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solver.h
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solver.h
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#include "mesh.h"
#include "arap.h"
#include "elastic.h"
#include <LBFGS.h>
using namespace LBFGSpp;
using json = nlohmann::json;
using namespace Eigen;
using namespace std;
class Rosenbrock
{
private:
int n;
Mesh* mesh;
Arap* arap;
Elastic* elas;
double alpha_arap = 1;
double alpha_neo = 1;
double eps = 1.5e-8;
bool stest = false;
public:
Rosenbrock(int n_, Mesh* m, Arap* a, Elastic* e, json& j_input, bool test=false) : n(n_) {
mesh = m;
arap = a;
elas = e;
alpha_arap = j_input["alpha_arap"];
alpha_neo = j_input["alpha_neo"];
stest = test;
}
VectorXd get_w(VectorXd& r0, VectorXd& r){
VectorXd w = VectorXd::Zero(r0.size()/3);
for(int i=0; i<r0.size()/9; i++){
Matrix3d R0, R;
R0<<r0[9*i+0],r0[9*i+1],r0[9*i+2],
r0[9*i+3],r0[9*i+4],r0[9*i+5],
r0[9*i+6],r0[9*i+7],r0[9*i+8];
R<<r[9*i+0],r[9*i+1],r[9*i+2],
r[9*i+3],r[9*i+4],r[9*i+5],
r[9*i+6],r[9*i+7],r[9*i+8];
Matrix3d exp_brac_w = R0.transpose()*R;
Matrix3d brac_w = exp_brac_w.log();
w[3*i+0] = brac_w(2,1);
w[3*i+1] = brac_w(0,2);
w[3*i+2] = brac_w(1,0);
}
return w;
}
//CHECK E,x-------------
VectorXd Ex(Mesh& mesh, Arap& arap, double E0, double eps){
VectorXd z = mesh.red_x();
VectorXd fake = VectorXd::Zero(z.size());
#pragma omp parallel for
for(int i=0; i<fake.size(); i++){
z[i] += 0.5*eps;
double Eleft = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[i] -= 0.5*eps;
z[i] -= 0.5*eps;
double Eright = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[i] += 0.5*eps;
fake[i] = (Eleft - Eright)/eps;
}
return fake;
}
//-----------------------
//CHECK E,r-------------
VectorXd Er(Mesh& mesh, Arap& arap, double E0, double eps){
VectorXd z = mesh.red_x();
VectorXd fake = VectorXd::Zero(mesh.red_w().size());
for(int i=0; i<fake.size(); i++){
mesh.red_w()[i] += 0.5*eps;
// mesh.setGlobalF(true, false, false);
double Eleft = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[i] -= 0.5*eps;
mesh.red_w()[i] -= 0.5*eps;
// mesh.setGlobalF(true, false, false);
double Eright = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[i] += 0.5*eps;
fake[i] = (Eleft - Eright)/(eps);
}
// mesh.setGlobalF(true, false, false);
return fake;
}
//-----------------------
//CHECK E,s-------------
VectorXd Es(Mesh& mesh, Arap& arap, double E0, double eps){
VectorXd z = mesh.red_x();
VectorXd fake = VectorXd::Zero(mesh.red_s().size());
for(int i=0; i<fake.size(); i++){
mesh.red_s()[i] += 0.5*eps;
// mesh.setGlobalF(false, true, false);
double Eleft = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_s()[i] -= 0.5*eps;
mesh.red_s()[i] -= 0.5*eps;
// mesh.setGlobalF(false, true, false);
double Eright = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_s()[i] += 0.5*eps;
fake[i] = (Eleft - Eright)/eps;
}
// mesh.setGlobalF(false, true, false);
return fake;
}
//-----------------------
//CHECK Exx--------------
MatrixXd Exx(Mesh& mesh, Arap& arap, double E0, double eps){
MatrixXd fake = MatrixXd::Zero(mesh.red_x().size(), mesh.red_x().size());
VectorXd z = mesh.red_x();
for(int i=0; i<fake.rows(); i++){
for(int j=0; j<fake.cols(); j++){
z[i] += eps;
z[j] += eps;
double Eij = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[i] -= eps;
z[j] -= eps;
z[i] += eps;
double Ei = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[i] -= eps;
z[j] += eps;
double Ej = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[j] -= eps;
fake(i,j) = ((Eij - Ei - Ej + E0)/(eps*eps));
}
}
return fake;
}
//-----------------------
//CHECK Exr/Erx-------------
MatrixXd Exr(Mesh& mesh, Arap& arap, double E0, double eps){
MatrixXd fake = MatrixXd::Zero(mesh.red_x().size(), mesh.red_w().size());
VectorXd z = mesh.red_x();
for(int i=0; i<fake.rows(); i++){
for(int j=0; j<fake.cols(); j++){
mesh.red_w()[j] += eps;
z[i] += eps;
// mesh.setGlobalF(true, false, false);
double Eij = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[j] -= eps;
z[i] -= eps;
mesh.red_w()[j] += eps;
// mesh.setGlobalF(true, false, false);
double Ei = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[j] -= eps;
z[i] += eps;
// mesh.setGlobalF(true, false, false);
double Ej = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[i] -= eps;
fake(i,j) = ((Eij - Ei - Ej + E0)/(eps*eps));
}
}
// mesh.setGlobalF(true, false, false);
return fake;
}
//-----------------------
//CHECK Exs-------------
MatrixXd Exs(Mesh& mesh, Arap& arap, double E0, double eps){
MatrixXd fake = MatrixXd::Zero(mesh.red_x().size(), mesh.red_s().size());
VectorXd z = mesh.red_x();
for(int i=0; i<fake.rows(); i++){
for(int j=0; j<fake.cols(); j++){
mesh.red_s()[j] += eps;
z[i] += eps;
// mesh.setGlobalF(false, true, false);
double Eij = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_s()[j] -= eps;
z[i] -= eps;
mesh.red_s()[j] += eps;
// mesh.setGlobalF(false, true, false);
double Ei = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_s()[j] -= eps;
z[i] += eps;
// mesh.setGlobalF(false, true, false);
double Ej = arap.Energy(mesh, z, mesh.red_w(), mesh.red_r(), mesh.red_s());
z[i] -= eps;
fake(i,j) = ((Eij - Ei - Ej + E0)/(eps*eps));
}
}
// mesh.setGlobalF(false, true, false);
return fake;
}
//-----------------------
//CHECK Err--------------
MatrixXd Err(Mesh& mesh, Arap& arap, double E0, double eps){
MatrixXd fake = MatrixXd::Zero(mesh.red_w().size(), mesh.red_w().size());
for(int i=0; i<fake.rows(); i++){
for(int j=0; j<fake.cols(); j++){
mesh.red_w()[j] += eps;
mesh.red_w()[i] += eps;
// mesh.setGlobalF(true, false, false);
double Eij = arap.Energy(mesh, mesh.red_x(), mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[j] -= eps;
mesh.red_w()[i] -= eps;
mesh.red_w()[j] += eps;
// mesh.setGlobalF(true, false, false);
double Ei = arap.Energy(mesh, mesh.red_x(), mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[j] -= eps;
mesh.red_w()[i] += eps;
// mesh.setGlobalF(true, false, false);
double Ej = arap.Energy(mesh, mesh.red_x(), mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[i] -= eps;
fake(i,j) = ((Eij - Ei - Ej + E0)/(eps*eps));
}
}
// mesh.setGlobalF(true, false, false);
return fake;
}
//-----------------------
//CHECK Ers--------------
MatrixXd Ers(Mesh& mesh, Arap& arap, double E0, double eps){
MatrixXd fake = MatrixXd::Zero(mesh.red_w().size(), mesh.red_s().size());
for(int i=0; i<fake.rows(); i++){
for(int j=0; j<fake.cols(); j++){
mesh.red_w()[i] += eps;
mesh.red_s()[j] += eps;
// mesh.setGlobalF(true, true, false);
double Eij = arap.Energy(mesh, mesh.red_x(), mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_s()[j] -= eps;
mesh.red_w()[i] -= eps;
mesh.red_w()[i] += eps;
// mesh.setGlobalF(true, true, false);
double Ei = arap.Energy(mesh, mesh.red_x(), mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_w()[i] -= eps;
mesh.red_s()[j] += eps;
// mesh.setGlobalF(true, true, false);
double Ej = arap.Energy(mesh, mesh.red_x(), mesh.red_w(), mesh.red_r(), mesh.red_s());
mesh.red_s()[j] -= eps;
fake(i,j) = ((Eij - Ei - Ej + E0)/(eps*eps));
}
}
// mesh.setGlobalF(true, true, false);
return fake;
}
//-----------------------
VectorXd Full_ARAP_Grad(Mesh& mesh, Arap& arap, Elastic& elas, double E0, double eps){
VectorXd fake = VectorXd::Zero(mesh.red_s().size());
for(int i=0; i<fake.size(); i++){
mesh.red_s()[i] += 0.5*eps;
// mesh.setGlobalF(false, true, false);
arap.minimize(mesh);
double Eleft = alpha_arap*arap.Energy(mesh);
mesh.red_s()[i] -= 0.5*eps;
mesh.red_s()[i] -= 0.5*eps;
// mesh.setGlobalF(false, true, false);
arap.minimize(mesh);
double Eright = alpha_arap*arap.Energy(mesh);
mesh.red_s()[i] += 0.5*eps;
fake[i] = (Eleft - Eright)/eps;
}
arap.minimize(mesh);
// mesh.setGlobalF(false, true, false);
// std::cout<<"FUll fake: "<<fake.transpose()<<std::endl;
return fake;
}
// VectorXd Full_NEO_Grad(Mesh& mesh, Arap& arap, Elastic& elas, double E0, double eps){
// VectorXd fake = VectorXd::Zero(mesh.red_s().size());
// for(int i=0; i<fake.size(); i++){
// mesh.red_s()[i] += 0.5*eps;
// // mesh.setGlobalF(false, true, false);
// double Eleft = alpha_neo*elas.Energy(mesh);
// mesh.red_s()[i] -= 0.5*eps;
// mesh.red_s()[i] -= 0.5*eps;
// // mesh.setGlobalF(false, true, false);
// double Eright = alpha_neo*elas.Energy(mesh);
// mesh.red_s()[i] += 0.5*eps;
// fake[i] = (Eleft - Eright)/eps;
// }
// // mesh.setGlobalF(false, true, false);
// // std::cout<<"FUll fake: "<<fake.transpose()<<std::endl;
// return fake;
// }
VectorXd WikipediaEnergy_grad(Mesh& mesh, Elastic& elas, double eps){
VectorXd fake = VectorXd::Zero(mesh.red_s().size());
for(int i=0; i<fake.size(); i++){
mesh.red_s()[i] += 0.5*eps;
double Eleft = elas.WikipediaEnergy(mesh);
mesh.red_s()[i] -= 0.5*eps;
mesh.red_s()[i] -= 0.5*eps;
double Eright = elas.WikipediaEnergy(mesh);
mesh.red_s()[i] += 0.5*eps;
fake[i] = (Eleft - Eright)/eps;
}
// mesh.setGlobalF(false, true, false);
// std::cout<<"FUll fake: "<<fake.transpose()<<std::endl;
return fake;
}
double operator()(const VectorXd& x, VectorXd& grad, bool computeGrad = true)
{
VectorXd reds = mesh->N()*x + mesh->AN()*mesh->AN().transpose()*mesh->red_s();
for(int i=0; i<reds.size(); i++){
mesh->red_s()[i] = reds[i];
}
double Eneo = alpha_neo*elas->Energy(*mesh);
int arap_iters = arap->minimize(*mesh);
double Earap = alpha_arap*arap->Energy(*mesh);
double fx = Eneo + Earap;
if(computeGrad){
VectorXd pegrad = alpha_neo*mesh->N().transpose()*elas->PEGradient(*mesh);
VectorXd arapgrad = alpha_arap*mesh->N().transpose()*arap->dEds(*mesh);
if(stest){
VectorXd fake_arap = mesh->N().transpose()*Full_ARAP_Grad(*mesh, *arap,*elas, fx, eps);
if ((arapgrad-fake_arap).norm()>10){
double E0 = arap->Energy(*mesh);
std::cout<<"fake arap issues"<<std::endl;
std::cout<<arapgrad.transpose()<<std::endl<<std::endl;
std::cout<<fake_arap.transpose()<<std::endl<<std::endl;
cout<<"s"<<endl;
std::cout<<x.transpose()<<endl<<endl;
cout<<"r"<<endl;
cout<<mesh->red_r().transpose()<<endl<<endl;
cout<<"x"<<endl;
cout<<mesh->red_x().transpose()<<endl<<endl;
cout<<"-------------------------------------"<<endl;
cout<<"Ex"<<endl;
VectorXd fakeEx = Ex(*mesh, *arap, E0, eps);
cout<<(arap->Ex().transpose()-fakeEx.transpose()).norm()<<endl<<endl;
cout<<"Er"<<endl;
VectorXd fakeEr = Er(*mesh, *arap, E0, eps);
cout<<(arap->Er().transpose()-fakeEr.transpose()).norm()<<endl<<endl;
cout<<"Es"<<endl;
VectorXd fakeEs = Es(*mesh, *arap,E0, eps);
cout<<(arap->Es().transpose() - fakeEs.transpose()).norm()<<endl<<endl;
MatrixXd fakeExx = Exx(*mesh, *arap, E0, eps);
cout<<"Exx"<<endl;
cout<<(fakeExx-MatrixXd(arap->Exx())).norm()<<endl<<endl;
cout<<endl<<endl;
MatrixXd fakeExr = Exr(*mesh, *arap, E0, eps);
cout<<"Exr"<<endl;
cout<<(fakeExr-MatrixXd(arap->Exr())).norm()<<endl<<endl;
cout<<endl<<endl;
cout<<"Exs"<<endl;
MatrixXd fakeExs = Exs(*mesh, *arap, E0, eps);
cout<<(fakeExs-MatrixXd(arap->Exs())).norm()<<endl<<endl;
cout<<endl;
cout<<"Err"<<endl;
MatrixXd fakeErr = Err(*mesh, *arap, E0, eps);
cout<<(fakeErr-MatrixXd(arap->Err())).norm()<<endl<<endl;
cout<<endl;
cout<<"Ers"<<endl;
MatrixXd fakeErs = Ers(*mesh, *arap, E0, eps);
cout<<(fakeErs-MatrixXd(arap->Ers())).norm()<<endl<<endl;
cout<<endl;
exit(0);
}
}
// VectorXd fake = alpha_neo*WikipediaEnergy_grad(*mesh, *elas, 1e-5);
// if ((pegrad-fake_neo).norm()>0.001){
// std::cout<<"fake physics issues"<<std::endl;
// std::cout<<x.transpose()<<std::endl;
// std::cout<<arapgrad.transpose()<<std::endl<<std::endl;
// std::cout<<fake_neo.transpose()<<std::endl<<std::endl;
// exit(0);
// }
for(int i=0; i< x.size(); i++){
grad[i] = pegrad[i];
grad[i] += arapgrad[i];
}
std::cout<<"BFGS: "<<Eneo<<", "<<Earap<<", "<<pegrad.norm()<<", "<<arapgrad.norm()<<","<<grad.norm()<<std::endl;
}
return fx;
}
};