void Triangles::BoundAnisotropy(Real8 anisomax)
{
if (verbosity > 1)
cout << " -- BoundAnisotropy by " << anisomax << endl;
Real8 h1=1.e30,h2=1e-30,rx=0;
Real8 coef = 1./(anisomax*anisomax);
Real8 hn1=1.e30,hn2=1e-30,rnx =1.e-30;
for (Int4 i=0;i<nbv;i++)
{
MatVVP2x2 Vp(vertices[i]);
h1=Min(h1,Vp.lmin());
h2=Max(h2,Vp.lmax());
rx = Max(rx,Vp.Aniso2());
Vp.BoundAniso2(coef);
hn1=Min(hn1,Vp.lmin());
hn2=Max(hn2,Vp.lmax());
rnx = Max(rnx,Vp.Aniso2());
vertices[i].m = Vp;
}
if (verbosity>2)
{
cout << " input : Hmin = " << sqrt(1/h2) << " Hmax = " << sqrt(1/h1)
<< " factor of anisotropy max = " << sqrt(rx) << endl;
cout << " output: Hmin = " << sqrt(1/hn2) << " Hmax = " << sqrt(1/hn1)
<< " factor of anisotropy max = " << sqrt(rnx) << endl;
}
}
Real Generalized_HullWhite::discountBondOption(Option::Type type, Real strike,
Time maturity,
Time bondMaturity) const {
Real _a = a();
Real v;
v = std::sqrt(Vp(0, maturity, bondMaturity));
Real f = termStructure()->discount(bondMaturity);
Real k = termStructure()->discount(maturity)*strike;
return blackFormula(type, k, f, v);
}
void Triangles::IntersectGeomMetric(const Real8 err=1,const int iso=0)
{
if(verbosity>1)
cout << " -- IntersectGeomMetric geometric err=" << err << (iso ? " iso " : " aniso " ) << endl;
Real8 ss[2]={0.00001,0.99999};
Real8 errC = 2*sqrt(2*err);
Real8 hmax = Gh.MaximalHmax();
Real8 hmin = Gh.MinimalHmin();
Real8 maxaniso = 1e6;
assert(hmax>0);
SetVertexFieldOn();
if (errC > 1) errC = 1;
for (Int4 i=0;i<nbe;i++)
for (int j=0;j<2;j++)
{
Vertex V;
VertexOnGeom GV;
// cerr << Number(edges[i]) << " " << ss[j] << endl;
Gh.ProjectOnCurve(edges[i],ss[j],V,GV);
{
GeometricalEdge * eg = GV;
Real8 s = GV;
R2 tg;
// cerr << i << " " << j << " " << Number(V) << " on = "
// << Gh.Number(eg) << " at s = " << s << " " << endl;
Real8 R1= eg->R1tg(s,tg);
// cerr << " R = " << 1/Max(R1,1e-20) << tg << " on x "
// << V.r << errC/ Max(R1,1e-20) << " hold=" <<V.m(tg) << " " << endl;
Real8 ht = hmax;
if (R1>1.0e-20)
{ // err relative to the length of the edge
ht = Min(Max(errC/R1,hmin),hmax);
}
Real8 hn = iso? ht : Min(hmax,ht*maxaniso);
//cerr << ht << " " << hn << "m=" << edges[i][j].m << endl;
assert(ht>0 && hn>0);
MatVVP2x2 Vp(1/(ht*ht),1/(hn*hn),tg);
//cerr << " : " ;
Metric MVp(Vp);
// cerr << " : " << MVp << endl;
edges[i][j].m.IntersectWith(MVp);
//cerr << " . " << endl;
}
}
// the problem is for the vertex on vertex
}
int main(){
LHDlib::RhoTable rhoTable;
// rhoTable.read("C:\\Users\\KeisukeFujii\\Dropbox\\visual_studio\\LHDdata\\flx\\lhd-r375q100b000a8020.flx");
rhoTable.read("C:\\Users\\KeisukeFujii\\Dropbox\\visual_studio\\LHDdata\\flx\\lhd-r390q100g120b000a8020.flx");
size_t size = 100;
std::vector<double> R_10(size), Z_10(size);
std::vector<double> R_11(size), Z_11(size);
std::vector<double> R_12(size), Z_12(size);
for (size_t i = 0; i < size; ++i){
double theta = 2.0*myconst::pi / size*i;
rhoTable.getRZfromRhoThetaPhi(1.0, theta, myconst::pi/10.0, R_10[i], Z_10[i]);
rhoTable.getRZfromRhoThetaPhi(1.1, theta, myconst::pi/10.0, R_11[i], Z_11[i]);
rhoTable.getRZfromRhoThetaPhi(1.2, theta, myconst::pi/10.0, R_12[i], Z_12[i]);
}
IGORdata::write_itx(R_10, Z_10, "RZ_10.itx", "RR_10", "ZZ_10");
IGORdata::write_itx(R_11, Z_11, "RZ_11.itx", "RR_11", "ZZ_11");
IGORdata::write_itx(R_12, Z_12, "RZ_12.itx", "RR_12", "ZZ_12");
size = 48;
std::vector<double> rho(size), Vp(size), dVpdrho(size), dVdrho(size);
for (size_t i = 0; i < size; ++i){
rho[i] = 1.2 / size*i;
Vp[i] = rhoTable.get_Vp(0.0, rho[i]);
dVpdrho[i] = rhoTable.get_dVpdrho(rho[i]);
dVdrho[i] = rhoTable.get_dVdrho(rho[i]);
}
IGORdata::write_itx(rho, Vp, "rho_Vp.itx", "rho", "Vp");
IGORdata::write_itx(dVpdrho, dVdrho, "dVdrho.itx", "dVpdrho", "dVdrho");
size_t xsize = 100, ysize(101);
std::vector<double> xaxis(xsize), yaxis(ysize);
std::vector<std::vector<double>> rhoM(xsize), theta(xsize), drhodx(xsize), drhody(xsize), drhodz(xsize);
for (size_t i = 0; i < xsize; ++i)
xaxis[i] = 2.5 + 2.5 / xsize * i;
for (size_t i = 0; i < ysize; ++i)
yaxis[i] = -1.0 + 2.0 / ysize * i;
for (size_t i = 0; i < xsize; ++i){
for (size_t j = 0; j < ysize; ++j){
double rho_, theta_;
double drhodx_[3];
rhoTable.get_rho_drho(xaxis[i], yaxis[j], myconst::pi*0.1, &rho_, &theta_, drhodx_);
rhoM[i].push_back(rho_);
theta[i].push_back(theta_);
drhodx[i].push_back(drhodx_[0]);
drhody[i].push_back(drhodx_[1]);
drhodz[i].push_back(drhodx_[2]);
}
}
IGORdata::write_edgeVector(xaxis, "xaxis.itx", "xaxis");
IGORdata::write_edgeVector(yaxis, "yaxis.itx", "yaxis");
IGORdata::write_itx(rhoM, "rhoMatrix.itx", "rhoMatrix");
IGORdata::write_itx(theta, "theta.itx", "theta");
IGORdata::write_itx(drhodx, "drhodx.itx", "drhodx");
IGORdata::write_itx(drhody, "drhody.itx", "drhody");
IGORdata::write_itx(drhodz, "drhodz.itx", "drhodz");
return 0;
}
void Triangles::IntersectConsMetric(const double * s,const Int4 nbsol,const int * typsols,
const Real8 hmin1,const Real8 hmax1,const Real8 coef,
const Real8 anisomax ,const Real8 CutOff,const int NbJacobi,
const int DoNormalisation,const int choice)
{ // the array of solution s is store
// sol0,sol1,...,soln on vertex 0
// sol0,sol1,...,soln on vertex 1
// etc.
const int dim = 2;
int sizeoftype[] = { 1, dim ,dim * (dim+1) / 2, dim * dim } ;
// computation of the nb of field
Int4 ntmp = 0;
if (typsols)
{
for (Int4 i=0;i<nbsol;i++)
ntmp += sizeoftype[typsols[i]];
}
else
ntmp = nbsol;
// n is the total number of fields
const Int4 n = ntmp;
Int4 i,k,iA,iB,iC,iv;
R2 O(0,0);
int RelativeMetric = CutOff>1e-30;
Real8 hmin = Max(hmin1,MinimalHmin());
Real8 hmax = Min(hmax1,MaximalHmax());
Real8 coef2 = 1/(coef*coef);
if(verbosity>1)
{
cout << " -- Construction of Metric: Nb of sol. " << n << " nbt = "
<< nbt << " nbv= " << nbv
<< " coef = " << coef << endl
<< " hmin = " << hmin << " hmax=" << hmax
<< " anisomax = " << anisomax << " Nb Jacobi " << NbJacobi ;
if (RelativeMetric)
cout << " RelativeErr with CutOff= " << CutOff << endl;
else
cout << " Absolute Err" <<endl;
}
double *ss=(double*)s, *ssiii = ss;
double sA,sB,sC;
Real8 *detT = new Real8[nbt];
Real8 *Mmass= new Real8[nbv];
Real8 *Mmassxx= new Real8[nbv];
Real8 *dxdx= new Real8[nbv];
Real8 *dxdy= new Real8[nbv];
Real8 *dydy= new Real8[nbv];
Real8 *workT= new Real8[nbt];
Real8 *workV= new Real8[nbv];
int *OnBoundary = new int[nbv];
for (iv=0;iv<nbv;iv++)
{
Mmass[iv]=0;
OnBoundary[iv]=0;
Mmassxx[iv]=0;
}
for (i=0;i<nbt;i++)
if(triangles[i].link) // the real triangles
{
const Triangle &t=triangles[i];
// coor of 3 vertices
R2 A=t[0];
R2 B=t[1];
R2 C=t[2];
// number of the 3 vertices
iA = Number(t[0]);
iB = Number(t[1]);
iC = Number(t[2]);
Real8 dett = ::Area2(A,B,C);
detT[i]=dett;
dett /= 6;
// construction of on boundary
int nbb =0;
for(int j=0;j<3;j++)
{
Triangle *ta=t.Adj(j);
if ( ! ta || !ta->link) // no adj triangle => edge on boundary
OnBoundary[Number(t[VerticesOfTriangularEdge[j][0]])]=1,
OnBoundary[Number(t[VerticesOfTriangularEdge[j][1]])]=1,
nbb++;
}
workT[i] = nbb;
Mmass[iA] += dett;
Mmass[iB] += dett;
Mmass[iC] += dett;
if((nbb==0)|| !choice)
{
Mmassxx[iA] += dett;
Mmassxx[iB] += dett;
Mmassxx[iC] += dett;
}
}
else
workT[i]=-1;
for (Int4 kcount=0;kcount<n;kcount++,ss++)
{ //for all solution
Real8 smin=ss[0],smax=ss[0];
Real8 h1=1.e30,h2=1e-30,rx=0;
Real8 coef = 1./(anisomax*anisomax);
Real8 hn1=1.e30,hn2=1e-30,rnx =1.e-30;
for ( iv=0,k=0; iv<nbv; iv++,k+=n )
{
dxdx[iv]=dxdy[iv]=dydy[iv]=0;
smin=Min(smin,ss[k]);
smax=Max(smax,ss[k]);
}
Real8 sdelta = smax-smin;
Real8 absmax=Max(Abs(smin),Abs(smax));
Real8 cnorm = DoNormalisation ? coef2/sdelta : coef2;
if(verbosity>2)
cout << " Solution " << kcount << " Min = " << smin << " Max = "
<< smax << " Delta =" << sdelta << " cnorm = " << cnorm << endl;
if ( sdelta < 1.0e-10*Max(absmax,1e-20) )
{
if (verbosity>2)
cout << " Solution " << kcount << " is constant. We skip. "
<< " Min = " << smin << " Max = " << smax << endl;
continue;
}
for (i=0;i<nbt;i++)
if(triangles[i].link)
{// for real all triangles
// coor of 3 vertices
R2 A=triangles[i][0];
R2 B=triangles[i][1];
R2 C=triangles[i][2];
// warning the normal is internal and the
// size is the length of the edge
R2 nAB = Orthogonal(B-A);
R2 nBC = Orthogonal(C-B);
R2 nCA = Orthogonal(A-C);
// remark : nAB + nBC + nCA == 0
// number of the 3 vertices
iA = Number(triangles[i][0]);
iB = Number(triangles[i][1]);
iC = Number(triangles[i][2]);
// for the test of boundary edge
// the 3 adj triangles
Triangle *tBC = triangles[i].TriangleAdj(OppositeEdge[0]);
Triangle *tCA = triangles[i].TriangleAdj(OppositeEdge[1]);
Triangle *tAB = triangles[i].TriangleAdj(OppositeEdge[2]);
// value of the P1 fonction on 3 vertices
sA = ss[iA*n];
sB = ss[iB*n];
sC = ss[iC*n];
R2 Grads = (nAB * sC + nBC * sA + nCA * sB ) /detT[i] ;
if(choice)
{
int nbb = 0;
Real8 dd = detT[i];
Real8 lla,llb,llc,llf;
Real8 taa[3][3],bb[3];
// construction of the trans of lin system
for (int j=0;j<3;j++)
{
int ie = OppositeEdge[j];
TriangleAdjacent ta = triangles[i].Adj(ie);
Triangle *tt = ta;
if (tt && tt->link)
{
Vertex &v = *ta.OppositeVertex();
R2 V = v;
Int4 iV = Number(v);
Real8 lA = ::Area2(V,B,C)/dd;
Real8 lB = ::Area2(A,V,C)/dd;
Real8 lC = ::Area2(A,B,V)/dd;
taa[0][j] = lB*lC;
taa[1][j] = lC*lA;
taa[2][j] = lA*lB;
Real8 xx = V.x-V.y;
Real8 yy = V.x + V.y;
//cout << " iv " << ss[iV*n] << " == " << (8*xx*xx+yy*yy)
// << " l = " << lA << " " << lB << " " << lC
// << " = " << lA+lB+lC << " " << V << " == " << A*lA+B*lB+C*lC << endl;
lla = lA,llb=lB,llc=lC,llf=ss[iV*n] ;
bb[j] = ss[iV*n] - ( sA*lA + sB*lB + sC*lC ) ;
}
else
{
nbb++;
taa[0][j]=0;
taa[1][j]=0;
taa[2][j]=0;
taa[j][j]=1;
bb[j]=0;
}
}
// resolution of 3x3 lineaire system transpose
Real8 det33 = det3x3(taa[0],taa[1],taa[2]);
Real8 cBC = det3x3(bb,taa[1],taa[2]);
Real8 cCA = det3x3(taa[0],bb,taa[2]);
Real8 cAB = det3x3(taa[0],taa[1],bb);
assert(det33);
// det33=1;
// verif
// cout << " " << (taa[0][0]*cBC + taa[1][0]*cCA + taa[2][0] * cAB)/det33 << " == " << bb[0] ;
// cout << " " << (taa[0][1]*cBC + taa[1][1]*cCA + taa[2][1] * cAB)/det33 << " == " << bb[1];
// cout << " " << (taa[0][2]*cBC + taa[1][2]*cCA + taa[2][2] * cAB)/det33 << " == " << bb[2]
// << " -- " ;
//cout << lla*sA + llb*sB+llc*sC+ (lla*llb* cAB + llb*llc* cBC + llc*lla*cCA)/det33
// << " == " << llf << endl;
// computation of the gradient in the element
// H( li*lj) = grad li grad lj + grad lj grad lj
// grad li = njk / detT ; with i j k ={A,B,C)
Real8 Hxx = cAB * ( nBC.x*nCA.x) + cBC * ( nCA.x*nAB.x) + cCA * (nAB.x*nBC.x);
Real8 Hyy = cAB * ( nBC.y*nCA.y) + cBC * ( nCA.y*nAB.y) + cCA * (nAB.y*nBC.y);
Real8 Hxy = cAB * ( nBC.y*nCA.x) + cBC * ( nCA.y*nAB.x) + cCA * (nAB.y*nBC.x)
+ cAB * ( nBC.x*nCA.y) + cBC * ( nCA.x*nAB.y) + cCA * (nAB.x*nBC.y);
Real8 coef = 1.0/(3*dd*det33);
Real8 coef2 = 2*coef;
// cout << " H = " << Hxx << " " << Hyy << " " << Hxy/2 << " coef2 = " << coef2 << endl;
Hxx *= coef2;
Hyy *= coef2;
Hxy *= coef2;
//cout << i << " H = " << 3*Hxx/dd << " " << 3*Hyy/dd << " " << 3*Hxy/(dd*2) << " nbb = " << nbb << endl;
if(nbb==0)
{
dxdx[iA] += Hxx;
dydy[iA] += Hyy;
dxdy[iA] += Hxy;
dxdx[iB] += Hxx;
dydy[iB] += Hyy;
dxdy[iB] += Hxy;
dxdx[iC] += Hxx;
dydy[iC] += Hyy;
dxdy[iC] += Hxy;
}
}
else
{
// if edge on boundary no contribution => normal = 0
if ( ! tBC || ! tBC->link ) nBC = O;
if ( ! tCA || ! tCA->link ) nCA = O;
if ( ! tAB || ! tAB->link ) nAB = O;
// remark we forgot a 1/2 because
// \int_{edge} w_i = 1/2 if i is in edge
// 0 if not
// if we don't take the boundary
// dxdx[iA] += ( nCA.x + nAB.x ) *Grads.x;
dxdx[iA] += ( nCA.x + nAB.x ) *Grads.x;
dxdx[iB] += ( nAB.x + nBC.x ) *Grads.x;
dxdx[iC] += ( nBC.x + nCA.x ) *Grads.x;
// warning optimization (1) the divide by 2 is done on the metrix construction
dxdy[iA] += (( nCA.y + nAB.y ) *Grads.x + ( nCA.x + nAB.x ) *Grads.y) ;
dxdy[iB] += (( nAB.y + nBC.y ) *Grads.x + ( nAB.x + nBC.x ) *Grads.y) ;
dxdy[iC] += (( nBC.y + nCA.y ) *Grads.x + ( nBC.x + nCA.x ) *Grads.y) ;
dydy[iA] += ( nCA.y + nAB.y ) *Grads.y;
dydy[iB] += ( nAB.y + nBC.y ) *Grads.y;
dydy[iC] += ( nBC.y + nCA.y ) *Grads.y;
}
} // for real all triangles
Int4 kk=0;
for ( iv=0,k=0 ; iv<nbv; iv++,k+=n )
if(Mmassxx[iv]>0)
{
dxdx[iv] /= 2*Mmassxx[iv];
// warning optimization (1) on term dxdy[iv]*ci/2
dxdy[iv] /= 4*Mmassxx[iv];
dydy[iv] /= 2*Mmassxx[iv];
// Compute the matrix with abs(eigen value)
Metric M(dxdx[iv], dxdy[iv], dydy[iv]);
MatVVP2x2 Vp(M);
//cout <<iv << " M = " << M << " aniso= " << Vp.Aniso() ;
Vp.Abs();
M = Vp;
dxdx[iv] = M.a11;
dxdy[iv] = M.a21;
dydy[iv] = M.a22;
// cout << " (abs) iv M = " << M << " aniso= " << Vp.Aniso() <<endl;
}
else kk++;
// correction of second derivate
// by a laplacien
Real8 *d2[3] = { dxdx, dxdy, dydy};
Real8 *dd;
for (int xy = 0;xy<3;xy++)
{
dd = d2[xy];
// do leat 2 iteration for boundary problem
for (int ijacobi=0;ijacobi<Max(NbJacobi,2);ijacobi++)
{
for (i=0;i<nbt;i++)
if(triangles[i].link) // the real triangles
{
// number of the 3 vertices
iA = Number(triangles[i][0]);
iB = Number(triangles[i][1]);
iC = Number(triangles[i][2]);
Real8 cc=3;
if(ijacobi==0)
cc = Max((Real8) ((Mmassxx[iA]>0)+(Mmassxx[iB]>0)+(Mmassxx[iC]>0)),1.);
workT[i] = (dd[iA]+dd[iB]+dd[iC])/cc;
}
for (iv=0;iv<nbv;iv++)
workV[iv]=0;
for (i=0;i<nbt;i++)
if(triangles[i].link) // the real triangles
{
// number of the 3 vertices
iA = Number(triangles[i][0]);
iB = Number(triangles[i][1]);
iC = Number(triangles[i][2]);
Real8 cc = workT[i]*detT[i];
workV[iA] += cc;
workV[iB] += cc;
workV[iC] += cc;
}
for (iv=0;iv<nbv;iv++)
if( ijacobi<NbJacobi || OnBoundary[iv])
dd[iv] = workV[iv]/(Mmass[iv]*6);
}
}
// constuction of the metrix from the Hessian dxdx. dxdy,dydy
Real8 rCutOff=CutOff*absmax;// relative cut off
for ( iv=0,k=0 ; iv<nbv; iv++,k+=n )
{ // for all vertices
//{
//Metric M(dxdx[iv], dxdy[iv], dydy[iv]);
// MatVVP2x2 Vp(M);
//cout << " iv M="<< M << " Vp = " << Vp << " aniso " << Vp.Aniso() << endl;
//}
MetricIso Miso;
Real8 ci = RelativeMetric ? coef2/(Max(Abs(ss[k]),rCutOff)) : cnorm ;
Metric Miv(dxdx[iv]*ci, dxdy[iv]*ci, dydy[iv]*ci);
MatVVP2x2 Vp(Miv);
Vp.Abs();
h1=Min(h1,Vp.lmin());
h2=Max(h2,Vp.lmax());
Vp.Maxh(hmin);
Vp.Minh(hmax);
rx = Max(rx,Vp.Aniso2());
Vp.BoundAniso2(coef);
hn1=Min(hn1,Vp.lmin());
hn2=Max(hn2,Vp.lmax());
rnx = Max(rnx,Vp.Aniso2());
Metric MVp(Vp);
vertices[iv].m.IntersectWith(MVp);
}// for all vertices
if (verbosity>2)
{
cout << " Solution " << kcount << endl;
cout << " before bounding : Hmin = " << sqrt(1/h2) << " Hmax = "
<< sqrt(1/h1) << " factor of anisotropy max = " << sqrt(rx) << endl;
cout << " after bounding : Hmin = " << sqrt(1/hn2) << " Hmax = "
<< sqrt(1/hn1) << " factor of anisotropy max = " << sqrt(rnx) << endl;
}
}// end for all solution
delete [] detT;
delete [] Mmass;
delete [] dxdx;
delete [] dxdy;
delete [] dydy;
delete [] workT;
delete [] workV;
delete [] Mmassxx;
delete [] OnBoundary;
}
