TShapeSizeB1.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) kraftche@cae.wisc.edu

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

/** \file TShapeSizeB1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeSizeB1.hpp"
#include "TMPDerivs.hpp"
#include "MsqError.hpp"

namespace MBMesquite
{

std::string TShapeSizeB1::get_name() const
{
    return "TShapeSizeB1";
}

TShapeSizeB1::~TShapeSizeB1() {}

bool TShapeSizeB1::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& /*err*/ )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        return false;
    }

    const double nT = sqr_Frobenius( T );
    const double f  = 1 / ( tau * tau );
    result          = ( 1 + f ) * nT - 4;
    return true;
}

bool TShapeSizeB1::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& /*err*/ )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        return false;
    }

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

bool TShapeSizeB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& T, double& result, MsqMatrix< 2, 2 >& 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 MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double f               = 1 / ( tau * tau );
    result                       = ( 1 + f ) * nT - 4;

    deriv_wrt_T = T;
    deriv_wrt_T *= 2 + 2 * f;
    deriv_wrt_T -= 2 * f / tau * nT * adjt;

    return true;
}

bool TShapeSizeB1::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 MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double nadj            = sqr_Frobenius( adjt );
    const double f               = 1 / ( tau * tau );
    result                       = nT + f * nadj - 6;

    deriv_wrt_T = T;
    deriv_wrt_T *= ( 1 + f * nT );
    deriv_wrt_T -= f * T * transpose( T ) * T;
    deriv_wrt_T -= f / tau * nadj * adjt;
    deriv_wrt_T *= 2;

    return true;
}

bool TShapeSizeB1::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 double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double f               = 1 / ( tau * tau );
    result                       = ( 1 + f ) * nT - 4;

    deriv_wrt_T = T;
    deriv_wrt_T *= 2 + 2 * f;
    deriv_wrt_T -= 2 * f / tau * nT * adjt;

    set_scaled_sum_outer_product( second_wrt_T, -4 * f / tau, T, adjt );
    pluseq_scaled_I( second_wrt_T, 2 + 2 * f );
    pluseq_scaled_outer_product( second_wrt_T, 6 * nT * f * f, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -2 * nT * f / tau );

    return true;
}
bool TShapeSizeB1::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 )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double nadj            = sqr_Frobenius( adjt );
    const double f               = 1 / ( tau * tau );
    result                       = nT + f * nadj - 6;

    //! \f$ \frac{\partial}{\partial T} |adj T|^2 \f$
    const MsqMatrix< 3, 3 > dNadj_dT = 2 * ( nT * T - T * transpose( T ) * T );
    deriv_wrt_T                      = T;
    deriv_wrt_T -= f / tau * nadj * adjt;
    deriv_wrt_T *= 2;
    deriv_wrt_T += f * dNadj_dT;

    // calculate negative of 2nd wrt T of (|adj T|^2 / tau^2) (sec 3.2.2)
    set_scaled_2nd_deriv_norm_sqr_adj( second_wrt_T, f, T );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -2 * f * f * nadj * tau, T );
    pluseq_scaled_outer_product( second_wrt_T, 6 * f * f * nadj, adjt );
    pluseq_scaled_sum_outer_product( second_wrt_T, -2 * f * f * tau, adjt, dNadj_dT );
    // calculate 2nd wrt T of this metric
    pluseq_scaled_I( second_wrt_T, 2.0 );

    return true;
}

}  // namespace MBMesquite