PottsElement.cpp

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*/
#include "PottsElement.hpp"
#include "RandomNumberGenerator.hpp"


template<unsigned DIM>
PottsElement<DIM>::PottsElement(unsigned index, const std::vector<Node<DIM>*>& rNodes)
    : MutableElement<DIM,DIM>(index, rNodes)
{
    this->RegisterWithNodes();
}

template<unsigned DIM>
PottsElement<DIM>::~PottsElement()
{
}

template<unsigned DIM>
void PottsElement<DIM>::AddNode(Node<DIM>* pNode,  const unsigned& rIndex)
{
    // Add element to this node
    pNode->AddElement(this->mIndex);

    // Add pNode to mNodes
    this->mNodes.push_back(pNode);
}

template<unsigned DIM>
double PottsElement<DIM>::GetAspectRatio()
{
    assert(DIM == 2); // LCOV_EXCL_LINE
    assert(this->GetNumNodes() != 0);

    if (this->GetNumNodes() <= 2)
    {
        return 1.0;
    }

    double eig_max;
    double eig_min;

    // See http://stackoverflow.com/questions/7059841/estimating-aspect-ratio-of-a-convex-hull for how to do it.
    switch(DIM)
    {
    case 2:
    {
        // Calculate entries of covariance matrix (var_x,cov_xy;cov_xy,var_y)
        double mean_x=0;
        double mean_y=0;

        for (unsigned i=0; i<this->GetNumNodes(); i++)
        {
            mean_x += this->mNodes[i]->rGetLocation()[0];
            mean_y += this->mNodes[i]->rGetLocation()[1];
        }
        mean_x /= this->GetNumNodes();
        mean_y /= this->GetNumNodes();

        double variance_x = 0;
        double variance_y = 0;
        double covariance_xy = 0;

        for (unsigned i=0; i<this->GetNumNodes(); i++)
        {
            variance_x += pow((this->mNodes[i]->rGetLocation()[0]-mean_x),2);
            variance_y += pow((this->mNodes[i]->rGetLocation()[1]-mean_y),2);
            covariance_xy += (this->mNodes[i]->rGetLocation()[0]-mean_x)*(this->mNodes[i]->rGetLocation()[1]-mean_y);
        }
        variance_x /= this->GetNumNodes();
        variance_y /= this->GetNumNodes();
        covariance_xy /= this->GetNumNodes();

        // Calculate max/min eigenvalues
        double trace = variance_x+variance_y;
        double det = variance_x*variance_y - covariance_xy*covariance_xy;

        eig_max = 0.5*(trace+sqrt(trace*trace - 4*det));
        eig_min = 0.5*(trace-sqrt(trace*trace - 4*det));

        break;
    }
//    case 3:
//    {
//        double mean_x = 0;
//        double mean_y = 0;
//        double mean_z = 0;
//
//        for (unsigned i=0; i<this->GetNumNodes(); i++)
//        {
//            mean_x += this->mNodes[i]->rGetLocation()[0];
//            mean_y += this->mNodes[i]->rGetLocation()[1];
//            mean_z += this->mNodes[i]->rGetLocation()[2];
//        }
//        mean_x /= this->GetNumNodes();
//        mean_y /= this->GetNumNodes();
//        mean_z /= this->GetNumNodes();
//
//        double variance_x = 0;
//        double variance_y = 0;
//        double variance_z = 0;
//
//        double covariance_xy = 0;
//        double covariance_xz = 0;
//        double covariance_yz = 0;
//
//        for (unsigned i=0; i<this->GetNumNodes(); i++)
//        {
//            double diff_x = this->mNodes[i]->rGetLocation()[0]-mean_x;
//            double diff_y = this->mNodes[i]->rGetLocation()[1]-mean_y;
//            double diff_z = this->mNodes[i]->rGetLocation()[2]-mean_z;
//
//            variance_x += diff_x*diff_x;
//            variance_y += diff_y*diff_y;
//            variance_z += diff_z*diff_z;
//            covariance_xy += diff_x*diff_y;
//            covariance_xz += diff_x*diff_z;
//            covariance_yz += diff_y*diff_z;
//        }
//        variance_x /= this->GetNumNodes();
//        variance_y /= this->GetNumNodes();
//        variance_z /= this->GetNumNodes();
//        covariance_xy /= this->GetNumNodes();
//        covariance_xz /= this->GetNumNodes();
//        covariance_yz /= this->GetNumNodes();
//
//        c_matrix<PetscScalar, 3, 3> covariance_matrix;
//
//        covariance_matrix(0,0) = variance_x;
//        covariance_matrix(0,1) = covariance_xy;
//        covariance_matrix(0,2) = covariance_xz;
//
//        covariance_matrix(1,0) = covariance_xy;
//        covariance_matrix(1,1) = variance_y;
//        covariance_matrix(1,2) = covariance_yz;
//
//        covariance_matrix(2,0) = covariance_xz;
//        covariance_matrix(2,1) = covariance_yz;
//        covariance_matrix(2,2) = variance_z;
//
//        const char N = 'N';
//        const char L = 'L';
//        PetscBLASInt size = DIM;
//        PetscReal eigs[DIM];
//        // Optimal work_size (102 entries) computed with a special call to LAPACKsyev_ (see documentation)
//        // and rounded to the next power of 2
//        const PetscBLASInt work_size = 128;
//        PetscScalar workspace[work_size];
//        PetscBLASInt info;
//        LAPACKsyev_(&N, &L, &size, covariance_matrix.data(), &size, eigs, workspace, (PetscBLASInt*) &work_size, &info);
//        assert(info == 0);
//
//        // Lapack returns eigenvalues in ascending order
//        eig_max = eigs[DIM-1];
//        eig_min = eigs[0] +eigs[1];
//        break;
//    }
    default:
        NEVER_REACHED;
    }

    // As matrix is symmetric positive semidefinite
    assert(eig_min >= 0);
    assert(eig_max >= 0);

    if (eig_min == 0)
    {
        EXCEPTION("All nodes in an element lie in the same line/plane (2D/3D) so aspect ratio is infinite. This interferes with calculation of the Hamiltonian.");
    }

    return eig_max/eig_min;
}

// Explicit instantiation
template class PottsElement<1>;
template class PottsElement<2>;
template class PottsElement<3>;