TShape3DB2.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) kraftche@cae.wisc.edu

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

/** \file TShape3DB2.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShape3DB2.hpp"
#include "MsqMatrix.hpp"
#include "MsqError.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

TShape3DB2::~TShape3DB2() {}

std::string TShape3DB2::get_name() const
{
    return "TShape3DB2";
}

// \mu_3(T) = \frac{ |T|^2 |adj(T)|^2 } {9 \tau^2} - 1
bool TShape3DB2::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    double f = sqr_Frobenius( T );
    double g = sqr_Frobenius( adj( T ) );
    double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = ( f * g ) / ( 9 * d * d ) - 1;
    return true;
}

bool TShape3DB2::evaluate_with_grad( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T,
                                     MsqError& err )
{
    double f = sqr_Frobenius( T );
    double g = sqr_Frobenius( adj( T ) );
    double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = ( f * g ) / ( 9 * d * d ) - 1;

    wrt_T = T;
    wrt_T *= ( g + f * f );
    wrt_T -= f * ( T * transpose( T ) * T );
    wrt_T -= f * g / d * transpose_adj( T );
    wrt_T *= 2 / ( 9 * d * d );

    return true;
}

bool TShape3DB2::evaluate_with_hess( const MsqMatrix< 3, 3 >& T, double& result, MsqMatrix< 3, 3 >& wrt_T,
                                     MsqMatrix< 3, 3 > second[6], MsqError& err )
{
    double f = sqr_Frobenius( T );
    double g = sqr_Frobenius( adj( T ) );
    double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double den = 1.0 / ( 9 * d * d );
    result           = f * g * den - 1;

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

    wrt_T = g * df + f * dg - 2 * f * g / d * transpose_adj( T );
    wrt_T *= den;

    set_scaled_2nd_deriv_norm_sqr_adj( second, den * f, T );
    pluseq_scaled_I( second, 2 * den * g );
    pluseq_scaled_sum_outer_product( second, den, dg, df );
    pluseq_scaled_sum_outer_product( second, -2 * den * g / d, df, dtau );
    pluseq_scaled_sum_outer_product( second, -2 * den * f / d, dg, dtau );
    pluseq_scaled_outer_product( second, 6 * den * f * g / ( d * d ), dtau );
    pluseq_scaled_2nd_deriv_of_det( second, -2 * den * f * g / d, T );

    return true;
}

}  // namespace MBMesquite