TShapeSizeB3.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 TShapeSizeB3.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeSizeB3.hpp"
#include "TMPDerivs.hpp"
#include "MsqError.hpp"

#include <iostream>

namespace MBMesquite
{

std::string TShapeSizeB3::get_name() const
{
    return "TShapeSizeB3";
}

TShapeSizeB3::~TShapeSizeB3() {}

bool TShapeSizeB3::evaluate( const MsqMatrix< 2, 2 >& 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;
    }

    result = sqr_Frobenius( T ) - 2.0 * std::log( tau ) - 2;
    return true;
}

bool TShapeSizeB3::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;
    }

    result      = sqr_Frobenius( T ) - 2.0 * std::log( tau ) - 2;
    deriv_wrt_T = T;
    deriv_wrt_T -= 1 / tau * transpose_adj( T );
    deriv_wrt_T *= 2;

    return true;
}

bool TShapeSizeB3::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;
    }

    result = sqr_Frobenius( T ) - 2.0 * std::log( tau ) - 2;

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double it              = 1 / tau;
    deriv_wrt_T                  = T;
    deriv_wrt_T -= it * adjt;
    deriv_wrt_T *= 2;

    set_scaled_outer_product( second_wrt_T, 2 * it * it, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -2 * it );
    pluseq_scaled_I( second_wrt_T, 2.0 );

    return true;
}

bool TShapeSizeB3::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;
    }

    double n = Frobenius( T );
    result   = n * n * n - 3 * MSQ_SQRT_THREE * ( log( tau ) + 1 );
    return true;
}

bool TShapeSizeB3::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;
    }

    double n = Frobenius( T );
    result   = n * n * n - 3 * MSQ_SQRT_THREE * ( log( tau ) + 1 );

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    deriv_wrt_T                  = T;
    deriv_wrt_T *= 3 * n;
    deriv_wrt_T -= 3 * MSQ_SQRT_THREE / tau * adjt;

    return true;
}

bool TShapeSizeB3::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;
    }

    double n = Frobenius( T );
    result   = n * n * n - 3 * MSQ_SQRT_THREE * ( log( tau ) + 1 );

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    const double it              = 1 / tau;
    deriv_wrt_T                  = T;
    deriv_wrt_T *= 3 * n;
    deriv_wrt_T -= 3 * MSQ_SQRT_THREE * it * adjt;

    if( n > 1e-50 )
    {
        set_scaled_outer_product( second_wrt_T, 3 / n, T );
        pluseq_scaled_I( second_wrt_T, 3 * n );
        pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -3 * MSQ_SQRT_THREE * it, T );
        pluseq_scaled_outer_product( second_wrt_T, 3 * MSQ_SQRT_THREE * it * it, adjt );
    }
    else
    {
        std::cout << "Warning: Division by zero avoided in TShapeSizeB3::evaluate_with_hess()" << std::endl;
    }

    return true;
}

}  // namespace MBMesquite