template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
{
EigenSolver<MatrixType> eig;
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
VERIFY_RAISES_ASSERT(eig.eigenvalues());
MatrixType a = MatrixType::Random(m.rows(),m.cols());
eig.compute(a, false);
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
}
SGMatrix<float64_t> CUWedge::diagonalize(SGNDArray<float64_t> C, SGMatrix<float64_t> V0,
double eps, int itermax)
{
int d = C.dims[0];
int L = C.dims[2];
SGMatrix<float64_t> V;
if (V0.num_rows == d && V0.num_cols == d)
{
V = V0.clone();
}
else
{
Map<MatrixXd> C0(C.get_matrix(0),d,d);
EigenSolver<MatrixXd> eig;
eig.compute(C0);
// sort eigenvectors
MatrixXd eigenvectors = eig.pseudoEigenvectors();
MatrixXd eigenvalues = eig.pseudoEigenvalueMatrix();
bool swap = false;
do
{
swap = false;
for (int j = 1; j < d; j++)
{
if ( eigenvalues(j,j) > eigenvalues(j-1,j-1) )
{
std::swap(eigenvalues(j,j),eigenvalues(j-1,j-1));
eigenvectors.col(j).swap(eigenvectors.col(j-1));
swap = true;
}
}
} while(swap);
V = SGMatrix<float64_t>::create_identity_matrix(d,1);
Map<MatrixXd> EV(V.matrix, d,d);
EV = eigenvalues.cwiseAbs().cwiseSqrt().inverse() * eigenvectors.transpose();
}
Map<MatrixXd> EV(V.matrix, d,d);
index_t * Cs_dims = SG_MALLOC(index_t, 3);
Cs_dims[0] = d;
Cs_dims[1] = d;
Cs_dims[2] = L;
SGNDArray<float64_t> Cs(Cs_dims,3);
sg_memcpy(Cs.array, C.array, Cs.dims[0]*Cs.dims[1]*Cs.dims[2]*sizeof(float64_t));
MatrixXd Rs(d,L);
std::vector<float64_t> crit;
crit.push_back(0.0);
for (int l = 0; l < L; l++)
{
Map<MatrixXd> Ci(C.get_matrix(l),d,d);
Map<MatrixXd> Csi(Cs.get_matrix(l),d,d);
Ci = 0.5 * (Ci + Ci.transpose());
Csi = EV * Ci * EV.transpose();
Rs.col(l) = Csi.diagonal();
crit.back() += Csi.cwiseAbs2().sum() - Rs.col(l).cwiseAbs2().sum();
}
float64_t iter = 0;
float64_t improve = 10;
while (improve > eps && iter < itermax)
{
MatrixXd B = Rs * Rs.transpose();
MatrixXd C1 = MatrixXd::Zero(d,d);
for (int id = 0; id < d; id++)
{
// rowSums
for (int l = 0; l < L; l++)
{
Map<MatrixXd> Csi(Cs.get_matrix(l),d,d);
C1.row(id) += Csi.row(id) * Rs(id,l);
}
}
MatrixXd D0 = B.cwiseProduct(B.transpose()) - B.diagonal() * B.diagonal().transpose();
MatrixXd A0 = MatrixXd::Identity(d,d) + (C1.cwiseProduct(B) - B.diagonal().asDiagonal() * C1.transpose()).cwiseQuotient(D0+MatrixXd::Identity(d,d));
EV = A0.inverse() * EV;
Map<MatrixXd> C0(C.get_matrix(0),d,d);
MatrixXd Raux = EV * C0 * EV.transpose();
MatrixXd aux = Raux.diagonal().cwiseAbs().cwiseSqrt().asDiagonal().inverse();
EV = aux * EV;
crit.push_back(0.0);
for (int l = 0; l < L; l++)
{
Map<MatrixXd> Ci(C.get_matrix(l),d,d);
Map<MatrixXd> Csi(Cs.get_matrix(l),d,d);
Csi = EV * Ci * EV.transpose();
Rs.col(l) = Csi.diagonal();
crit.back() += Csi.cwiseAbs2().sum() - Rs.col(l).cwiseAbs2().sum();
}
improve = CMath::abs(crit.back() - crit[iter]);
iter++;
}
if (iter == itermax)
SG_SERROR("Convergence not reached\n")
return V;
}