TShapeSize2DNB2.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 TShapeSize2DNB2.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeSize2DNB2.hpp"
#include "MsqMatrix.hpp"
#include "TMPDerivs.hpp"

namespace MBMesquite
{

std::string TShapeSize2DNB2::get_name() const
{
    return "TShapeSize2DNB2";
}

TShapeSize2DNB2::~TShapeSize2DNB2() {}

/** \f$ \mu(T) = \frac{|T|^2+2}{2\psi(T)} - 1 \f$
 *  \f$ \psi(T) = \sqrt{|T|^2 + 2 \tau}\f$
 *  \f$ \tau = det(T) \f$
 */
bool TShapeSize2DNB2::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& )
{
    double frob_sqr = sqr_Frobenius( T );
    double psi      = sqrt( frob_sqr + 2.0 * det( T ) );

    double a = 1e-12;
    while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
    {
        MsqMatrix< 2, 2 > Tdelta( T );
        Tdelta( 0, 0 ) += a;
        Tdelta( 1, 1 ) += a;
        a *= 2.0;
        frob_sqr = sqr_Frobenius( Tdelta );
        psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
        if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
    }

    result -= 1.0;
    return true;
}

bool TShapeSize2DNB2::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                          double& result,
                                          MsqMatrix< 2, 2 >& deriv_wrt_T,
                                          MsqError& /*err*/ )
{
    double frob_sqr = sqr_Frobenius( T );
    double psi      = sqrt( frob_sqr + 2.0 * det( T ) );

    double a = 1e-12;
    while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
    {
        MsqMatrix< 2, 2 > Tdelta( T );
        Tdelta( 0, 0 ) += a;
        Tdelta( 1, 1 ) += a;
        a *= 2.0;
        frob_sqr = sqr_Frobenius( Tdelta );
        psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
        if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
    }

    // MsqMatrix<2,2> d_psi = 1.0/psi * (T + transpose_adj(T));
    // deriv_wrt_T = (1.0/psi) * (T - result * d_psi);
    if( psi > 1e-50 )
    {
        const double f = result / ( psi * psi );
        deriv_wrt_T    = transpose_adj( T );
        deriv_wrt_T *= -f;
        deriv_wrt_T += ( 1.0 / psi - f ) * T;
    }

    result -= 1.0;

    return true;
}

bool TShapeSize2DNB2::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
                                          double& result,
                                          MsqMatrix< 2, 2 >& deriv_wrt_T,
                                          MsqMatrix< 2, 2 > second[3],
                                          MsqError& /*err*/ )
{
    double frob_sqr = sqr_Frobenius( T );
    double psi      = sqrt( frob_sqr + 2.0 * det( T ) );

    double a = 1e-12;
    while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) )
    {
        MsqMatrix< 2, 2 > Tdelta( T );
        Tdelta( 0, 0 ) += a;
        Tdelta( 1, 1 ) += a;
        a *= 2.0;
        frob_sqr = sqr_Frobenius( Tdelta );
        psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
        if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi;
    }

    const double inv_psi    = 1.0 / psi;
    MsqMatrix< 2, 2 > d_psi = T + transpose_adj( T );
    d_psi *= inv_psi;

    deriv_wrt_T = d_psi;
    deriv_wrt_T *= -result;
    deriv_wrt_T += T;
    deriv_wrt_T *= inv_psi;

    set_scaled_2nd_deriv_wrt_psi( second, -result * inv_psi, psi, T );
    pluseq_scaled_outer_product( second, 2 * result * inv_psi * inv_psi, d_psi );
    pluseq_scaled_sum_outer_product( second, -inv_psi * inv_psi, d_psi, T );
    pluseq_scaled_I( second, inv_psi );

    result -= 1.0;

    return true;
}

}  // namespace MBMesquite