UblasCustomFunctions.cpp

/*

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*/

#include "UblasCustomFunctions.hpp"

c_vector<double, 1> Create_c_vector(double x)
{
    c_vector<double, 1> v;
    v[0] = x;
    return v;
}

c_vector<double, 2> Create_c_vector(double x, double y)
{
    c_vector<double, 2> v;
    v[0] = x;
    v[1] = y;
    return v;
}

c_vector<double, 3> Create_c_vector(double x, double y, double z)
{
    c_vector<double, 3> v;
    v[0] = x;
    v[1] = y;
    v[2] = z;
    return v;
}

c_vector<double,3> CalculateEigenvectorForSmallestNonzeroEigenvalue(c_matrix<double, 3, 3>& rA)
{
    //Check for symmetry
    if (norm_inf( rA - trans(rA)) > 10*DBL_EPSILON)
    {
        EXCEPTION("Matrix should be symmetric");
    }

    // Find the eigenvector by brute-force using the power method.
    // We can't use the inverse method, because the matrix might be singular

    c_matrix<double,3,3> copy_A(rA);
    //Eigenvalue 1
    c_vector<double, 3> eigenvec1 = scalar_vector<double>(3, 1.0);

    double eigen1 = CalculateMaxEigenpair(copy_A, eigenvec1);

    // Take out maximum eigenpair
    c_matrix<double, 3, 3> wielandt_reduce_first_vector = identity_matrix<double>(3,3);
    wielandt_reduce_first_vector -= outer_prod(eigenvec1, eigenvec1);
    copy_A = prod(wielandt_reduce_first_vector, copy_A);

    c_vector<double, 3> eigenvec2 = scalar_vector<double>(3, 1.0);
    double eigen2 = CalculateMaxEigenpair(copy_A, eigenvec2);

    // Take out maximum (second) eigenpair
    c_matrix<double, 3, 3> wielandt_reduce_second_vector = identity_matrix<double>(3,3);
    wielandt_reduce_second_vector -= outer_prod(eigenvec2, eigenvec2);
    copy_A = prod(wielandt_reduce_second_vector, copy_A);

    c_vector<double, 3> eigenvec3 = scalar_vector<double>(3, 1.0);
    double eigen3 = CalculateMaxEigenpair(copy_A, eigenvec3);

    //Look backwards through the eigenvalues, checking that they are non-zero
    if (eigen3 >= DBL_EPSILON)
    {
        return eigenvec3;
    }
    if (eigen2 >= DBL_EPSILON)
    {
        return eigenvec2;
    }
    UNUSED_OPT(eigen1);
    assert( eigen1 > DBL_EPSILON);
    return eigenvec1;
}

double CalculateMaxEigenpair(c_matrix<double, 3, 3>& rA, c_vector<double, 3>& rEigenvector)
{
    double norm = 0.0;
    double step = DBL_MAX;
    while (step > DBL_EPSILON) //Machine precision
    {
        c_vector<double, 3> old_value(rEigenvector);
        rEigenvector = prod(rA, rEigenvector);
        norm = norm_2(rEigenvector);
        rEigenvector /= norm;
        if (norm < DBL_EPSILON)
        {
            //We don't care about a zero eigenvector, so don't polish it
            break;
        }
        step = norm_inf(rEigenvector-old_value);
    }
    return norm;
}