TShapeNB1.cpp

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

    Copyright 2006 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

    (2006) [email protected]

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

/** \file TShapeNB1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeNB1.hpp"
#include "MsqMatrix.hpp"
#include "TMPDerivs.hpp"

#include <iostream>

namespace MBMesquite
{

std::string TShapeNB1::get_name() const
{
    return "TShapeNB1";
}

TShapeNB1::~TShapeNB1() {}

bool TShapeNB1::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& /*err*/ )
{
    result = sqr_Frobenius( T ) - 2.0 * det( T );
    return true;
}

bool TShapeNB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                    double& result,
                                    MsqMatrix< 2, 2 >& deriv_wrt_T,
                                    MsqError& /*err*/ )
{
    result      = sqr_Frobenius( T ) - 2.0 * det( T );
    deriv_wrt_T = T;
    deriv_wrt_T -= transpose_adj( T );
    deriv_wrt_T *= 2;
    return true;
}

bool TShapeNB1::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
                                    double& result,
                                    MsqMatrix< 2, 2 >& deriv_wrt_T,
                                    MsqMatrix< 2, 2 > second_wrt_T[3],
                                    MsqError& /*err*/ )
{
    result      = sqr_Frobenius( T ) - 2.0 * det( T );
    deriv_wrt_T = T;
    deriv_wrt_T -= transpose_adj( T );
    deriv_wrt_T *= 2;
    set_scaled_I( second_wrt_T, 2.0 );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -2.0 );
    return true;
}

bool TShapeNB1::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& /*err*/ )
{
    double f = Frobenius( T );
    double d = det( T );
    result   = f * f * f - 3 * MSQ_SQRT_THREE * d;
    return true;
}

bool TShapeNB1::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
                                    double& result,
                                    MsqMatrix< 3, 3 >& deriv_wrt_T,
                                    MsqError& /*err*/ )
{
    double f = Frobenius( T );
    double d = det( T );
    result   = f * f * f - 3 * MSQ_SQRT_THREE * d;

    deriv_wrt_T = T;
    deriv_wrt_T *= f;
    deriv_wrt_T -= MSQ_SQRT_THREE * transpose_adj( T );
    deriv_wrt_T *= 3;
    return true;
}

bool TShapeNB1::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
                                    double& result,
                                    MsqMatrix< 3, 3 >& deriv_wrt_T,
                                    MsqMatrix< 3, 3 > second_wrt_T[6],
                                    MsqError& /*err*/ )
{
    double f = Frobenius( T );
    double d = det( T );
    result   = f * f * f - 3 * MSQ_SQRT_THREE * d;

    deriv_wrt_T = T;
    deriv_wrt_T *= f;
    deriv_wrt_T -= MSQ_SQRT_THREE * transpose_adj( T );
    deriv_wrt_T *= 3;

    set_scaled_2nd_deriv_of_det( second_wrt_T, -3 * MSQ_SQRT_THREE, T );
    if( f > 1e-50 )
        pluseq_scaled_outer_product( second_wrt_T, 3.0 / f, T );
    else
        std::cout << "Warning: Division by zero avoided in TShapeNB1::evaluate_with_hess()" << std::endl;
    pluseq_scaled_I( second_wrt_T, 3.0 * f );
    return true;
}

}  // namespace MBMesquite