TShapeOrientB1.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]
    (2010) [email protected]

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

/** \file TShapeOrientB1.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeOrientB1.hpp"
#include "MsqMatrix.hpp"
#include "MsqError.hpp"
#include "TMPDerivs.hpp"
#include "TMPCommon.hpp"

namespace MBMesquite
{

std::string TShapeOrientB1::get_name() const
{
    return "TShapeOrientB1";
}

TShapeOrientB1::~TShapeOrientB1() {}

bool TShapeOrientB1::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& err )
{
    const double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = 0.5 / tau * ( Frobenius( T ) - trace( T ) / MSQ_SQRT_TWO );
    return true;
}

bool TShapeOrientB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                         double& result,
                                         MsqMatrix< 2, 2 >& deriv_wrt_T,
                                         MsqError& err )
{
    const double norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_TWO;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    result = 0.5 * inv_tau * ( norm - invroot * trace( T ) );

    deriv_wrt_T = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * transpose_adj( T );
    deriv_wrt_T *= inv_tau;
    return true;
}

bool TShapeOrientB1::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 norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_TWO;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    const double f = norm - invroot * trace( T );
    result         = 0.5 * inv_tau * f;

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    deriv_wrt_T                  = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= inv_tau;

    const double a = 0.5 * inv_tau * invnorm;
    set_scaled_outer_product( second_wrt_T, -a * invnorm * invnorm, T );
    pluseq_scaled_I( second_wrt_T, a );
    pluseq_scaled_outer_product( second_wrt_T, f * inv_tau * inv_tau * inv_tau, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5 * f * inv_tau * inv_tau, T );
    pluseq_scaled_sum_outer_product( second_wrt_T, -0.5 * inv_tau * inv_tau * invnorm, T, adjt );
    pluseq_scaled_sum_outer_product_I( second_wrt_T, 0.5 * inv_tau * inv_tau * invroot, adjt );
    return true;
}

bool TShapeOrientB1::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    const double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = 0.5 / tau * ( Frobenius( T ) - trace( T ) / MSQ_SQRT_THREE );
    return true;
}

bool TShapeOrientB1::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
                                         double& result,
                                         MsqMatrix< 3, 3 >& deriv_wrt_T,
                                         MsqError& err )
{
    const double norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_THREE;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    result = 0.5 * inv_tau * ( norm - invroot * trace( T ) );

    deriv_wrt_T = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * transpose_adj( T );
    deriv_wrt_T *= inv_tau;
    return true;
}

bool TShapeOrientB1::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 norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_THREE;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    const double f = norm - invroot * trace( T );
    result         = 0.5 * inv_tau * f;

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    deriv_wrt_T                  = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= inv_tau;

    const double a = 0.5 * inv_tau * invnorm;
    set_scaled_outer_product( second_wrt_T, -a * invnorm * invnorm, T );
    pluseq_scaled_I( second_wrt_T, a );
    pluseq_scaled_outer_product( second_wrt_T, f * inv_tau * inv_tau * inv_tau, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5 * f * inv_tau * inv_tau, T );
    pluseq_scaled_sum_outer_product( second_wrt_T, -0.5 * inv_tau * inv_tau * invnorm, T, adjt );
    pluseq_scaled_sum_outer_product_I( second_wrt_T, 0.5 * inv_tau * inv_tau * invroot, adjt );
    return true;
}

}  // namespace MBMesquite