Exemple #1
0
	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;
}