VecF32 LinearAlgebra::eigenValue(const Mat2x<F32,2,2> &m){
F32 T = m.trace();
F32 D = m.determinant();
F32 sum = T*T/4 -D;
VecF32 eigen_value(2);
if(sum>0)
{
sum = std::sqrt(sum);
eigen_value(0) = T/2 + (sum);
eigen_value(1) = T/2 - (sum);
return eigen_value;
}else{
return VecF32();
}
}
void
Element::polarDecompositionEigen( const ColumnMajorMatrix & Fhat, ColumnMajorMatrix & Rhat, SymmTensor & strain_increment )
{
const int ND = 3;
ColumnMajorMatrix eigen_value(ND,1), eigen_vector(ND,ND);
ColumnMajorMatrix invUhat(ND,ND), logVhat(ND,ND);
ColumnMajorMatrix n1(ND,1), n2(ND,1), n3(ND,1), N1(ND,1), N2(ND,1), N3(ND,1);
ColumnMajorMatrix Chat = Fhat.transpose() * Fhat;
Chat.eigen(eigen_value,eigen_vector);
for(int i = 0; i < ND; i++)
{
N1(i) = eigen_vector(i,0);
N2(i) = eigen_vector(i,1);
N3(i) = eigen_vector(i,2);
}
const Real lamda1 = std::sqrt(eigen_value(0));
const Real lamda2 = std::sqrt(eigen_value(1));
const Real lamda3 = std::sqrt(eigen_value(2));
const Real log1 = std::log(lamda1);
const Real log2 = std::log(lamda2);
const Real log3 = std::log(lamda3);
ColumnMajorMatrix Uhat = N1 * N1.transpose() * lamda1 + N2 * N2.transpose() * lamda2 + N3 * N3.transpose() * lamda3;
invertMatrix(Uhat,invUhat);
Rhat = Fhat * invUhat;
strain_increment = N1 * N1.transpose() * log1 + N2 * N2.transpose() * log2 + N3 * N3.transpose() * log3;
}
