Split the cells if they have a large heuristic_1 or
// policies disagree on them.
TriMesh new_mesh(mesh);
Point center;
uint new_nodes = 0;
for(uint f = 0; f < F; f++){
if(area(f) < 2e-4){
continue;
}
if(new_nodes > 200) break;
if(heuristic(f) > cutoff){
center = convert(mesh.center_of_face(f));
new_mesh.insert(center);
new_nodes++;
}
}
cout << "Added " << new_nodes << " new nodes..." << endl;
cout << "Refining..." << endl;
new_mesh.refine(0.125,1.0);
new_mesh.lloyd(10);
//new_mesh.insert(Point(0,0));
new_mesh.freeze();
// Write out all the information
string out_file_base = var_map["outfile_base"].as<string>();
arch.write(out_file_base + ".stats");
cout << "Writing..."
<< "\n\tCGAL mesh file: " << out_file_base << ".tri"
<< "\n\tShewchuk node file: " << out_file_base << ".node"
<< "\n\tShewchuk ele file: " << out_file_base << ".ele" << endl;
new_mesh.write_cgal(out_file_base + ".tri");
new_mesh.write_shewchuk(out_file_base);
}
