AWShape2DNB1.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

    (2010) [email protected]

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

/** \file AWShape2DNB1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "AWShape2DNB1.hpp"
#include "MsqMatrix.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

std::string AWShape2DNB1::get_name() const
{
    return "AWShape2DNB1";
}

AWShape2DNB1::~AWShape2DNB1() {}

bool AWShape2DNB1::evaluate( const MsqMatrix< 2, 2 >& A, const MsqMatrix< 2, 2 >& W, double& result, MsqError& )
{
    MsqMatrix< 2, 2 > tmp = det( W ) * transpose( A ) * A;
    tmp -= det( A ) * W * transpose( W );
    result = sqr_Frobenius( tmp );
    return true;
}

bool AWShape2DNB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& A,
                                       const MsqMatrix< 2, 2 >& W,
                                       double& result,
                                       MsqMatrix< 2, 2 >& deriv_wrt_A,
                                       MsqError& )
{
    const double alpha          = det( A );
    const double omega          = det( W );
    const MsqMatrix< 2, 2 > AtA = transpose( A ) * A;
    const MsqMatrix< 2, 2 > WtW = transpose( W ) * W;
    const MsqMatrix< 2, 2 > AWt = A * transpose( W );
    const double alphaWtW       = alpha * sqr_Frobenius( WtW );
    const double omegaAtA       = omega * sqr_Frobenius( AtA );
    const double omegaAWt       = omega * sqr_Frobenius( AWt );
    result                      = omega * omegaAtA;
    result += alpha * alphaWtW;
    result -= 2 * alpha * omegaAWt;

    deriv_wrt_A = 4 * omega * omega * A * transpose( A ) * A;
    deriv_wrt_A -= 4 * alpha * omega * AWt * W;
    deriv_wrt_A += 2 * ( alphaWtW - omegaAWt ) * transpose_adj( A );
    return true;
}

}  // namespace MBMesquite