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; }