double computeLoss() {
// compute loss w.r.t to oracle hypothesis and current weights w
assert(oracle);
if (hope_select==1)
loss = (features.dot(w) + cost) - (oracle->features.dot(w) - oracle->cost);
else
loss = (features.dot(w) + cost) - (oracle->features.dot(w));
if (loss < 0) {
cerr << "Warning! Loss < 0! this_score=" << features.dot(w) << " oracle_score=" << oracle->features.dot(w) << " this_cost=" << cost << " oracle_cost=" << oracle->cost << endl;
loss = 0;
}
return loss;
}
Vec RQR_Multiply(const VECTOR &v,
const SparseKalmanMatrix &RQR,
const SparseVector &Z,
double H) {
int state_dim = Z.size();
if(v.size() != state_dim + 2) {
report_error("wrong sizes in RQR_Multiply");
}
// Partition v = [eta, epsilon, 0]
ConstVectorView eta(v, 0, state_dim);
double epsilon = v[state_dim];
// Partition this
Vec RQRZ = RQR * Z.dense();
double ZRQRZ_plus_H = Z.dot(RQRZ) + H;
Vec ans(v.size());
VectorView(ans, 0, state_dim) = (RQR * eta).axpy(RQRZ, epsilon);
ans[state_dim] = RQRZ.dot(eta) + ZRQRZ_plus_H * epsilon;
return ans;
}
// partial reorthogonalization
double EigenTriangle::solve(int maxIter, double tol)
{
int n = graph -> VertexCount();
srand(time(0));
if (maxIter > n)
maxIter = n;
double na = adjMatrix.norm();
double phi = tol * na;
double delta = tol * sqrt(na);
vector<Triplet<double> > omega_vector;
//MatrixXd omega = MatrixXd::Zero(n + 2, n + 2);
for (int i = 0; i < n + 2; i ++)
{
//omega(i, i - 1) = phi;
if (i > 0)
omega_vector.push_back(Triplet<double>(i, i - 1, phi));
omega_vector.push_back(Triplet<double>(i, i, 1));
}
omega.resize(n + 2, n + 2);
omega.setFromTriplets(omega_vector.begin(), omega_vector.end());
//std::cout << omega << std::endl;
vector<SparseVector<double> > v;
//v.push_back(SparseVector::Random(n));
SparseVector<double> firstV(n);
for (int i = 0; i < 100; i ++)
firstV.coeffRef(i % n) = i;
v.push_back(firstV);
v[0] /= v[0].norm();
VectorXd alpha(n);
VectorXd beta(n + 1);
beta[0] = 0;
SparseVector<double> w;
bool flag = false;
int num = 0; // reorthogonalization times
int last = -1;
for (int i = 0; i < maxIter; i ++)
{
if ((i + 1) * 100 / maxIter > last)
{
last = (i + 1) * 100 / maxIter;
std::cout << "\r" << "[EigenTriangle] Processing " << last << "% ..." << std::flush;
}
//printf("== Iter %d ===\n", i);
w = adjMatrix * v[i];
alpha.coeffRef(i) = w.dot(v[i]);
if (i == maxIter - 1)
break;
w -= alpha[i] * v[i];
if (i > 0)
w -= beta[i] * v[i - 1];
beta[i + 1] = w.norm();
v.push_back(w / beta[i + 1]);
if (flag)
{
flag = false;
for (int j = 0; j <= i; j ++)
v[i + 1] -= v[j].dot(v[i + 1]) * v[j];
for (int j = 0; j <= i; j ++)
omega.coeffRef(i + 1, j) = phi;
//for (int j = 0; j <= i; j ++)
// printf("%.5lf\n", v[i + 1].dot(v[j]));
}
else
{
omega.coeffRef(i + 1, 0) = 0.0;
if (i > 0)
{
omega.coeffRef(i + 1, 0) = 1.0 / beta(i) * ((alpha(0) - alpha(i)) * omega.coeffRef(i, 0) - beta(i - 1) * omega.coeffRef(i - 1, 0)) + delta;
}
for (int j = 1; j <= i; j ++)
{
omega.coeffRef(i + 1, j) = 1.0 / beta(i) * (beta(j) * omega.coeffRef(i, j + 1) + (alpha(j) - alpha(i)) * omega.coeffRef(i, j) - beta(j - 1) * omega.coeffRef(i, j - 1) - beta(i - 1) * omega.coeffRef(i - 1, j)) + delta;
}
}
double mx = 0.0;
for (int j = 0; j <= i; j ++)
if (mx < fabs(omega.coeffRef(i + 1, j)))
mx = fabs(omega.coeffRef(i + 1, j));
if (mx > sqrt(tol))
{
for (int j = 0; j <= i; j ++)
omega.coeffRef(i + 1, j) = phi;
num ++;
for (int j = 0; j <= i; j ++)
v[i + 1] -= v[i + 1].dot(v[j]) * v[j];
flag = true;
}
}
printf("\n");
int k = maxIter;
MatrixXd T = MatrixXd::Zero(k, k);
for (int i = 0; i < k; i ++)
{
T(i, i) = alpha[i];
if (i < k - 1)
T(i, i + 1) = beta[i + 1];
if (i > 0)
T(i, i - 1) = beta[i];
}
//std::cout << T << std::endl;
Eigen::EigenSolver<MatrixXd> eigenSolver;
eigenSolver.compute(T, false);
Eigen::VectorXcd eigens = eigenSolver.eigenvalues();
double res = 0;
for (int i = 0; i < eigens.size(); i ++)
{
std::complex<double> tmp = eigens[i];
res += pow(tmp.real(), 3) / 6;
std::cout << i << ": " << tmp << std::endl;
}
//res /= 6;
return res;
}