TUntangleBeta.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 TUntangleBeta.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

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

namespace MBMesquite
{

TUntangleBeta::~TUntangleBeta() {}

std::string TUntangleBeta::get_name() const
{
    return "untangle beta";
}

template < unsigned DIM >
inline bool TUntangleBeta::eval( const MsqMatrix< DIM, DIM >& T, double& result )
{
    double tau = det( T );
    double d   = tau - mGamma;
    double f   = fabs( d ) - d;
    result     = 0.125 * f * f * f;
    return true;
}

template < unsigned DIM >
inline bool TUntangleBeta::grad( const MsqMatrix< DIM, DIM >& T, double& result, MsqMatrix< DIM, DIM >& deriv_wrt_T )
{
    double tau = det( T );
    if( tau < mGamma )
    {
        double d    = mGamma - tau;
        result      = d * d * d;
        deriv_wrt_T = -3 * d * d * transpose_adj( T );
    }
    else
    {
        result      = 0.0;
        deriv_wrt_T = MsqMatrix< DIM, DIM >( 0.0 );
    }
    return true;
}

template < unsigned DIM >
inline bool TUntangleBeta::hess( const MsqMatrix< DIM, DIM >& T,
                                 double& result,
                                 MsqMatrix< DIM, DIM >& deriv_wrt_T,
                                 MsqMatrix< DIM, DIM >* second_wrt_T )
{
    double tau = det( T );
    if( tau < mGamma )
    {
        const MsqMatrix< DIM, DIM > adjt = transpose_adj( T );
        double d                         = mGamma - tau;
        result                           = d * d * d;
        deriv_wrt_T                      = -3 * d * d * adjt;
        set_scaled_outer_product( second_wrt_T, 6 * d, adjt );
        pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -3 * d * d, T );
    }
    else
    {
        result      = 0.0;
        deriv_wrt_T = MsqMatrix< DIM, DIM >( 0.0 );
        set_scaled_I( second_wrt_T, 0.0 );  // zero everything
    }
    return true;
}

TMP_T_TEMPL_IMPL_COMMON( TUntangleBeta )

}  // namespace MBMesquite