bool Polygon::convertToInequalityConstraints(Eigen::MatrixXd& A, Eigen::VectorXd& b) const
{
Eigen::MatrixXd V(nVertices(), 2);
for (unsigned int i = 0; i < nVertices(); ++i)
V.row(i) = vertices_[i];
// Create k, a list of indices from V forming the convex hull.
// TODO: Assuming counter-clockwise ordered convex polygon.
// MATLAB: k = convhulln(V);
Eigen::MatrixXi k;
k.resizeLike(V);
for (unsigned int i = 0; i < V.rows(); ++i)
k.row(i) << i, (i+1) % V.rows();
Eigen::RowVectorXd c = V.colwise().mean();
V.rowwise() -= c;
A = Eigen::MatrixXd::Constant(k.rows(), V.cols(), NAN);
unsigned int rc = 0;
for (unsigned int ix = 0; ix < k.rows(); ++ix) {
Eigen::MatrixXd F(2, V.cols());
F.row(0) << V.row(k(ix, 0));
F.row(1) << V.row(k(ix, 1));
Eigen::FullPivLU<Eigen::MatrixXd> luDecomp(F);
if (luDecomp.rank() == F.rows()) {
A.row(rc) = F.colPivHouseholderQr().solve(Eigen::VectorXd::Ones(F.rows()));
++rc;
}
}
A = A.topRows(rc);
b = Eigen::VectorXd::Ones(A.rows());
b = b + A * c.transpose();
return true;
}
Eigen::VectorXd
l2r_l1hinge_spdc::convert_w2alpha(const Eigen::VectorXd &alp) const {
Eigen::RowVectorXd w = Eigen::RowVectorXd::Zero(num_fea_);
if (num_ins_ < alp.size()) {
for (int i = 0; i < num_ins_; ++i)
if (alp[i] > 0.0)
w += (alp[i] * y_[i]) * x_.row(i);
} else {
for (int i = 0; i < alp.size(); ++i)
if (alp[i] > 0.0)
w += (alp[i] * y_[i]) * x_.row(i);
}
return w.transpose();
}