TInverseMeanRatio.cpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2007 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

    (2008) [email protected]

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

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

#include "Mesquite.hpp"
#include "TInverseMeanRatio.hpp"
#include "MsqMatrix.hpp"
#include "MsqError.hpp"

namespace MBMesquite
{

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

TInverseMeanRatio::~TInverseMeanRatio() {}

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

bool TInverseMeanRatio::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                            double& result,
                                            MsqMatrix< 2, 2 >& deriv_wrt_T,
                                            MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        deriv_wrt_T = MsqMatrix< 2, 2 >( 0.0 );
        return false;
    }
    else
    {
        result      = sqr_Frobenius( T ) / ( 2 * d );
        deriv_wrt_T = transpose_adj( T );
        deriv_wrt_T *= -result;
        deriv_wrt_T += T;
        deriv_wrt_T *= 1.0 / d;
        result -= 1.0;
        return true;
    }
}

bool TInverseMeanRatio::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
                                            double& result,
                                            MsqMatrix< 2, 2 >& dA,
                                            MsqMatrix< 2, 2 > d2A[3],
                                            MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        dA = d2A[0] = d2A[1] = d2A[2] = MsqMatrix< 2, 2 >( 0.0 );
        return false;
    }
    else
    {
        const double inv_det = 1.0 / d;
        result               = sqr_Frobenius( T ) * 0.5 * inv_det;

        const MsqMatrix< 2, 2 > AT = transpose_adj( T );
        dA                         = AT;
        dA *= -result;
        dA += T;
        dA *= inv_det;

        const double p3                    = -result * inv_det;
        const double p1                    = -2.0 * p3 * inv_det;
        const double p2                    = -inv_det * inv_det;
        const MsqMatrix< 2, 2 > AT_T_op_00 = outer( AT.row( 0 ), T.row( 0 ) );
        const MsqMatrix< 2, 2 > AT_T_op_11 = outer( AT.row( 1 ), T.row( 1 ) );
        d2A[0] = p1 * outer( AT.row( 0 ), AT.row( 0 ) ) + p2 * ( AT_T_op_00 + transpose( AT_T_op_00 ) );
        d2A[1] = p1 * outer( AT.row( 0 ), AT.row( 1 ) ) +
                 p2 * ( outer( AT.row( 0 ), T.row( 1 ) ) + outer( T.row( 0 ), AT.row( 1 ) ) );
        d2A[2] = p1 * outer( AT.row( 1 ), AT.row( 1 ) ) + p2 * ( AT_T_op_11 + transpose( AT_T_op_11 ) );

        d2A[0]( 0, 0 ) += inv_det;
        d2A[0]( 1, 1 ) += inv_det;
        d2A[1]( 0, 1 ) += p3;
        d2A[1]( 1, 0 ) -= p3;
        d2A[2]( 0, 0 ) += inv_det;
        d2A[2]( 1, 1 ) += inv_det;

        result -= 1.0;
        return true;
    }
}

bool TInverseMeanRatio::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    else
    {
        const double det_cbrt = MBMesquite::cbrt( d );
        result                = sqr_Frobenius( T ) / ( 3 * det_cbrt * det_cbrt ) - 1;
        return true;
    }
}

bool TInverseMeanRatio::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
                                            double& result,
                                            MsqMatrix< 3, 3 >& deriv_wrt_T,
                                            MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        deriv_wrt_T = MsqMatrix< 3, 3 >( 0.0 );
        return false;
    }

    const double inv_det             = 1.0 / d;
    const double inv_det_cbrt        = MBMesquite::cbrt( inv_det );
    const double inv_3_det_twothirds = inv_det_cbrt * inv_det_cbrt / 3.0;
    const double fnorm               = sqr_Frobenius( T );
    result                           = fnorm * inv_3_det_twothirds - 1;
    deriv_wrt_T                      = transpose_adj( T );
    deriv_wrt_T *= -fnorm * inv_det / 3.0;
    deriv_wrt_T += T;
    deriv_wrt_T *= 2.0 * inv_3_det_twothirds;
    return true;
}

bool TInverseMeanRatio::evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
                                            double& result,
                                            MsqMatrix< 3, 3 >& dA,
                                            MsqMatrix< 3, 3 > d2A[6],
                                            MsqError& err )
{
    const double d = det( T );
    if( invalid_determinant( d ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        dA = MsqMatrix< 3, 3 >( 0.0 );
        return false;
    }

    const double f0 = 1.0 / d;
    const double c  = MBMesquite::cbrt( f0 );
    const double f1 = 1.0 / 3.0 * c * c;
    const double f2 = sqr_Frobenius( T );
    result          = f1 * f2;

    const double f3 = 2 * f1;
    const double f4 = result * ( 10.0 / 9.0 ) * f0 * f0;
    const double f5 = ( 1.0 / 3.0 ) * f0 * f3;
    const double f6 = 2 * f5;
    const double f7 = f2 * f5;

    const MsqMatrix< 3, 3 > AT = transpose_adj( T );
    dA                         = AT;
    dA *= ( -1.0 / 3.0 ) * f0 * f2;
    dA += T;
    dA *= f3;

    MsqMatrix< 3, 3 > op;
    int i    = 0;
    double s = 1;
    for( int r = 0; r < 3; ++r )
    {
        d2A[i] = outer( AT.row( r ), AT.row( r ) );
        d2A[i] *= f4;
        op = outer( AT.row( r ), T.row( r ) );
        op += transpose( op );
        op *= f6;
        d2A[i] -= op;

        d2A[i]( 0, 0 ) += f3;
        d2A[i]( 1, 1 ) += f3;
        d2A[i]( 2, 2 ) += f3;

        ++i;

        for( int cc = r + 1; cc < 3; ++cc )
        {
            d2A[i] = outer( AT.row( r ), AT.row( cc ) );
            d2A[i] *= f4;
            op = outer( AT.row( r ), T.row( cc ) );
            op += outer( T.row( r ), AT.row( cc ) );
            op *= f6;
            d2A[i] -= op;

            MsqMatrix< 1, 3 > rt = T.row( 3 - r - cc );
            rt *= s * f7;
            d2A[i]( 0, 1 ) -= rt( 0, 2 );
            d2A[i]( 0, 2 ) += rt( 0, 1 );
            d2A[i]( 1, 0 ) += rt( 0, 2 );
            d2A[i]( 1, 2 ) -= rt( 0, 0 );
            d2A[i]( 2, 0 ) -= rt( 0, 1 );
            d2A[i]( 2, 1 ) += rt( 0, 0 );

            ++i;
            s = -s;
        }
    }

    result -= 1.0;
    return true;
}

}  // namespace MBMesquite