TUntangle1.cpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2009 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retain certain rights to this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2009) kraftche@cae.wisc.edu

  ***************************************************************** */

/** \file TUntangle1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TUntangle1.hpp"
#include "TMPDerivs.hpp"
#include "TMPCommon.hpp"

#include <iostream>

namespace MBMesquite
{

TUntangle1::~TUntangle1() {}

std::string TUntangle1::get_name() const
{
    return "Untangle1";
}

template < unsigned DIM >
inline bool TUntangle1::eval( const MsqMatrix< DIM, DIM >& T, double& result )
{
    double tau = det( T );
    result     = 0.5 * ( sqrt( tau * tau + mFactor ) - tau );
    return true;
}

template < unsigned DIM >
inline bool TUntangle1::grad( const MsqMatrix< DIM, DIM >& T, double& result, MsqMatrix< DIM, DIM >& deriv_wrt_T )
{
    double tau = det( T );
    double g   = sqrt( tau * tau + mFactor );
    if( g > 1e-50 )
    {
        double f    = tau / g - 1;
        result      = 0.5 * ( g - tau );
        deriv_wrt_T = transpose_adj( T );
        deriv_wrt_T *= 0.5 * f;
        return true;
    }
    else
    {
        std::cout << "Warning: Division by zero avoided in TUntangle1::grad()" << std::endl;
        return false;
    }
}

template < unsigned DIM >
inline bool TUntangle1::hess( const MsqMatrix< DIM, DIM >& T, double& result, MsqMatrix< DIM, DIM >& deriv_wrt_T,
                              MsqMatrix< DIM, DIM >* second_wrt_T )
{
    const MsqMatrix< DIM, DIM > adjt = transpose_adj( T );
    double tau                       = det( T );
    double g                         = sqrt( tau * tau + mFactor );
    if( g == 0 ) return false;
    double f = 0.5 * ( tau / g - 1 );
    result   = 0.5 * ( g - tau );

    deriv_wrt_T = adjt;
    deriv_wrt_T *= f;

    set_scaled_outer_product( second_wrt_T, 0.5 * mFactor / ( g * g * g ), adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, f, T );

    return true;
}

TMP_T_TEMPL_IMPL_COMMON( TUntangle1 )

}  // namespace MBMesquite