TShape2DNB2.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 TShape2DNB2.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShape2DNB2.hpp"
#include "MsqMatrix.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

std::string TShape2DNB2::get_name() const
{
    return "TShape2DNB2";
}

TShape2DNB2::~TShape2DNB2() {}

bool TShape2DNB2::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& )
{
    const double tau     = det( T );
    MsqMatrix< 2, 2 > TT = transpose( T ) * T;
    TT( 0, 0 ) -= tau;
    TT( 1, 1 ) -= tau;
    result = sqr_Frobenius( TT );
    return true;
}

bool TShape2DNB2::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                      double& result,
                                      MsqMatrix< 2, 2 >& deriv_wrt_T,
                                      MsqError& /*err*/ )
{
    const MsqMatrix< 2, 2 > TtT = transpose( T ) * T;
    const double tau            = det( T );
    const double nTtT           = sqr_Frobenius( TtT );
    const double nT             = sqr_Frobenius( T );
    result                      = nTtT + 2 * tau * ( tau - nT );

    deriv_wrt_T = T * TtT;
    deriv_wrt_T -= tau * T;
    deriv_wrt_T += ( tau - 0.5 * nT ) * transpose_adj( T );
    deriv_wrt_T *= 4;

    return true;
}

bool TShape2DNB2::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*/ )
{
    const MsqMatrix< 2, 2 > TtT = transpose( T ) * T;
    const double tau            = det( T );
    const double nTtT           = sqr_Frobenius( TtT );
    const double nT             = sqr_Frobenius( T );
    result                      = nTtT + 2 * tau * ( tau - nT );

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    deriv_wrt_T                  = T * TtT;
    deriv_wrt_T -= tau * T;
    deriv_wrt_T += ( tau - 0.5 * nT ) * adjt;
    deriv_wrt_T *= 4;

    set_scaled_outer_product( second_wrt_T, 1, T );
    second_wrt_T[1] = transpose( second_wrt_T[1] );
    second_wrt_T[0] += TtT;
    second_wrt_T[2] += TtT;
    const MsqMatrix< 2, 2 > TTt = T * transpose( T );
    second_wrt_T[0]( 0, 0 ) += TTt( 0, 0 );
    second_wrt_T[0]( 1, 1 ) += TTt( 0, 0 );
    second_wrt_T[1]( 0, 0 ) += TTt( 0, 1 );
    second_wrt_T[1]( 1, 1 ) += TTt( 0, 1 );
    second_wrt_T[2]( 0, 0 ) += TTt( 1, 1 );
    second_wrt_T[2]( 1, 1 ) += TTt( 1, 1 );

    pluseq_scaled_I( second_wrt_T, -tau );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5 * nT );
    pluseq_scaled_sum_outer_product( second_wrt_T, -1, T, adjt );

    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, tau );
    pluseq_scaled_outer_product( second_wrt_T, 1, adjt );

    second_wrt_T[1] *= 4;
    second_wrt_T[0] *= 4;
    second_wrt_T[2] *= 4;

    return true;
}

}  // namespace MBMesquite