double pztgeom(double x, double prob, int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(prob))
return x + prob;
#endif
if (prob <= 0 || prob > 1) return R_NaN;
if (x < 1) return ACT_DT_0;
if (!R_FINITE(x)) return ACT_DT_1;
/* limiting case as prob approaches one is point mass at one */
if (prob == 1) return (x >= 1) ? ACT_DT_1 : ACT_DT_0;
return ACT_DT_Cval(pgeom(x - 1, prob, /*l._t.*/0, /*log_p*/0));
}
int main(int argc, char** argv)
{
int ppw=20; // Point per wavelength
std::string filename="ellipsecavitynormcond10.txt";
std::vector<double> freqs;
freqs.push_back(9.9771201566136298);
freqs.push_back(28.807002784875433);
freqs.push_back(60.218097688523919);
freqs.push_back(91.632551202864647);
std::vector<double> norm_sl(freqs.size());
std::vector<double> norm_dl(freqs.size());
std::vector<double> norm_combined1(freqs.size());
std::vector<double> norm_combined2(freqs.size());
std::vector<double> cond_sl(freqs.size());
std::vector<double> cond_dl(freqs.size());
std::vector<double> cond_combined1(freqs.size());
std::vector<double> cond_combined2(freqs.size());
clock_t start, finish;
double time;
start=clock();
#ifdef BEM2DMPI
MPI_Init(&argc, &argv);
int nprow=4; // Number of rows in process grid
int npcol=2; // Number of columns in process grid
int mb=24; // Row Block size
int nb=24; // Column Block size
bem2d::BlacsSystem* b=bem2d::BlacsSystem::Initialize(nprow,npcol,mb,nb);
// Exit if Context could not be created or process does not belong to context
if (!b) {
std::cout << "Could not create Blacs context" << std::endl;
MPI_Finalize();
exit(1);
}
if ((b->get_myrow()==-1)&&(b->get_mycol()==-1)) {
MPI_Finalize();
exit(0);
}
#endif
for (int j=0;j<freqs.size();j++){
int n=10;
double a= 1;
double ah=1.3;
double b=0.5;
double bh=0.6;
double t0=0.3*bem2d::PI;
double t1=acos(-a/ah*cos(t0));
double alpha=bh*sin(t1)-b*sin(t0);
//bem2d::freqtype k={n*bem2d::PI/2/b,0};
bem2d::freqtype k={freqs[j],0};
double eta1=k.re; // Coupling between conj. double and single layer pot.
double eta2=cbrt(k.re*k.re);
bem2d::Point p0(-a*cos(t0),b*sin(t0));
bem2d::Point p1(-a*cos(t0),alpha+b*sin(t0));
bem2d::Point p2(-a*cos(t0),-alpha-b*sin(t0));
bem2d::Point p3(-a*cos(t0),-b*sin(t0));
bem2d::pCurve cobj(new bem2d::Circle);
bem2d::AnalyticCurve circle(n,cobj);
int L=0;
bem2d::pCurve Arc(new bem2d::EllipseArc(a,b,bem2d::PI-t0,-bem2d::PI+t0));
bem2d::AnalyticCurve ellipseArc(ppw,k,Arc,0,L);
bem2d::pCurve Arc2(new bem2d::EllipseArc(ah,bh,-t1,t1));
bem2d::AnalyticCurve ellipseArc2(ppw,k,Arc2,0,L);
bem2d::Line l0(p1,p0,ppw,k,L);
bem2d::Line l1(p3,p2,ppw,k,L);
std::vector<bem2d::pGeometry> geoms;
geoms.push_back(ellipseArc2.GetGeometry());
geoms.push_back(l0.GetGeometry());
geoms.push_back(ellipseArc.GetGeometry());
geoms.push_back(l1.GetGeometry());
bem2d::pGeometry pgeom(new bem2d::Geometry(geoms));
bem2d::PolBasis::AddBasis(0,pgeom); // Add constant basis functions
// Discretize the single and double layer potential
bem2d::SingleLayer sl(k);
bem2d::ConjDoubleLayer cdl(k);
bem2d::DoubleLayer dl(k);
bem2d::QuadOption quadopts;
quadopts.L=5;
quadopts.N=5;
quadopts.sigma=0.15;
#ifdef BEM2DMPI
if (b->IsRoot()){
std::cout << "Discretize Kernels with n=" << pgeom->size() << std::endl;
}
#else
std::cout << "Discretize Kernels with n=" << pgeom->size() << std::endl;
#endif
bem2d::Matrix dsl=*(DiscreteKernel(*pgeom,quadopts,sl));
bem2d::Matrix ddl=(*DiscreteKernel(*pgeom,quadopts,dl));
bem2d::Matrix dcdl=*(DiscreteKernel(*pgeom,quadopts,cdl));
bem2d::Matrix Id=*(EvalIdent(*pgeom, quadopts));
bem2d::Matrix combined1=Id+2.0*dcdl-bem2d::complex(0,2.0)*eta1*dsl;
bem2d::Matrix combined2=Id+2.0*dcdl-bem2d::complex(0,2.0)*eta2*dsl;
dsl=2.0*bem2d::ChangeBasis(dsl,Id);
ddl=2.0*bem2d::ChangeBasis(ddl,Id);
dcdl=2.0*bem2d::ChangeBasis(dcdl,Id);
combined1=bem2d::ChangeBasis(combined1,Id);
combined2=bem2d::ChangeBasis(combined2,Id);
#ifdef BEM2DMPI
if (b->IsRoot()){
std::cout << "Compute norms and condition numbers" << std::endl;
}
#else
std::cout << "Compute norms and condition numbers" << std::endl;
#endif
bem2d::L2NormCond(dsl,norm_sl[j],cond_sl[j]);
bem2d::L2NormCond(ddl,norm_dl[j],cond_dl[j]);
bem2d::L2NormCond(combined1,norm_combined1[j],cond_combined1[j]);
bem2d::L2NormCond(combined2,norm_combined2[j],cond_combined2[j]);
//bem2d::WriteMatrix("cavity_matrix2", combined1);
}
finish=clock();
time=(double(finish)-double(start))/CLOCKS_PER_SEC/60;
#ifdef BEM2DMPI
if (b->IsRoot()){
#endif
std::ofstream out(filename.c_str());
out << "Single Layer" << std::endl;
for (int j=0;j<freqs.size();j++){
out << "k=" << freqs[j] << " Norm: " << norm_sl[j] << " Norm of Inverse: " << cond_sl[j]/norm_sl[j] << " Condition Nr.: " << cond_sl[j] << std::endl;
}
out << "Double Layer" << std::endl;
for (int j=0;j<freqs.size();j++){
out << "k=" << freqs[j] << " Norm: " << norm_dl[j] << " Norm of Inverse: " << cond_dl[j]/norm_dl[j] << " Condition Nr.: " << cond_dl[j] << std::endl;
}
out << "Combined Layer eta=k" << std::endl;
for (int j=0;j<freqs.size();j++){
out << "k=" << freqs[j] << " Norm: " << norm_combined1[j] << " Norm of Inverse: " << cond_combined1[j]/norm_combined1[j] << " Condition Nr.: " << cond_combined1[j] << std::endl;
}
out << "Combined Layer eta=k^(2/3)" << std::endl;
for (int j=0;j<freqs.size();j++){
out << "k=" << freqs[j] << " Norm: " << norm_combined2[j] << " Norm of Inverse: " << cond_combined2[j]/norm_combined2[j] << " Condition Nr.: " << cond_combined2[j] << std::endl;
}
out << "Overalll time (minutes): " << time << std::endl;
std::cout << "Overall time (minutes): " << time << std::endl;
out.close();
#ifdef BEM2DMPI
}
#endif
#ifdef BEM2DMPI
bem2d::BlacsSystem::Release();
MPI_Finalize();
#endif
}
