Exemple #1
0
static const Eigen::MatrixXcd executeEigenSolver(const QList< Analitza::Expression >& args, bool computeEigenvectors, QStringList &errors)
{
    const int nargs = args.size();
    
    if (nargs != 1) {
        errors.append(QCoreApplication::tr("Invalid parameter count for '%1'. Should have 1 parameter").arg(EigenvaluesCommand::id));
        
        return Eigen::MatrixXcd();
    }
    
    const Analitza::Matrix *matrix = static_cast<const Analitza::Matrix*>(args.first().tree());
    
    if (!matrix->isSquare()) {
        errors.append(QCoreApplication::tr("To use '%1' command the input matrix must be square").arg(EigenvaluesCommand::id));
        
        return Eigen::MatrixXcd();
    }
    
    const int m = matrix->rowCount();
    const int n = matrix->columnCount();
    
    Eigen::MatrixXd realmatrix(m, n);
    
    for (int i = 0; i < m; ++i) {
        for (int j = 0; j < n; ++j) {
            if (matrix->at(i,j)->type() == Analitza::Object::value) {
                const Analitza::Cn *entry = static_cast<const Analitza::Cn*>(matrix->at(i,j));
                const Analitza::Cn::ValueFormat entryformat = entry->format();
                
                //Don't allow complex numbers
                if (entryformat == Analitza::Cn::Char || entryformat == Analitza::Cn::Real || 
                    entryformat == Analitza::Cn::Integer || entryformat == Analitza::Cn::Boolean) {
                        realmatrix(i,j) = entry->value();
                } else {
                    errors.append(QCoreApplication::tr("Invalid parameter type in matrix entry (%1,%2) for '%3', it must be a number value")
                                 .arg(i).arg(j).arg(EigenvaluesCommand::id));
                    
                    return Eigen::MatrixXcd();
                }
            } else {
                errors.append(QCoreApplication::tr("Invalid parameter type in matrix entry (%1,%2) for '%3', it must be a number value")
                .arg(i).arg(j).arg(EigenvaluesCommand::id));
                
                return Eigen::MatrixXcd();
            }
        }
    }
    
    Q_ASSERT(nargs > 0);
    
    Eigen::EigenSolver<Eigen::MatrixXd> eigensolver;
    eigensolver.compute(realmatrix, computeEigenvectors);
    
    Eigen::MatrixXcd ret;
    
    if (computeEigenvectors)
        ret = eigensolver.eigenvectors();
    else
        ret = eigensolver.eigenvalues();
    
    return ret;
}
// full reorthogonalization
double                  EigenTriangle::solve(int maxIter)
{
    int n = graph -> VertexCount();
    srand(time(0));
    // check if rows == cols()
    if (maxIter > n)
        maxIter = n;
    vector<VectorXd> v;
    v.push_back(VectorXd::Random(n));
    v[0] = v[0] / v[0].norm();
    VectorXd alpha(n);
    VectorXd beta(n + 1);
    beta[0] = 0;
    VectorXd w;
    int last = 0;
    printf("%d\n", maxIter);
    for (int i = 0; i < maxIter; i ++)
    {
        if (i * 100 / maxIter > last + 10 || i == maxIter - 1)
        {
            last = (i + 1) * 100 / maxIter;
            std::cout << "\r" << "[EigenTriangle] Processing " << last << "% ..." << std::flush;
        }
        w = adjMatrix * v[i];
        alpha[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]);
        for (int j = 0; j <= i; j ++)
        {
            v[i + 1] = v[i + 1] - v[i + 1].dot(v[j]) * v[j];
        }
    }
    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, /* computeEigenvectors = */ 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);
        printf("%.5lf\n", tmp.real());
    }
    res /= 6;
    return res;
}
// 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;
}
void
approx_relpose_generalized
(
    const Eigen::Matrix<double,6,6> &w1,
    const Eigen::Matrix<double,6,6> &w2,
    const Eigen::Matrix<double,6,6> &w3,
    const Eigen::Matrix<double,6,6> &w4,
    const Eigen::Matrix<double,6,6> &w5,
    const Eigen::Matrix<double,6,6> &w6,
    std::vector<Eigen::Vector3d> &rsolns
)
{

    const Eigen::Matrix<double,15,35> A = computeA(w1,w2,w3,w4,w5,w6);
    Eigen::Matrix<double,15,35> gbA;
    gbA << A.col(0),A.col(1),A.col(2),A.col(3),A.col(4),A.col(5),A.col(7),A.col(9),A.col(11),A.col(15),A.col(18),A.col(21),A.col(24),A.col(28),A.col(13),A.col(6),A.col(8),A.col(10),A.col(12),A.col(16),A.col(19),A.col(22),A.col(25),A.col(29),A.col(14),A.col(17),A.col(20),A.col(23),A.col(26),A.col(30),A.col(32),A.col(27),A.col(31),A.col(33),A.col(34);

    const Eigen::Matrix<double,15,20> G = gbA.block<15,15>(0,0).lu().solve(gbA.block<15,20>(0,15));

    Eigen::Matrix<double,20,20> M = Eigen::Matrix<double,20,20>::Zero();
    M.block<10,20>(0,0) = -G.block<10,20>(5,0);
    M(10,4) = 1;
    M(11,5) = 1;
    M(12,6) = 1;
    M(13,7) = 1;
    M(14,8) = 1;
    M(15,9) = 1;
    M(16,13) = 1;
    M(17,14) = 1;
    M(18,15) = 1;
    M(19,18) = 1;
    
    const Eigen::EigenSolver< Eigen::Matrix<double,20,20> > eigensolver(M,true);
    const Eigen::EigenSolver< Eigen::Matrix<double,20,20> >::EigenvalueType evalues = eigensolver.eigenvalues();
    const Eigen::EigenSolver< Eigen::Matrix<double,20,20> >::EigenvectorsType evecs = eigensolver.eigenvectors();

    rsolns.clear();
    rsolns.reserve(evalues.size());
    for ( size_t i = 0; i < evalues.size(); i++ )
    {
        if ( evalues[i].imag() != 0 ) continue;
        const double zsoln = evalues(i).real();
        const double xsoln = evecs(16,i).real()/evecs(19,i).real();
        const double ysoln = evecs(17,i).real()/evecs(19,i).real();
        Eigen::Vector3d rsoln;
        rsoln << xsoln, ysoln, zsoln;
        rsolns.push_back(rsoln);
    }

}