IGL_INLINE void igl::polar_dec(
const Eigen::PlainObjectBase<DerivedA> & A,
Eigen::PlainObjectBase<DerivedR> & R,
Eigen::PlainObjectBase<DerivedT> & T,
Eigen::PlainObjectBase<DerivedU> & U,
Eigen::PlainObjectBase<DerivedS> & S,
Eigen::PlainObjectBase<DerivedV> & V)
{
using namespace std;
using namespace Eigen;
typedef typename DerivedA::Scalar Scalar;
const Scalar th = std::sqrt(Eigen::NumTraits<Scalar>::dummy_precision());
Eigen::SelfAdjointEigenSolver<DerivedA> eig;
feclearexcept(FE_UNDERFLOW);
eig.computeDirect(A.transpose()*A);
if(fetestexcept(FE_UNDERFLOW) || eig.eigenvalues()(0)/eig.eigenvalues()(2)<th)
{
cout<<"resorting to svd 1..."<<endl;
return polar_svd(A,R,T,U,S,V);
}
S = eig.eigenvalues().cwiseSqrt();
V = eig.eigenvectors();
U = A * V;
R = U * S.asDiagonal().inverse() * V.transpose();
T = V * S.asDiagonal() * V.transpose();
S = S.reverse().eval();
V = V.rowwise().reverse().eval();
U = U.rowwise().reverse().eval() * S.asDiagonal().inverse();
if(R.determinant() < 0)
{
// Annoyingly the .eval() is necessary
auto W = V.eval();
const auto & SVT = S.asDiagonal() * V.adjoint();
W.col(V.cols()-1) *= -1.;
R = U*W.transpose();
T = W*SVT;
}
if(std::fabs(R.squaredNorm()-3.) > th)
{
cout<<"resorting to svd 2..."<<endl;
return polar_svd(A,R,T,U,S,V);
}
}
