TShapeSize3DB2.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) [email protected]

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

/** \file TShapeSize3DB2.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeSize3DB2.hpp"
#include "TMPDerivs.hpp"
#include "MsqError.hpp"

namespace MBMesquite
{

std::string TShapeSize3DB2::get_name() const
{
    return "TShapeSize3DB2";
}

TShapeSize3DB2::~TShapeSize3DB2() {}

bool TShapeSize3DB2::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const double f = sqr_Frobenius( T );
    const double g = sqr_Frobenius( adj( T ) );
    result         = ( f + g ) / ( 6 * tau ) - 1;
    return true;
}

bool TShapeSize3DB2::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
                                         double& result,
                                         MsqMatrix< 3, 3 >& deriv_wrt_T,
                                         MsqError& err )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const double f = sqr_Frobenius( T );
    const double g = sqr_Frobenius( adj( T ) );
    result         = ( f + g ) / ( 6 * tau );

    deriv_wrt_T = -transpose( T ) * T;
    deriv_wrt_T( 0, 0 ) += 1 + f;
    deriv_wrt_T( 1, 1 ) += 1 + f;
    deriv_wrt_T( 2, 2 ) += 1 + f;
    deriv_wrt_T = T * deriv_wrt_T;
    deriv_wrt_T -= 3 * result * transpose_adj( T );
    deriv_wrt_T *= 1.0 / ( 3 * tau );

    result -= 1.0;
    return true;
}

bool TShapeSize3DB2::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
                                         double& result,
                                         MsqMatrix< 3, 3 >& wrt_T,
                                         MsqMatrix< 3, 3 > second[6],
                                         MsqError& err )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const double f = sqr_Frobenius( T );
    const double g = sqr_Frobenius( adj( T ) );
    result         = ( f + g ) / ( 6 * tau );

    MsqMatrix< 3, 3 > dtau = transpose_adj( T );
    MsqMatrix< 3, 3 > dg   = -transpose( T ) * T;
    dg( 0, 0 ) += f;
    dg( 1, 1 ) += f;
    dg( 2, 2 ) += f;
    dg = T * dg;
    dg *= 2;

    wrt_T = T;
    wrt_T += 0.5 * dg;
    wrt_T *= 1.0 / 3.0;
    wrt_T -= result * dtau;
    wrt_T *= 1.0 / tau;

    set_scaled_2nd_deriv_norm_sqr_adj( second, 1.0 / 6.0, T );
    pluseq_scaled_I( second, 1.0 / 3.0 );
    pluseq_scaled_sum_outer_product( second, -1. / 3. / tau, T, dtau );
    pluseq_scaled_sum_outer_product( second, -1. / 6. / tau, dg, dtau );
    pluseq_scaled_outer_product( second, 2 * result / tau, dtau );
    pluseq_scaled_2nd_deriv_of_det( second, -result, T );
    hess_scale( second, 1.0 / tau );

    result -= 1.0;
    return true;
}

}  // namespace MBMesquite