// This function is called every time a keyboard button is pressed
bool key_down(igl::viewer::Viewer& viewer, unsigned char key, int modifier)
{
using namespace std;
using namespace Eigen;
if (key >= '1' && key <= '9')
{
double t = double((key - '1')+1) / 9.0;
VectorXd v = B.col(2).array() - B.col(2).minCoeff();
v /= v.col(0).maxCoeff();
vector<int> s;
for (unsigned i=0; i<v.size();++i)
if (v(i) < t)
s.push_back(i);
MatrixXd V_temp(s.size()*4,3);
MatrixXi F_temp(s.size()*4,3);
for (unsigned i=0; i<s.size();++i)
{
V_temp.row(i*4+0) = TV.row(TT(s[i],0));
V_temp.row(i*4+1) = TV.row(TT(s[i],1));
V_temp.row(i*4+2) = TV.row(TT(s[i],2));
V_temp.row(i*4+3) = TV.row(TT(s[i],3));
F_temp.row(i*4+0) << (i*4)+0, (i*4)+1, (i*4)+3;
F_temp.row(i*4+1) << (i*4)+0, (i*4)+2, (i*4)+1;
F_temp.row(i*4+2) << (i*4)+3, (i*4)+2, (i*4)+0;
F_temp.row(i*4+3) << (i*4)+1, (i*4)+2, (i*4)+3;
}
viewer.data.clear();
viewer.data.set_mesh(V_temp,F_temp);
viewer.data.set_face_based(true);
}
return false;
}
void ConsistencyTest::printOBJ(int numberOfPrints, string printToHere, MatrixXd& cB, Simulation& cSim, MatrixXi& cTT){
double refinement = 9;
double t = ((refinement - 1)+1) / 9.0;
VectorXd v = cB.col(2).array() - cB.col(2).minCoeff();
v /= v.col(0).maxCoeff();
vector<int> s;
for (unsigned i=0; i<v.size();++i){
if (v(i) < t){
s.push_back(i);
}
}
MatrixXd V_temp(s.size()*4,3);
MatrixXi F_temp(s.size()*4,3);
for (unsigned i=0; i<s.size();++i)
{
V_temp.row(i*4+0) = cSim.integrator->TV.row(cSim.integrator->TT(s[i],0));
V_temp.row(i*4+1) = cSim.integrator->TV.row(cSim.integrator->TT(s[i],1));
V_temp.row(i*4+2) = cSim.integrator->TV.row(cSim.integrator->TT(s[i],2));
V_temp.row(i*4+3) = cSim.integrator->TV.row(cSim.integrator->TT(s[i],3));
F_temp.row(i*4+0) << (i*4)+0, (i*4)+1, (i*4)+3;
F_temp.row(i*4+1) << (i*4)+0, (i*4)+2, (i*4)+1;
F_temp.row(i*4+2) << (i*4)+3, (i*4)+2, (i*4)+0;
F_temp.row(i*4+3) << (i*4)+1, (i*4)+2, (i*4)+3;
}
cout<<printToHere + to_string(numberOfPrints)<<endl;
system(("mkdir -p "+printToHere).c_str());
igl::writeOBJ(printToHere + to_string(numberOfPrints)+".obj", V_temp, F_temp);
return;
}
// [[Rcpp::export]]
List wasserstein_auto_(NumericVector p_, NumericVector q_, NumericMatrix cost_matrix_,
double epsilon, double desired_alpha){
// compute distance between p and q
// p corresponds to the weights of a N-sample
// each q corresponds to the weights of a M-sample
// Thus cost_matrix must be a N x M cost matrix
// epsilon is a regularization parameter, equal to 1/lambda in some references
int N = p_.size();
int M = q_.size();
Map<VectorXd> p(as<Map<VectorXd> >(p_));
Map<VectorXd> q(as<Map<VectorXd> >(q_));
Map<MatrixXd> cost_matrix(as<Map<MatrixXd> >(cost_matrix_));
// avoid to take exp(k) when k is less than -500,
// as K then contains zeros, and then the upcoming computations divide by zero
MatrixXd K = (cost_matrix.array() * (-1./epsilon)); // K = exp(- M / epsilon)
for (int i = 0; i < N; i++){
for (int j = 0; j < M; j++){
if (K(i,j) < -500){
K(i,j) = exp(-500);
} else {
K(i,j) = exp(K(i,j));
}
}
}
MatrixXd K_transpose = K.transpose();
MatrixXd K_tilde = p.array().inverse().matrix().asDiagonal() * K; // diag(1/p) %*% K
VectorXd u = VectorXd::Constant(N, 1./N);
//
VectorXd marginal1, marginal2;
MatrixXd transportmatrix;
VectorXd v;
double alpha = 0;
double beta = 0;
int niterations_max = 1000;
int iteration = 0;
// for (int iteration = 0; iteration < niterations; iteration ++){
while ((iteration < niterations_max) and (alpha < desired_alpha)){
iteration ++;
u = 1. / (K_tilde * (q.array() / (K_transpose * u).array()).matrix()).array();
if (iteration % 10 == 1){
// check if criterion is satisfied
v = q.array() / (K_transpose * u).array();
transportmatrix = u.col(0).asDiagonal() * K * v.col(0).asDiagonal();
marginal1 = transportmatrix.rowwise().sum();
marginal2 = transportmatrix.colwise().sum();
alpha = 10;
for (int i = 0; i < N; i++){
beta = std::min(p(i) / marginal1(i), q(i) / marginal2(i));
alpha = std::min(alpha, beta);
}
// cerr << "alpha = " << alpha << endl;
}
}
v = q.array() / (K_transpose * u).array();
// compute the optimal transport matrix between p and the first q
transportmatrix = u.col(0).asDiagonal() * K * v.col(0).asDiagonal();
// MatrixXd uXIv = u.array() * ((K.array() * cost_matrix.array()).matrix() * v).array();
// NumericVector d = wrap(uXIv.colwise().sum());
return List::create(Named("transportmatrix") = wrap(transportmatrix),
Named("u") = wrap(u),
Named("v") = wrap(v),
Named("iteration") = iteration);
}