TShapeSizeOrientB2.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 TRel2DShapeSizeOrientBarrierAlt1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeSizeOrientB2.hpp"
#include "MsqMatrix.hpp"
#include "MsqError.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

std::string TShapeSizeOrientB2::get_name() const
{
    return "TShapeSizeOrientB2";
}

TShapeSizeOrientB2::~TShapeSizeOrientB2() {}

bool TShapeSizeOrientB2::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& err )
{
    double d = det( T );
    if( TMetric::invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    MsqMatrix< 2, 2 > T_inv = 1 / d * adj( T );
    pluseq_scaled_I( T_inv, -1.0 );
    result = sqr_Frobenius( T_inv );
    return true;
}

bool TShapeSizeOrientB2::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    double d = det( T );
    if( TMetric::invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    MsqMatrix< 3, 3 > T_inv = 1 / d * adj( T );
    pluseq_scaled_I( T_inv, -1.0 );
    result = sqr_Frobenius( T_inv );
    return true;
}

/** \f$ \frac{1}{\tau^2}|T|^2 - \frac{2}{\tau}tr(adj T) + 2 \f$ */
bool TShapeSizeOrientB2::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 ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double it              = 1.0 / tau;
    result                       = it * ( it * sqr_Frobenius( T ) - 2.0 * trace( T ) ) + 2.0;
    deriv_wrt_T                  = T;
    deriv_wrt_T *= it * it;
    deriv_wrt_T( 0, 0 ) -= it;
    deriv_wrt_T( 1, 1 ) -= it;
    deriv_wrt_T += it * it * ( trace( T ) - it * sqr_Frobenius( T ) ) * adjt;
    deriv_wrt_T *= 2.0;
    return true;
}

/** \f$ \frac{1}{\tau^2}|adj T|^2 - \frac{2}{\tau}tr(adj T) + 3 \f$ */
bool TShapeSizeOrientB2::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 ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 3, 3 > adjt = adj( T );
    const double it              = 1.0 / tau;
    result                       = it * ( it * sqr_Frobenius( adjt ) - 2.0 * trace( adjt ) ) + 3.0;

    deriv_wrt_T = T;
    deriv_wrt_T *= sqr_Frobenius( T );
    deriv_wrt_T -= T * transpose( T ) * T;
    deriv_wrt_T *= it * it;

    deriv_wrt_T += it * it * ( trace( adjt ) - it * sqr_Frobenius( adjt ) ) * transpose( adjt );

    double f = trace( T ) * it;
    deriv_wrt_T( 0, 0 ) -= f;
    deriv_wrt_T( 1, 1 ) -= f;
    deriv_wrt_T( 2, 2 ) -= f;

    deriv_wrt_T += it * transpose( T );

    deriv_wrt_T *= 2.0;
    return true;
}

bool TShapeSizeOrientB2::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
                                             double& result,
                                             MsqMatrix< 2, 2 >& deriv_wrt_T,
                                             MsqMatrix< 2, 2 > second[3],
                                             MsqError& err )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double it              = 1.0 / tau;
    result                       = it * ( it * sqr_Frobenius( T ) - 2.0 * trace( T ) ) + 2.0;
    deriv_wrt_T                  = T;
    deriv_wrt_T *= it * it;
    deriv_wrt_T( 0, 0 ) -= it;
    deriv_wrt_T( 1, 1 ) -= it;
    deriv_wrt_T += it * it * ( trace( T ) - it * sqr_Frobenius( T ) ) * adjt;
    deriv_wrt_T *= 2.0;

    set_scaled_outer_product( second, it * it * it * ( 6 * it * sqr_Frobenius( T ) - 4 * trace( T ) ), adjt );
    pluseq_scaled_I( second, 2 * it * it );
    pluseq_scaled_2nd_deriv_of_det( second, 2 * it * it * ( trace( T ) - it * sqr_Frobenius( T ) ) );
    pluseq_scaled_sum_outer_product( second, -4 * it * it * it, T, adjt );
    pluseq_scaled_sum_outer_product_I( second, 2 * it * it, adjt );

    return true;
}

bool TShapeSizeOrientB2::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
                                             double& result,
                                             MsqMatrix< 3, 3 >& deriv_wrt_T,
                                             MsqMatrix< 3, 3 > second[6],
                                             MsqError& err )
{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 3, 3 > adjt = adj( T );
    const double it              = 1.0 / tau;
    const double nadjt           = sqr_Frobenius( adjt );
    const double nT              = sqr_Frobenius( T );
    const double tadjT           = trace( adjt );
    result                       = it * ( it * nadjt - 2.0 * tadjT ) + 3.0;

    const MsqMatrix< 3, 3 > TTtT = T * transpose( T ) * T;
    deriv_wrt_T                  = T;
    deriv_wrt_T *= nT;
    deriv_wrt_T -= TTtT;
    deriv_wrt_T *= it * it;

    deriv_wrt_T += it * it * ( tadjT - it * nadjt ) * transpose( adjt );

    const double tT = trace( T );
    double f        = tT * it;
    deriv_wrt_T( 0, 0 ) -= f;
    deriv_wrt_T( 1, 1 ) -= f;
    deriv_wrt_T( 2, 2 ) -= f;

    deriv_wrt_T += it * transpose( T );

    deriv_wrt_T *= 2.0;

    set_scaled_2nd_deriv_norm_sqr_adj( second, it * it, T );

    const double yf = -it * it * it * it;
    const double sf = -2;
    const double zf = -it * it * sf;

    pluseq_scaled_2nd_deriv_of_det( second, yf * 2 * nadjt * tau + zf * tadjT, T );
    pluseq_scaled_outer_product( second, yf * -6 * nadjt - 2 * zf * tadjT * it, transpose( adjt ) );
    MsqMatrix< 3, 3 > dnadj_dT = 2 * ( nT * T - TTtT );
    pluseq_scaled_sum_outer_product( second, yf * 2 * tau, dnadj_dT, transpose( adjt ) );
    pluseq_scaled_2nd_deriv_tr_adj( second, sf * it );
    MsqMatrix< 3, 3 > dtradj_dT = -transpose( T );
    dtradj_dT( 0, 0 ) += tT;
    dtradj_dT( 1, 1 ) += tT;
    dtradj_dT( 2, 2 ) += tT;
    pluseq_scaled_sum_outer_product( second, zf, dtradj_dT, transpose( adjt ) );

    return true;
}

}  // namespace MBMesquite