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InterpolateTraits.h
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//
// InterpolateTraits.h
// testigl
//
// Created by Amir Vaxman on 30/09/14.
// Copyright (c) 2014 Amir Vaxman. All rights reserved.
//
#ifndef MoebiusCode_InterpolateTraits_h
#define MoebiusCode_InterpolateTraits_h
#include "AuxSparse.h"
#include "MobiusFromShapes.h"
#include "InitialSolution3DTraits.h"
#include "QuadConstSolver.h"
#include "QuaternionOps.h"
#include "ExtraFunctions.h"
//currently not treating the const indices at all
class InterpolateTraits2D{
public:
double OffWeight;
double PosWeight;
MatrixXi E2V, E2F, E2Fi, F;
VectorXi InnerEdges, ConstIndices;
SparseMatrix<Complex> d0;
SparseMatrix<Complex> IDMat;
VectorXcd SourceVc;
SparseMatrix<Complex> gGlobal;
//VectorXd OrigLengths, DeformLengths, PrescribeLengths;
VectorXcd InitSolution;
VectorXcd InterpEdgeDeviations;
VectorXcd ConstPoses;
Vector2cd Interpcd;
double SmoothFactor;
double CloseFactor;
double ConstTolerance;
double VertexTolerance;
void Initialize(const VectorXcd& inSourceVc, const VectorXcd& inTargetVc, const VectorXcd& inInterpEdgeDeviations, const Vector2cd& inInterpcd, const MatrixXi& inF, const MatrixXi& inE2V, const VectorXi& inInnerEdges, const MatrixXi& inE2F, const MatrixXi& inE2Fi, const VectorXi& inConstIndices, const VectorXcd& inConstPoses, const SparseMatrix<Complex> ind0, double t, const VectorXcd& inInitSolution){
F=inF; E2V=inE2V; E2F=inE2F; InnerEdges=inInnerEdges; E2F=inE2F; E2Fi=inE2Fi; ConstIndices=inConstIndices;
InitSolution=inInitSolution;
d0=ind0;
SourceVc=inSourceVc;
ConstPoses=inConstPoses;
Interpcd=inInterpcd;
InterpEdgeDeviations=inInterpEdgeDeviations;
//InitialSolution2DTraits ist;
//ist.Initialize(ConstIndices, SourceVc, TargetConstPoses, TargetConstX);
//cout<<"Finding Base Mobius Transformation:"<<endl;
//QuadConstSolver<InitialSolution2DTraits, Complex> qcs(ist);
//TargetConstX=qcs.Solve(TargetConstX, 1.0, 25);
//for (int i=0;i<ConstIndices.size();i++)
// InterpConstX(i)=exp(log(TargetConstX(i))*t);
//cout<<"TargetConstX: "<<TargetConstX<<endl;
//retrieving interpolated const positions by Poisson, keeping the first constant
/*vector<pair<int,int> > ConstPairs;
for (int i=0;i<ConstIndices.size();i++)
for (int j=i+1;j<ConstIndices.size();j++)
ConstPairs.push_back(pair<int,int>(i,j));*/
//computing current deform error
/*VectorXcd InterpConstDeviations(ConstPairs.size());
MatrixXcd dConst(ConstPairs.size(), ConstIndices.size());
dConst.setZero();
VectorXcd MobEdgeVectors(ConstPairs.size());
for (int i=0;i<ConstPairs.size();i++){
MobEdgeVectors(i)=InterpConstX(ConstPairs[i].second)*(SourceConstPoses(ConstPairs[i].second)-SourceConstPoses(ConstPairs[i].first))*InterpConstX(ConstPairs[i].first);
InterpConstDeviations(i)=TargetConstX(ConstPairs[i].second)*(SourceConstPoses(ConstPairs[i].second)-SourceConstPoses(ConstPairs[i].first))*TargetConstX(ConstPairs[i].first);
InterpConstDeviations(i)/=(TargetConstPoses(ConstPairs[i].second)-TargetConstPoses(ConstPairs[i].first));
//cout<<"InterpConstDeviations: "<<InterpConstDeviations(i)<<endl;
InterpConstDeviations(i)=exp(log(InterpConstDeviations(i))*t);
//cout<<"InterpConstDeviations: "<<InterpConstDeviations(i)<<endl;
dConst(i,ConstPairs[i].first)=-InterpConstDeviations(i);
dConst(i,ConstPairs[i].second)=InterpConstDeviations(i);
}
//cout<<"MobEdgeVectors: "<<MobEdgeVectors<<endl;
//cout<<"Source Edge Vectors: "<<dConst*SourceConstPoses<<endl;
//cout<<"InterpConstDeviations: "<<InterpConstDeviations<<endl;
//cout<<"TargetEdgeDeviations: "<<TargetEdgeDeviations<<endl;
//cout<<"Error with Target positions:"<<dConst*TargetConstPoses-MobEdgeVectors<<endl;
VectorXcd torhs(ConstIndices.size()); torhs.setZero();
torhs(0)=SourceConstPoses(0);
VectorXcd rhs=MobEdgeVectors-dConst*torhs;
MatrixXcd dConstSmall=dConst.block(0,1, ConstPairs.size(), ConstIndices.size()-1);
VectorXcd ConstSolution = (dConstSmall.adjoint()*dConstSmall).llt().solve(dConstSmall.adjoint()*rhs);
//InterpConstPoses(0)=torhs(0);
//InterpConstPoses.tail(ConstIndices.size()-1)=ConstSolution;
//cout<<"SourceConstPoses: "<<SourceConstPoses<<endl;
//cout<<"TargetConstPoses: "<<TargetConstPoses<<endl;
//cout<<"InterpConstPoses: "<<InterpConstPoses<<endl;*/
//Interpolating edge deviations
/*InterpEdgeDeviations.resize(TargetEdgeDeviations.size());
for (int i=0;i<TargetEdgeDeviations.size();i++)
InterpEdgeDeviations(i)=exp(log(TargetEdgeDeviations(i))*t);*/
igl::speye(SourceVc.rows()+SourceVc.rows(), IDMat);
SmoothFactor=100;
CloseFactor=10e-5;
ConstTolerance=10e-9;
VertexTolerance=10e-5;
}
VectorXcd EvalEnergy(const VectorXcd& CurrSolution){
//VectorXcd CurrSolution(CurrSolutionReal.size()/2);
//CurrSolution.array().real()=CurrSolutionReal.head(CurrSolutionReal.size()/2);
//CurrSolution.array().imag()=CurrSolutionReal.tail(CurrSolutionReal.size()/2);
VectorXcd CurrMobRecips=CurrSolution.head(SourceVc.rows());
VectorXcd CurrLocations=CurrSolution.segment(SourceVc.rows(),SourceVc.rows());
VectorXcd CurrEdges=(d0*CurrLocations).cwiseProduct(InterpEdgeDeviations);
VectorXcd CurrMobiusEdges(E2V.rows());
for (int i=0;i<E2V.rows();i++)
CurrMobiusEdges(i)=CurrMobRecips(E2V(i,0))*(SourceVc(E2V(i,1))-SourceVc(E2V(i,0)))*CurrMobRecips(E2V(i,1));
VectorXcd EnergyVec=SmoothFactor*(CurrMobiusEdges-CurrEdges);
VectorXcd CloseVec=CloseFactor*(CurrSolution-InitSolution);
//VectorXcd MobVec=MobConstFactor*MobConstMat*CurrSolution;
VectorXcd PosVec(ConstIndices.size());
for (int i=0;i<ConstIndices.size();i++)
PosVec(i)=CurrLocations(ConstIndices(i))-ConstPoses(i);
VectorXcd ConstVec(CloseVec.size()+EnergyVec.size()+PosVec.size());
ConstVec<<CloseVec, EnergyVec, PosVec;
return ConstVec;
}
SparseMatrix<Complex> EvalGradient(const VectorXcd& CurrSolution){
//VectorXcd CurrSolution(CurrSolutionReal.size()/2);
//CurrSolution.array().real()=CurrSolutionReal.head(CurrSolutionReal.size()/2);
//CurrSolution.array().imag()=CurrSolutionReal.tail(CurrSolutionReal.size()/2);
VectorXcd CurrMobRecips=CurrSolution.head(SourceVc.rows());
VectorXcd CurrLocations=CurrSolution.segment(SourceVc.rows(),SourceVc.rows());
SparseMatrix<Complex> gCurrEdges=-SparseDiagonalMatrix<Complex>(InterpEdgeDeviations)*d0;
SparseMatrix<Complex> gCurrMobiusEdges(E2V.rows(), SourceVc.rows());
vector<Triplet<Complex> > gCurrMobiusEdgesTris;
for (int i=0;i<E2V.rows();i++){
gCurrMobiusEdgesTris.push_back(Triplet<Complex>(i,E2V(i,1),CurrMobRecips(E2V(i,0))*(SourceVc(E2V(i,1))-SourceVc(E2V(i,0)))));
gCurrMobiusEdgesTris.push_back(Triplet<Complex>(i,E2V(i,0),CurrMobRecips(E2V(i,1))*(SourceVc(E2V(i,1))-SourceVc(E2V(i,0)))));
}
gCurrMobiusEdges.setFromTriplets(gCurrMobiusEdgesTris.begin(), gCurrMobiusEdgesTris.end());
SparseMatrix<Complex> gAMAPEnergy=SparseBlock<Complex>(gCurrMobiusEdges, gCurrEdges,true);
SparseMatrix<Complex> gPos(ConstIndices.size(), CurrSolution.size());
vector<Triplet<Complex> > gPosTris;
for (int i=0;i<ConstIndices.size();i++)
gPosTris.push_back(Triplet<Complex>(i,SourceVc.rows()+ConstIndices(i),1.0));
gPos.setFromTriplets(gPosTris.begin(), gPosTris.end());
SparseMatrix<Complex> ComplexGradient=SparseBlock<Complex>(SparseBlock<Complex>(CloseFactor*IDMat,SmoothFactor*gAMAPEnergy, false),gPos,false);//, gPos, false);
return ComplexGradient;
}
void Reformulate(int CurrIter, int MaxIterations, const VectorXcd& CurrSolution)
{
InitSolution=CurrSolution;
SmoothFactor*=0.95;
}
double GetConstError(const VectorXcd& CurrSolution)
{
VectorXcd CurrMobRecips=CurrSolution.head(SourceVc.rows());
VectorXcd CurrLocations=CurrSolution.segment(SourceVc.rows(),SourceVc.rows());
VectorXcd CurrEdges=(d0*CurrLocations).cwiseProduct(InterpEdgeDeviations);
VectorXcd CurrMobiusEdges(E2V.rows());
for (int i=0;i<E2V.rows();i++)
CurrMobiusEdges(i)=CurrMobRecips(E2V(i,0))*(SourceVc(E2V(i,1))-SourceVc(E2V(i,0)))*CurrMobRecips(E2V(i,1));
VectorXcd EnergyVec=(CurrMobiusEdges-CurrEdges);
VectorXcd PosVec(ConstIndices.size());
for (int i=0;i<ConstIndices.size();i++)
PosVec(i)=CurrLocations(ConstIndices(i))-ConstPoses(i);
VectorXcd ConstVec(EnergyVec.size()+PosVec.size());
ConstVec<<EnergyVec, PosVec;
//return PosVec.lpNorm<Infinity>();
return EnergyVec.lpNorm<Infinity>();
}
bool isTerminate(const VectorXcd& CurrSolution){
//VectorXcd CurrSolution(CurrSolutionReal.size()/2);
//CurrSolution.array().real()=CurrSolutionReal.head(CurrSolutionReal.size()/2);
//CurrSolution.array().imag()=CurrSolutionReal.tail(CurrSolutionReal.size()/2);
VectorXcd CurrLocations=CurrSolution.segment(SourceVc.rows(),SourceVc.rows());
VectorXcd InitLocations=InitSolution.segment(SourceVc.rows(),SourceVc.rows());
bool NoVerticesMoved=((CurrLocations-InitLocations).lpNorm<Infinity>()<VertexTolerance);
cout<<"Vertex Movement: "<<(CurrLocations-InitLocations).lpNorm<Infinity>()<<endl;
bool WithinConstTolerance=(GetConstError(CurrSolution) < ConstTolerance);
return (WithinConstTolerance || NoVerticesMoved);
}
};
class InterpolateTraits3D{
public:
double OffWeight;
double PosWeight;
MatrixXi E2V, E2F, E2Fi, F;
VectorXi InnerEdges, ConstIndices;
VectorXd InitSolution;
VectorXd InterpConstPoses;
VectorXd InterpEdgeDeviations;
MatrixXd SourceVq;
MatrixXd ConstPoses;
SparseMatrix<double> d0;
SparseMatrix<double> IDMat;
double SmoothFactor;
double CloseFactor;
double ConstTolerance;
void Initialize(const MatrixXd& inSourceVq, const MatrixXd& TargetVq, const MatrixXd& TargetX, const MatrixXd& TargetEdgeDeviations, const MatrixXi& inF, const MatrixXi& inE2V, const VectorXi& inInnerEdges, const MatrixXi& inE2F, const MatrixXi& inE2Fi, const VectorXi& inConstIndices, const MatrixXd& inConstPoses, const SparseMatrix<double>& ind0, const double t, const VectorXd& inInitSolution){
F=inF; E2V=inE2V; E2F=inE2F; InnerEdges=inInnerEdges; E2F=inE2F; E2Fi=inE2Fi; ConstIndices=inConstIndices;
InitSolution=inInitSolution;
SourceVq=inSourceVq;
ConstPoses=inConstPoses;
d0=ind0;
MatrixXd SourceConstPoses(ConstIndices.size(),4);
MatrixXd TargetConstPoses(ConstIndices.size(),4);
InterpConstPoses.resize(3*ConstIndices.size());
MatrixXd InterpConstX(ConstIndices.size(),4);
VectorXd TargetConstX(4*ConstIndices.size());
for (int i=0;i<ConstIndices.size();i++){
SourceConstPoses.row(i)=SourceVq.row(ConstIndices(i));
TargetConstPoses.row(i)=TargetVq.row(ConstIndices(i));
TargetConstX.segment(4*i,4)=TargetX.row(ConstIndices(i)).transpose();
}
InitialSolution3DTraits ist;
ist.Initialize(ConstIndices, SourceVq, TargetConstPoses, TargetConstX);
QuadConstSolver<InitialSolution3DTraits, double> qcs(ist);
TargetConstX=qcs.Solve(TargetConstX, 1.0, 25);
for (int i=0;i<ConstIndices.size();i++)
InterpConstX.row(i)=QExp(QLog(TargetConstX.segment(4*i,4).transpose())*t);
//cout<<"TargetConstX: "<<TargetConstX<<endl;
//retrieving interpolated const positions by Poisson, keeping the first constant
vector<pair<int,int> > ConstPairs;
for (int i=0;i<ConstIndices.size();i++)
for (int j=i+1;j<ConstIndices.size();j++)
ConstPairs.push_back(pair<int,int>(i,j));
//computing current deform error
MatrixXd InterpConstDeviations(ConstPairs.size(),4);
MatrixXd dConst(ConstPairs.size(), ConstIndices.size());
dConst.setZero();
MatrixXd MobEdgeVectors(ConstPairs.size(),4);
for (int i=0;i<ConstPairs.size();i++){
MobEdgeVectors.row(i)=QMult1(QConj1(InterpConstX.row(ConstPairs[i].second)),QMult1(SourceConstPoses.row(ConstPairs[i].second)-SourceConstPoses.row(ConstPairs[i].first),InterpConstX.row(ConstPairs[i].first)));
InterpConstDeviations.row(i)=QMult1(QConj1(TargetConstX.segment(4*ConstPairs[i].second,4).transpose()),QMult1(SourceConstPoses.row(ConstPairs[i].second)-SourceConstPoses.row(ConstPairs[i].first), TargetConstX.segment(4*ConstPairs[i].first,4).transpose()));
InterpConstDeviations.row(i)=QMult1(InterpConstDeviations.row(i),QInv1(TargetConstPoses.row(ConstPairs[i].second)-TargetConstPoses.row(ConstPairs[i].first)));
//cout<<"InterpConstDeviations: "<<InterpConstDeviations(i)<<endl;
InterpConstDeviations.row(i)=QExp(QLog(InterpConstDeviations.row(i))*t);
//cout<<"InterpConstDeviations: "<<InterpConstDeviations(i)<<endl;
dConst(i,ConstPairs[i].first)=-1.0;
dConst(i,ConstPairs[i].second)=1.0;
}
//cout<<"MobEdgeVectors: "<<MobEdgeVectors<<endl;
//cout<<"Source Edge Vectors: "<<dConst*SourceConstPoses<<endl;
//cout<<"InterpConstDeviations: "<<InterpConstDeviations<<endl;
//cout<<"Error with Target positions:"<<dConst*TargetConstPoses-MobEdgeVectors<<endl;
MatrixXd torhs(ConstIndices.size(),3); torhs.setZero();
torhs.row(0)=SourceConstPoses.row(0).tail(3);
MatrixXd rhs=MobEdgeVectors.block(0,1,MobEdgeVectors.rows(), 3)-dConst*torhs;
MatrixXd dConstSmall=dConst.block(0,1, ConstPairs.size(), ConstIndices.size()-1);
MatrixXd ConstSolution = (dConstSmall.adjoint()*dConstSmall).llt().solve(dConstSmall.adjoint()*rhs);
InterpConstPoses.setZero();
InterpConstPoses.segment(0,3)=torhs.row(0).transpose();
for (int i=1;i<ConstIndices.size();i++)
InterpConstPoses.segment(3*i,3)=ConstSolution.row(i-1);
//cout<<"SourceConstPoses: "<<SourceConstPoses<<endl;
//cout<<"TargetConstPoses: "<<TargetConstPoses<<endl;
//cout<<"InterpConstPoses: "<<InterpConstPoses<<endl;
//Interpolating edge deviations
InterpEdgeDeviations.resize(TargetEdgeDeviations.size());
for (int i=0;i<E2V.rows();i++)
InterpEdgeDeviations.segment(4*i,4)=QExp(QLog(TargetEdgeDeviations.row(i))*t).transpose();
//cout<<"TargetEdgeDeviations: "<<TargetEdgeDeviations<<endl;
//cout<<"InterpEdgeDeviations: "<<InterpEdgeDeviations<<endl;
igl::speye(4*SourceVq.rows()+3*SourceVq.rows(), IDMat);
SmoothFactor=10;
CloseFactor=10e-5;
ConstTolerance=10e-7;
//checking finite element gradient of a random choice
/*VectorXd CurrSolution=InitSolution+100*VectorXd::Random(InitSolution.rows(), InitSolution.cols());
VectorXd CurrConst=EvalEnergy(CurrSolution);
SparseMatrix<double> FEGradient(CurrConst.size(), CurrSolution.size());
vector<Triplet<double> > FEGradientTris;
for (int i=0;i<CurrSolution.size();i++){
VectorXd vh(CurrSolution.size()); vh.setZero(); vh(i)=10e-5;
VectorXd CurrGradient=(EvalEnergy(CurrSolution+vh)-EvalEnergy(CurrSolution-vh))/(2*10e-5);
//cout<<CurrGradient<<endl;
for (int j=0;j<CurrGradient.size();j++)
if (abs(CurrGradient(j))>10e-7)
FEGradientTris.push_back(Triplet<double>(j,i,CurrGradient(j)));
}
FEGradient.setFromTriplets(FEGradientTris.begin(), FEGradientTris.end());
SparseMatrix<double> OrigGradient=EvalGradient(CurrSolution);
SparseMatrix<double> DiffMat=FEGradient-OrigGradient;
double maxcoeff=-32767.0;
int Maxi,Maxj;
for (int k=0; k<DiffMat.outerSize(); ++k)
for (SparseMatrix<double>::InnerIterator it(DiffMat,k); it; ++it){
if (maxcoeff<abs(it.value())){
maxcoeff=abs(it.value());
Maxi=it.row();
Maxj=it.col();
}
if (abs(it.value())>10e-6){
cout<<"Gradient Discrepancy at: ("<<it.row()<<","<<it.col()<<") of "<<it.value()<<endl;
cout<<"FE Gradient: "<<FEGradient.coeffRef(it.row(), it.col())<<endl;
cout<<"Calculated gradient: "<<OrigGradient.coeffRef(it.row(),it.col())<<endl;
}
}
cout<<"Maximum gradient difference: "<<maxcoeff<<endl;
cout<<"At Location: ("<<Maxi<<","<<Maxj<<")"<<endl;
//cout<<"E2V.rows()="<<E2V.rows()<<endl;
//cout<<"OrigVq.rows()="<<OrigVq.rows()<<endl;
//cout<<"VarIndices.rows()="<<VarIndices.rows()<<endl;*/
}
VectorXd EvalEnergy(const VectorXd& CurrSolution){
VectorXd CurrX=CurrSolution.head(4*SourceVq.rows());
VectorXd CurrLocations=CurrSolution.segment(4*SourceVq.rows(),3*SourceVq.rows());
VectorXd ExtEdgeVectors(4*E2V.rows()); ExtEdgeVectors.setZero();
VectorXd CurrWij=d0*CurrLocations;
for (int i=0;i<E2V.rows();i++){
RowVector4d ExtCurrWij; ExtCurrWij<<0,CurrWij.segment(3*i,3).transpose();
ExtEdgeVectors.segment(4*i,4)=QMult1(InterpEdgeDeviations.segment(4*i,4).transpose(),ExtCurrWij).transpose();
}
VectorXd EnergyVec(4*E2V.rows());
VectorXd MobEdgeVectors(4*E2V.rows());;
for (int i=0;i<E2V.rows();i++){
RowVector4d Xi=CurrX.segment(4*E2V(i,0),4).transpose();
RowVector4d Xj=CurrX.segment(4*E2V(i,1),4).transpose();
MobEdgeVectors.segment(4*i,4)=QMult1(QMult1(QConj1(Xj),SourceVq.row(E2V(i,1))-SourceVq.row(E2V(i,0))),Xi).transpose();
}
EnergyVec=MobEdgeVectors-ExtEdgeVectors;
VectorXd CloseVec=(CurrSolution-InitSolution);
VectorXd PosVec(3*ConstIndices.size());
for (int i=0;i<ConstIndices.size();i++)
PosVec.segment(3*i,3)=CurrLocations.segment(3*ConstIndices(i),3)-InterpConstPoses.segment(3*i,3);
VectorXd BasicConstVec(EnergyVec.size()+CloseVec.size()+PosVec.size());
BasicConstVec<<CloseFactor*CloseVec,SmoothFactor*EnergyVec, PosVec;
//cout<<CloseVec.size()<<","<<EnergyVec.size()<<","<<PosVec.size()<<endl;
return BasicConstVec;
}
SparseMatrix<double> EvalGradient(const VectorXd& CurrSolution){
VectorXd CurrX=CurrSolution.head(4*SourceVq.rows());
VectorXd CurrLocations=CurrSolution.segment(4*SourceVq.rows(),3*SourceVq.rows());
VectorXd ExtEdgeVectors(4*E2V.rows()); ExtEdgeVectors.setZero();
VectorXd CurrWij=d0*CurrLocations;
for (int i=0;i<E2V.rows();i++){
RowVector4d ExtCurrWij; ExtCurrWij<<0,CurrWij.segment(3*i,3).transpose();
ExtEdgeVectors.segment(4*i,4)=QMult1(InterpEdgeDeviations.segment(4*i,4).transpose(),ExtCurrWij).transpose();
}
vector<Triplet<double> > gMobEdgesTris, gCurrEdgesTris;
for (int i=0;i<E2V.rows();i++){
int MatPosi=4*E2V(i,0);
int MatPosj=4*E2V(i,1);
int CurrRow=4*i;
RowVector4d Xi=CurrX.segment(4*E2V(i,0),4).transpose();
RowVector4d Xj=CurrX.segment(4*E2V(i,1),4).transpose();
RowVector4d Cij=InterpEdgeDeviations.segment(4*i,4).transpose();
RowVector4d ResttoRight=QMult1(SourceVq.row(E2V(i,1))-SourceVq.row(E2V(i,0)),Xi);
RowVector4d ResttoLeft=QMult1(QConj1(Xj),SourceVq.row(E2V(i,1))-SourceVq.row(E2V(i,0)));
//Derivative by Gj, using rest to right as "e":
//[diff(qce',rq) diff(qce',vqx), diff(qce', vqy), diff(qce', vqz)]=
//[ re, vex, vey, vez]
//[ vex, -re, -vez, vey]
//[ vey, vez, -re, -vex]
//[ vez, -vey, vex, -re]
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosj, ResttoRight(0)));
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosj+1,ResttoRight(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosj+2,ResttoRight(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosj+3,ResttoRight(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosj, ResttoRight(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosj+1,-ResttoRight(0)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosj+2,-ResttoRight(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosj+3, ResttoRight(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosj, ResttoRight(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosj+1, ResttoRight(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosj+2,-ResttoRight(0)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosj+3,-ResttoRight(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosj, ResttoRight(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosj+1,-ResttoRight(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosj+2, ResttoRight(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosj+3,-ResttoRight(0)));
//Derivative by Gi, using rest to left as "e":
//[ re, -vex, -vey, -vez]
//[ vex, re, -vez, vey]
//[ vey, vez, re, -vex]
//[ vez, -vey, vex, re]
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosi, ResttoLeft(0)));
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosi+1,-ResttoLeft(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosi+2,-ResttoLeft(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i,MatPosi+3,-ResttoLeft(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosi, ResttoLeft(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosi+1, ResttoLeft(0)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosi+2,-ResttoLeft(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+1,MatPosi+3, ResttoLeft(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosi, ResttoLeft(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosi+1, ResttoLeft(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosi+2, ResttoLeft(0)));
gMobEdgesTris.push_back(Triplet<double>(4*i+2,MatPosi+3,-ResttoLeft(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosi, ResttoLeft(3)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosi+1,-ResttoLeft(2)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosi+2, ResttoLeft(1)));
gMobEdgesTris.push_back(Triplet<double>(4*i+3,MatPosi+3, ResttoLeft(0)));
//Derivative with relation to positions
//Derivative by Wij (with proper sign), using rest to left (Cij) as "e":
//[ re, -vex, -vey, -vez]
//[ vex, re, -vez, vey]
//[ vey, vez, re, -vex]
//[ vez, -vey, vex, re]
//gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+4*E2V(i,1), Cij(0)));
gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+3*E2V(i,1), -Cij(1)));
gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+3*E2V(i,1)+1,-Cij(2)));
gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+3*E2V(i,1)+2,-Cij(3)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+4*E2V(i,1), Cij(1)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+3*E2V(i,1), Cij(0)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+3*E2V(i,1)+1,-Cij(3)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+3*E2V(i,1)+2, Cij(2)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+4*E2V(i,1), Cij(2)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+3*E2V(i,1), Cij(3)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+3*E2V(i,1)+1, Cij(0)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+3*E2V(i,1)+2,-Cij(1)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+4*E2V(i,1), Cij(3)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+3*E2V(i,1),-Cij(2)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+3*E2V(i,1)+1, Cij(1)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+3*E2V(i,1)+2,Cij(0)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+4*E2V(i,0), -Cij(0)));
gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+3*E2V(i,0),Cij(1)));
gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+3*E2V(i,0)+1,Cij(2)));
gCurrEdgesTris.push_back(Triplet<double>(4*i,CurrX.size()+3*E2V(i,0)+2,Cij(3)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+4*E2V(i,0), -Cij(1)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+3*E2V(i,0), -Cij(0)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+3*E2V(i,0)+1,Cij(3)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+1,CurrX.size()+3*E2V(i,0)+2, -Cij(2)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+4*E2V(i,0), -Cij(2)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+3*E2V(i,0), -Cij(3)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+3*E2V(i,0)+1, -Cij(0)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+2,CurrX.size()+3*E2V(i,0)+2,Cij(1)));
//gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+4*E2V(i,0), -Cij(3)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+3*E2V(i,0),Cij(2)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+3*E2V(i,0)+1, -Cij(1)));
gCurrEdgesTris.push_back(Triplet<double>(4*i+3,CurrX.size()+3*E2V(i,0)+2,-Cij(0)));
}
SparseMatrix<double> gMobEdges(4*E2V.rows(),CurrSolution.size());
gMobEdges.setFromTriplets(gMobEdgesTris.begin(), gMobEdgesTris.end());
SparseMatrix<double> gCurrEdges(4*E2V.rows(), CurrSolution.size());
gCurrEdges.setFromTriplets(gCurrEdgesTris.begin(),gCurrEdgesTris.end());
SparseMatrix<double> gAMAPEnergy=gMobEdges-gCurrEdges;
SparseMatrix<double> gPos(3*ConstIndices.size(), CurrSolution.size());
vector<Triplet<double> > gPosTris;
for (int i=0;i<ConstIndices.size();i++)
for (int j=0;j<3;j++)
gPosTris.push_back(Triplet<double>(3*i+j, 4*SourceVq.rows()+3*ConstIndices(i)+j,1.0));
gPos.setFromTriplets(gPosTris.begin(), gPosTris.end());
SparseMatrix<double> BasicGradient=SparseBlock<double>(SparseBlock<double>(CloseFactor*IDMat, SmoothFactor*gAMAPEnergy,false),gPos,false);
return BasicGradient;
}
void Reformulate(int CurrIter, int MaxIterations, const VectorXd& CurrSolution)
{
InitSolution=CurrSolution;
SmoothFactor*=0.5;
}
double GetConstError(const VectorXd& CurrSolution)
{
VectorXd CurrLocations=CurrSolution.segment(4*SourceVq.rows(),3*SourceVq.rows());
VectorXd PosVec(3*ConstIndices.size());
for (int i=0;i<ConstIndices.size();i++)
PosVec.segment(3*i,3)=CurrLocations.segment(3*ConstIndices(i),3)-InterpConstPoses.segment(3*i,3);
return PosVec.lpNorm<Infinity>();
}
bool isTerminate(const VectorXd& CurrSolution){
//VectorXcd CurrSolution(CurrSolutionReal.size()/2);
//CurrSolution.array().real()=CurrSolutionReal.head(CurrSolutionReal.size()/2);
//CurrSolution.array().imag()=CurrSolutionReal.tail(CurrSolutionReal.size()/2);
VectorXd CurrLocations=CurrSolution.segment(4*SourceVq.rows(),3*SourceVq.rows());
VectorXd InitLocations=InitSolution.segment(4*SourceVq.rows(),3*SourceVq.rows());
bool NoVerticesMoved=((CurrLocations-InitLocations).lpNorm<Infinity>()<ConstTolerance);
bool WithinConstTolerance=(GetConstError(CurrSolution) < ConstTolerance);
return (WithinConstTolerance && NoVerticesMoved);
}
};
/*class MobiusBoundedInterpolatationTraits3D{
MatrixXi E2V, E2F, E2Fi, F, F2E;
MatrixXd F2ESigns;
VectorXi InnerEdges, ConstIndices, VarIndices;
SparseMatrix<double> d0Var;
VectorXd d0Rhs;
vector<vector<int> > AdjFaces;
vector<vector<int> > AdjFacesi;
MatrixXd OrigVq, DeformVq;
VectorXd InitSolution;
VectorXd AbsOrigCR, AbsDeformCR, AbsInterpCR;
VectorXd RealOrigCR, RealDeformCR, RealInterpCR;
VectorXi VarLocIndices;
SparseMatrix<double> IDMat;
SparseMatrix<double> NormSumMatrix;
SparseMatrix<double> CornerDiffLCRSmall, CornerDiffSmall, CornerDiffMat;
double CloseFactor;
double SmoothFactor;
vector<pair<int, int> > CornerPairs;
void Initialize(const MatrixXd& inOrigVq, const MatrixXd& inDeformVq, const MatrixXi& inF, MatrixXi& inF2E, MatrixXd& inF2ESigns, const MatrixXi& inE2V, const VectorXi& inInnerEdges, const MatrixXi& inE2F, const MatrixXi& inE2Fi, vector<vector<int> >& inAdjFaces, vector<vector<int> >& inAdjFacesi, const VectorXi& inConstIndices, VectorXi& inVarIndices, SparseMatrix<double>& ind0var, VectorXd& ind0Rhs, VectorXd inAbsOrigCR, VectorXd& inAbsDeformCR, VectorXd& inRealOrigCR, VectorXd& inRealDeformCR, vector<pair<int,int> >& inCornerPairs,const double t, const VectorXd& inInitSolution){
F=inF; E2V=inE2V; F2E=inF2E; F2ESigns=inF2ESigns; E2F=inE2F; InnerEdges=inInnerEdges; E2F=inE2F; E2Fi=inE2Fi; ConstIndices=inConstIndices;
OrigVq=inOrigVq;
DeformVq=inDeformVq;
InitSolution=inInitSolution;
AbsInterpCR.resize(InnerEdges.size());
RealInterpCR.resize(InnerEdges.size());
AbsOrigCR=inAbsOrigCR;
AbsDeformCR=inAbsDeformCR;
RealOrigCR=inRealOrigCR;
RealDeformCR=inRealDeformCR;
VarIndices=inVarIndices;
d0Var=ind0var; d0Rhs=ind0Rhs;
CornerPairs=inCornerPairs;
AdjFaces=inAdjFaces;
AdjFacesi=inAdjFacesi;
for (int i=0;i<InnerEdges.rows();i++){
AbsInterpCR(i)=exp(log(AbsOrigCR(i))*(1-t)+log(AbsDeformCR(i))*t);
RealInterpCR(i)=exp(log(RealOrigCR(i))*(1-t)+log(RealDeformCR(i))*t);
}
//assuming CornerPairs is two per edge on the order of inneredges!!!
vector<Triplet<double> > CornerDiffLCRTris, CornerDiffTris;
//creating smoothness matrix for G values
for (int i=0;i<InnerEdges.size();i++){
CornerDiffLCRTris.push_back(Triplet<double>(2*i, CornerPairs[i].first,1.0));
CornerDiffLCRTris.push_back(Triplet<double>(2*i+1, CornerPairs[i].second,-AbsInterpCR(i)));
CornerDiffTris.push_back(Triplet<double>(2*i, CornerPairs[i].first,1.0));
CornerDiffTris.push_back(Triplet<double>(2*i+1, CornerPairs[i].second,-1.0));
}
CornerDiffLCRSmall.resize(2*InnerEdges.size(), 3*F.rows());
CornerDiffLCRSmall.setFromTriplets(CornerDiffLCRTris.begin(), CornerDiffLCRTris.end());
CornerDiffSmall.resize(2*InnerEdges.size(), 3*F.rows());
CornerDiffSmall.setFromTriplets(CornerDiffTris.begin(), CornerDiffTris.end());
SparseMatrix<double> eye4;
igl::speye(4, eye4);
SparseMatrix<double> CornerDiffOnlyG=Eigen::kroneckerProduct(CornerDiffSmall,eye4);
SparseMatrix<double> ZeroMat(CornerDiffOnlyG.rows(), 3*VarIndices.size());
CornerDiffMat=SparseBlock(CornerDiffOnlyG, ZeroMat, true);
VarLocIndices.resize(12*F.rows()+3*VarIndices.size());
for (int i=0;i<12*F.rows();i++)
VarLocIndices(i)=i;
for (int i=0;i<VarIndices.size();i++)
for (int j=0;j<3;j++)
VarLocIndices(12*F.rows()+3*i+j)=12*F.rows()+3*VarIndices(i)+j;
igl::speye(12*F.rows()+3*VarIndices.size(), IDMat);
//constructing sum matrix
vector<Triplet<double> > NormSumTris;
for (int i=0;i<3*F.rows();i++)
for(int j=0;j<4;j++)
NormSumTris.push_back(Triplet<double>(i,4*i+j,1.0));
NormSumMatrix.resize(3*F.rows(),12*F.rows()+3*VarIndices.size());
NormSumMatrix.setFromTriplets(NormSumTris.begin(), NormSumTris.end());
CloseFactor=10e-6;
SmoothFactor=100;
}
VectorXd EvalEnergy(const VectorXd& CurrSolution){
VectorXd CurrGInv=CurrSolution.head(12*F.rows());
VectorXd CurrLocations=CurrSolution.tail(3*VarIndices.size());
VectorXd CompVec(12*F.rows());
VectorXd EdgeVectors=d0Var*CurrLocations-d0Rhs;
for (int i=0;i<F.rows();i++){
for (int j=0;j<3;j++){
RowVector4d GiInv=CurrGInv.segment(4*(3*i+j),4).transpose();
RowVector4d GjInv=CurrGInv.segment(4*(3*i+(j+1)%3),4).transpose();
//cout<<"GiInv: "<<GiInv<<endl;
//cout<<"GjInv: "<<GjInv<<endl;
RowVector4d CurrEdgeVector=QMult(QMult(QConj(GjInv),OrigVq.row(F(i,(j+1)%3))-OrigVq.row(F(i,j))),GiInv);
//cout<<"Transformed Edge Vector for ("<<i<<","<<j<<") is: ("<<CurrEdgeVector<<")"<<endl;
//cout<<"Edge Vector is: ("<<EdgeVectors.segment(3*F2E(i,j),3)*F2ESigns(i,j)<<")"<<endl;
CurrEdgeVector.tail(3)-=EdgeVectors.segment(3*F2E(i,j),3)*F2ESigns(i,j);
CompVec.segment(4*(3*i+j),4)=CurrEdgeVector.transpose();
}
}
VectorXd EnergyVec=SmoothFactor*CornerDiffMat*CurrSolution;
VectorXd CloseVec=CloseFactor*(CurrSolution-InitSolution);
VectorXd LCRVec=CornerDiffLCRSmall*NormSumMatrix*(CurrSolution.cwiseAbs2());
/*VectorXd IAPVec(3*CornerPairs.size());
for (int i=0;i<CornerPairs.size();i++){
RowVector4d Gi=CurrGInv.segment(4*CornerPairs[i].first,4);
RowVector4d Gj=CurrGInv.segment(4*CornerPairs[i].second,4);
RowVector4d GiGj=QMult(QConj(Gj),Gi);
IAPVec.segment(3*i,3)=GiGj.tail(3);
}
IAPVec=IAPVec*IAPConstFactor;*/ /*
VectorXd ConstVec(CloseVec.size()+EnergyVec.size()+CompVec.size()+LCRVec.size());
ConstVec<<CloseVec,EnergyVec, CompVec, LCRVec;//, RCRVec;
//ConstVec=CompVec;
return ConstVec;
}
SparseMatrix<double> EvalGradient(const VectorXd& CurrSolution){
VectorXd CurrGInv=CurrSolution.head(12*F.rows());
VectorXd CurrLocations=CurrSolution.tail(3*VarIndices.size());
vector<Triplet<double> > gCompTris;
for (int i=0;i<F.rows();i++){
for (int j=0;j<3;j++){
int MatPosi=4*(3*i+j);
int MatPosj=4*(3*i+(j+1)%3);
int CurrRow=4*(3*i+j);
RowVector4d GiInv=CurrGInv.segment(4*(3*i+j),4).transpose();
RowVector4d GjInv=CurrGInv.segment(4*(3*i+(j+1)%3),4).transpose();
RowVector4d ResttoRight=QMult(OrigVq.row(F(i,(j+1)%3))-OrigVq.row(F(i,j)),GiInv);
RowVector4d ResttoLeft=QMult(QConj(GjInv),OrigVq.row(F(i,(j+1)%3))-OrigVq.row(F(i,j)));
//Derivative by Gj, using rest to right as "e":
//[diff(qce',rq) diff(qce',vqx), diff(qce', vqy), diff(qce', vqz)]=
//[ re, vex, vey, vez]
//[ vex, -re, -vez, vey]
//[ vey, vez, -re, -vex]
//[ vez, -vey, vex, -re]
gCompTris.push_back(Triplet<double>(CurrRow,MatPosj, ResttoRight(0)));
gCompTris.push_back(Triplet<double>(CurrRow,MatPosj+1,ResttoRight(1)));
gCompTris.push_back(Triplet<double>(CurrRow,MatPosj+2,ResttoRight(2)));
gCompTris.push_back(Triplet<double>(CurrRow,MatPosj+3,ResttoRight(3)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosj, ResttoRight(1)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosj+1,-ResttoRight(0)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosj+2,-ResttoRight(3)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosj+3, ResttoRight(2)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosj, ResttoRight(2)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosj+1, ResttoRight(3)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosj+2,-ResttoRight(0)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosj+3,-ResttoRight(1)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosj, ResttoRight(3)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosj+1,-ResttoRight(2)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosj+2, ResttoRight(1)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosj+3,-ResttoRight(0)));
//Derivative by Gi, using rest to left as "e":
//[ re, -vex, -vey, -vez]
//[ vex, re, -vez, vey]
//[ vey, vez, re, -vex]
//[ vez, -vey, vex, re]
gCompTris.push_back(Triplet<double>(CurrRow,MatPosi, ResttoLeft(0)));
gCompTris.push_back(Triplet<double>(CurrRow,MatPosi+1,-ResttoLeft(1)));
gCompTris.push_back(Triplet<double>(CurrRow,MatPosi+2,-ResttoLeft(2)));
gCompTris.push_back(Triplet<double>(CurrRow,MatPosi+3,-ResttoLeft(3)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosi, ResttoLeft(1)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosi+1, ResttoLeft(0)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosi+2,-ResttoLeft(3)));
gCompTris.push_back(Triplet<double>(CurrRow+1,MatPosi+3, ResttoLeft(2)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosi, ResttoLeft(2)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosi+1, ResttoLeft(3)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosi+2, ResttoLeft(0)));
gCompTris.push_back(Triplet<double>(CurrRow+2,MatPosi+3,-ResttoLeft(1)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosi, ResttoLeft(3)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosi+1,-ResttoLeft(2)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosi+2, ResttoLeft(1)));
gCompTris.push_back(Triplet<double>(CurrRow+3,MatPosi+3, ResttoLeft(0)));
//Derivative with relation to positions
gCompTris.push_back(Triplet<double>(CurrRow+1,CurrGInv.size()+3*F(i,(j+1)%3), -1.0));
gCompTris.push_back(Triplet<double>(CurrRow+2,CurrGInv.size()+3*F(i,(j+1)%3)+1,-1.0));
gCompTris.push_back(Triplet<double>(CurrRow+3,CurrGInv.size()+3*F(i,(j+1)%3)+2,-1.0));
gCompTris.push_back(Triplet<double>(CurrRow+1,CurrGInv.size()+3*F(i,j), 1.0));
gCompTris.push_back(Triplet<double>(CurrRow+2,CurrGInv.size()+3*F(i,j)+1,1.0));
gCompTris.push_back(Triplet<double>(CurrRow+3,CurrGInv.size()+3*F(i,j)+2,1.0));
}
}
SparseMatrix<double> gCompFull(12*F.rows(), 3*OrigVq.rows()+CurrGInv.size());
SparseMatrix<double> gComp(12*F.rows(), 3*VarIndices.size()+CurrGInv.size());
gCompFull.setFromTriplets(gCompTris.begin(),gCompTris.end());
igl::slice(gCompFull,VarLocIndices, 2,gComp);
SparseMatrix<double> gLCR=CornerDiffLCRSmall*NormSumMatrix*SparseDiagonalMatrix<double>(2*CurrSolution);
SparseMatrix<double> Gradient=SparseBlock<double>(SparseBlock<double>(CloseFactor*IDMat, SmoothFactor*CornerDiffMat, false), SparseBlock<double>(gComp,gLCR, false),false);
return Gradient;
}
void Reformulate(int CurrIter, int MaxIterations, VectorXd CurrSolution){
}
double GetConstError(VectorXd CurrError)
{
return CurrError.lpNorm<Infinity>();
}
};*/
#endif