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)
{
    PetscBLASInt info;
    c_vector<PetscReal, 3> eigenvalues_real_part;
    c_vector<PetscReal, 3> eigenvalues_imaginary_part;
    c_vector<PetscScalar, 4*3 > workspace;
    c_matrix<PetscScalar, 3, 3> right_eigenvalues;

    char dont_compute_left_evectors = 'N';
    char compute_right_evectors = 'V';

    PetscBLASInt matrix_size = 3;
    PetscBLASInt matrix_ld = matrix_size;
    PetscBLASInt workspace_size = 4*matrix_size;

    c_matrix<PetscScalar, 3, 3> a_transpose;
    noalias(a_transpose) = trans(rA);

    // PETSc alias for dgeev or dgeev_
    LAPACKgeev_(&dont_compute_left_evectors, &compute_right_evectors,
                &matrix_size, a_transpose.data(), &matrix_ld,
                eigenvalues_real_part.data(), eigenvalues_imaginary_part.data(),
                NULL, &matrix_ld,
                right_eigenvalues.data(), &matrix_ld,
                workspace.data(), &workspace_size,
                &info);
    assert(info==0);

    // If this fails a complex eigenvalue was found
    assert(norm_2(eigenvalues_imaginary_part) < DBL_EPSILON);

    unsigned index_of_smallest = UINT_MAX;
    double min_eigenvalue = DBL_MAX;

    for (unsigned i=0; i<3; i++)
    {
        double eigen_magnitude = fabs(eigenvalues_real_part(i));
        if (eigen_magnitude < min_eigenvalue && eigen_magnitude >= DBL_EPSILON)
        {
            // A zero eigenvalue is ignored
            min_eigenvalue = eigen_magnitude;
            index_of_smallest = i;
        }
    }
    assert (min_eigenvalue != DBL_MAX);
    assert (index_of_smallest != UINT_MAX);
    assert (min_eigenvalue >= DBL_EPSILON);

    c_vector<double, 3> output;
    output(0) = right_eigenvalues(index_of_smallest, 0);
    output(1) = right_eigenvalues(index_of_smallest, 1);
    output(2) = right_eigenvalues(index_of_smallest, 2);

    return output;
}