/* Extend an initial (under-)approximation of the affine hull of basic
* set represented by the tableau "tab"
* by looking for points that do not satisfy one of the equalities
* in the current approximation and adding them to that approximation
* until no such points can be found any more.
*
* The caller of this function ensures that "tab" is bounded or
* that tab->basis and tab->n_unbounded have been set appropriately.
*/
static struct isl_basic_set *extend_affine_hull(struct isl_tab *tab,
struct isl_basic_set *hull)
{
int i, j;
unsigned dim;
if (!tab || !hull)
goto error;
dim = tab->n_var;
if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
goto error;
for (i = 0; i < dim; ++i) {
struct isl_vec *sample;
struct isl_basic_set *point;
for (j = 0; j < hull->n_eq; ++j) {
sample = outside_point(tab, hull->eq[j], 1);
if (!sample)
goto error;
if (sample->size > 0)
break;
isl_vec_free(sample);
sample = outside_point(tab, hull->eq[j], 0);
if (!sample)
goto error;
if (sample->size > 0)
break;
isl_vec_free(sample);
if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
goto error;
}
if (j == hull->n_eq)
break;
if (tab->samples)
tab = isl_tab_add_sample(tab, isl_vec_copy(sample));
if (!tab)
goto error;
point = isl_basic_set_from_vec(sample);
hull = affine_hull(hull, point);
if (!hull)
return NULL;
}
return hull;
error:
isl_basic_set_free(hull);
return NULL;
}
int main(int argc, char **argv)
{
int numPanels= 1000, recursions = 4, p = 5, k = 3, max_iterations = 500;
FMMOptions opts = get_options(argc,argv);
opts.sparse_local = true;
SolverOptions solver_options;
bool second_kind = false;
char *mesh_name;
bool mesh = false;
// solve / PC settings
SOLVERS solver = SOLVE_GMRES;
PRECONDITIONERS pc = IDENTITY;
// use lazy evaluator by default
// opts.lazy_evaluation = true;
// parse command line args
// check if no arguments given
printf("\nLaplaceBEM on a sphere\n");
if (argc == 1) printHelpAndExit();
printf("parameters : \n");
printf("============ \n");
for (int i = 1; i < argc; ++i) {
if (strcmp(argv[i],"-theta") == 0) {
i++;
printf("theta = %s\n", argv[i]);
} else if (strcmp(argv[i],"-recursions") == 0) {
i++;
recursions = atoi(argv[i]);
// print out problem size based on the # of recursions
printf("N = %i\n", 2* (int) pow(4, recursions));
} else if (strcmp(argv[i],"-eval") == 0) {
i++;
} else if (strcmp(argv[i], "-ncrit") == 0) {
i++;
printf("ncrit = %s\n", argv[i]);
} else if (strcmp(argv[i], "-printtree") == 0) {
} else if (strcmp(argv[i],"-p") == 0) {
i++;
p = atoi(argv[i]);
solver_options.max_p = p;
printf("max-p = %i\n", p);
} else if (strcmp(argv[i],"-k") == 0) {
i++;
k = atoi(argv[i]);
} else if (strcmp(argv[i],"-second_kind") == 0) {
second_kind = true;
printf("second-kind = True\n");
} else if (strcmp(argv[i],"-fixed_p") == 0) {
solver_options.variable_p = false;
printf("relaxed = False\n");
} else if (strcmp(argv[i],"-solver_tol") == 0) {
i++;
solver_options.residual = (double)atof(argv[i]);
printf("solver_tol = %.2e\n", solver_options.residual);
} else if (strcmp(argv[i],"-max_iters") == 0) {
i++;
max_iterations = atoi(argv[i]);
} else if (strcmp(argv[i],"-gmres") == 0) {
solver = SOLVE_GMRES;
} else if (strcmp(argv[i],"-fgmres") == 0) {
solver = SOLVE_FGMRES;
} else if (strcmp(argv[i],"-local") == 0) {
solver = SOLVE_FGMRES;
pc = LOCAL;
} else if (strcmp(argv[i],"-diagonal") == 0) {
pc = DIAGONAL;
} else if (strcmp(argv[i],"-help") == 0) {
printHelpAndExit();
} else if (strcmp(argv[i],"-mesh") == 0) {
i++;
mesh_name = argv[i];
mesh = true;
}
else {
printf("[W]: Unknown command line arg: \"%s\"\n",argv[i]);
printHelpAndExit();
}
}
printf("============\n");
solver_options.max_iters = max_iterations;
solver_options.restart = max_iterations;
// opts.sparse_local = true;
double tic, toc;
// Init the FMM Kernel
typedef LaplaceSphericalBEM kernel_type;
kernel_type K(p,k);
// useful typedefs
typedef kernel_type::point_type point_type;
typedef kernel_type::source_type source_type;
typedef kernel_type::target_type target_type;
typedef kernel_type::charge_type charge_type;
typedef kernel_type::result_type result_type;
// Init points and charges
std::vector<source_type> panels(numPanels);
std::vector<charge_type> charges(numPanels);
if (mesh) {
printf("reading mesh from: %s\n",mesh_name);
MeshIO::readMsh<point_type,source_type>(mesh_name, panels); // , panels);
} else {
Triangulation::UnitSphere(panels, recursions);
// initialiseSphere(panels, charges, recursions); //, ProblemOptions());
}
// run case solving for Phi (instead of dPhi/dn)
if (second_kind)
for (auto& it : panels) it.switch_BC();
// set constant Phi || dPhi/dn for each panel
charges.resize(panels.size());
// set up a more complicated charge, from BEM++
for (unsigned i=0; i<panels.size(); i++) {
#if BEMCPP_TEST
auto center = panels[i].center;
double x = center[0], y = center[1], z = center[2];
double r = norm(center);
charges[i] = 2*x*z/(r*r*r*r*r) - y/(r*r*r);
#else
charges[i] = 1.;
#endif
}
// charges = std::vector<charge_type>(panels.size(),1.);
// Build the FMM structure
FMM_plan<kernel_type> plan = FMM_plan<kernel_type>(K, panels, opts);
// generate the RHS and initial condition
std::vector<charge_type> x(panels.size(),0.);
tic = get_time();
std::vector<result_type> b(panels.size(),0.);
double tic2, toc2;
// generate RHS using temporary FMM plan
{
tic2 = get_time();
for (auto& it : panels) it.switch_BC();
toc2 = get_time();
printf("Flipping BC: %g\n",toc2-tic2);
tic2 = get_time();
FMM_plan<kernel_type> rhs_plan = FMM_plan<kernel_type>(K,panels,opts);
toc2 = get_time();
printf("Creating plan: %g\n",toc2-tic2);
tic2 = get_time();
b = rhs_plan.execute(charges);
toc2 = get_time();
printf("Executing plan: %g\n",toc2-tic2);
for (auto& it : panels) it.switch_BC();
}
toc = get_time();
double setup_time = toc-tic;
// Solve the system using GMRES
// generate the Preconditioner
tic = get_time();
Preconditioners::Diagonal<charge_type> M(K,
plan.source_begin(),
plan.source_end()
);
// M.print();
SolverOptions inner_options(1e-2,1,2);
inner_options.variable_p = true;
/*
// Preconditioners::FMGMRES<FMM_plan<kernel_type>,Preconditioners::Diagonal<charge_type>> inner(plan, b, inner_options, M);
// Local preconditioner
Preconditioners::LocalInnerSolver<FMM_plan<kernel_type>, Preconditioners::Diagonal<result_type>> local(K, panels, b);
// block diagonal preconditioner
Preconditioners::BlockDiagonal<FMM_plan<kernel_type>> block_diag(K,panels);
*/
// Initial low accuracy solve
//
/*
double tic2, toc2;
tic2 = get_time();
{
printf("Initial solve starting..\n");
// initial solve to 1e-2 accuracy, 5 iterations, P = 2
SolverOptions initial_solve(5e-3,50,3);
// fmm_gmres(plan, x, b, solver_options, M);
GMRES(plan, x, b, initial_solve, M);
printf("Initial solve finished..\n");
}
toc2 = get_time();
printf("Initial solve took: %.4es\n",toc2-tic2);
*/
// Outer GMRES solve with diagonal preconditioner & relaxation
FGMRESContext<result_type> context(x.size(), solver_options.restart);
if (second_kind) printf("2nd-kind equation being solved\n");
else printf("1st-kind equation being solved\n");
#if 1
if (solver == SOLVE_GMRES && pc == IDENTITY){
printf("Solver: GMRES\nPreconditioner: Identity\n");
// straight GMRES, no preconditioner
// DirectMV<kernel_type> MV(K, panels, panels);
GMRES(plan,x,b,solver_options);
}
else if (solver == SOLVE_GMRES && pc == DIAGONAL) {
printf("Solver: GMRES\nPreconditioner: Diagonal\n");
// GMRES, diagonal preconditioner
GMRES(plan, x, b, solver_options, M, context);
}
#else
else if (solver == SOLVE_GMRES && pc == DIAGONAL) {
printf("Solver: GMRES\nPreconditioner: Diagonal\n");
// GMRES, diagonal preconditioner
GMRES(plan,x,b,solver_options, M, context);
}
else if (solver == SOLVE_FGMRES && pc == IDENTITY) {
printf("Solver: FMRES\nPreconditioner: Identity\n");
// GMRES, diagonal preconditioner
FGMRES(plan,x,b,solver_options);
}
else if (solver == SOLVE_FGMRES && pc == DIAGONAL) {
printf("Solver: FGMRES\nPreconditioner: Block Diagonal\n");
// GMRES, diagonal preconditioner
FGMRES(plan,x,b,solver_options, block_diag, context);
}
else if (solver == SOLVE_FGMRES && pc == LOCAL) {
printf("Solver: FGMRES\nPreconditioner: Local solve\n");
// FGMRES, Local inner solver
FGMRES(plan,x,b,solver_options, local, context);
}
else {
printf("[E] no valid solver / preconditioner option chosen\n");
exit(0);
}
#endif
// GMRES(MV,x,b,solver_options, M, context);
// FGMRES(plan,x,b,solver_options, inner, context); // , context);
// Outer/Inner FGMRES / GMRES (Diagonal)
toc = get_time();
double solve_time = toc-tic;
printf("\nTIMING:\n");
printf("\tsetup : %.4es\n",setup_time);
printf("\tsolve : %.4es\n",solve_time);
// check errors -- analytical solution for dPhi/dn = 1.
double e = 0.;
double e2 = 0.;
#if BEMCPP_TEST
std::vector<result_type> analytical(panels.size());
for (unsigned i=0; i<panels.size(); i++) {
auto center = panels[i].center;
double x = center[0], y = center[1], z = center[2];
double r = norm(center);
analytical[i] = -(-6 * x * z / (r*r*r*r*r*r) + 2 * y / (r*r*r*r));
}
auto ai = analytical.begin();
for (auto xi : x) {
// printf("approx: %.4g, analytical: %.4g\n",xi,*ai);
e += (xi-*ai)*(xi-*ai);
e2 += (*ai)*(*ai);
++ai;
}
#else
double an = 1.;
for (auto xi : x) { e += (xi-an)*(xi-an); e2 += an*an; }
#endif
#define EXTERNAL_ERROR
#ifdef EXTERNAL_ERROR
std::vector<target_type> outside_point(1);
outside_point[0] = target_type(point_type(3.,3.,3.),point_type(3.,3.,3.),point_type(3.,3.,3.));
outside_point[0].center = point_type(3.,3.,3.);
std::vector<result_type> outside_result_1(1);
std::vector<result_type> outside_result_2(1);
outside_result_1[0] = 0.;
outside_result_2[0] = 0.;
// first layer
Direct::matvec(K, panels.begin(), panels.end(), x.begin(), outside_point.begin(), outside_point.end(), outside_result_2.begin());
// for (auto& pi : panels) pi.switch_BC();
for (auto& op : outside_point) op.switch_BC();
Direct::matvec(K, panels.begin(), panels.end(), charges.begin(), outside_point.begin(), outside_point.end(), outside_result_1.begin());
double exact = 1. / norm(static_cast<point_type>(outside_point[0])) * 1;
double outside_result = (outside_result_2[0]-outside_result_1[0])/4/M_PI;
double outside_error = fabs(outside_result-exact)/fabs(exact);
printf("external phi: %.5g, exact: %.5g, error: %.4e\n",outside_result,exact, outside_error);
#endif
printf("relative error: %.3e\n",sqrt(e/e2));
}
void NavigationPolygon::make_polygons_from_outlines() {
List<TriangulatorPoly> in_poly,out_poly;
Vector2 outside_point(-1e10,-1e10);
for(int i=0; i<outlines.size(); i++) {
DVector<Vector2> ol = outlines[i];
int olsize = ol.size();
if (olsize<3)
continue;
DVector<Vector2>::Read r=ol.read();
for(int j=0; j<olsize; j++) {
outside_point.x = MAX( r[j].x, outside_point.x );
outside_point.y = MAX( r[j].y, outside_point.y );
}
}
outside_point+=Vector2(0.7239784,0.819238); //avoid precision issues
for(int i=0; i<outlines.size(); i++) {
DVector<Vector2> ol = outlines[i];
int olsize = ol.size();
if (olsize<3)
continue;
DVector<Vector2>::Read r=ol.read();
int interscount=0;
//test if this is an outer outline
for(int k=0; k<outlines.size(); k++) {
if (i==k)
continue; //no self intersect
DVector<Vector2> ol2 = outlines[k];
int olsize2 = ol2.size();
if (olsize2<3)
continue;
DVector<Vector2>::Read r2=ol2.read();
for(int l=0; l<olsize2; l++) {
if (Geometry::segment_intersects_segment_2d(r[0],outside_point,r2[l],r2[(l+1)%olsize2],NULL)) {
interscount++;
}
}
}
bool outer = (interscount%2)==0;
TriangulatorPoly tp;
tp.Init(olsize);
for(int j=0; j<olsize; j++) {
tp[j]=r[j];
}
if (outer)
tp.SetOrientation(TRIANGULATOR_CCW);
else {
tp.SetOrientation(TRIANGULATOR_CW);
tp.SetHole(true);
}
in_poly.push_back(tp);
}
TriangulatorPartition tpart;
if (tpart.ConvexPartition_HM(&in_poly,&out_poly)==0) { //failed!
print_line("convex partition failed!");
return;
}
polygons.clear();
vertices.resize(0);
Map<Vector2,int> points;
for(List<TriangulatorPoly>::Element*I = out_poly.front(); I; I=I->next()) {
TriangulatorPoly& tp = I->get();
struct Polygon p;
for(int i=0; i<tp.GetNumPoints(); i++) {
Map<Vector2,int>::Element *E=points.find(tp[i]);
if (!E) {
E=points.insert(tp[i],vertices.size());
vertices.push_back(tp[i]);
}
p.indices.push_back(E->get());
}
polygons.push_back(p);
}
emit_signal(CoreStringNames::get_singleton()->changed);
}