TShapeOrientB2.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

    (2009) kraftche@cae.wisc.edu

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

/** \file TShapeOrientB2.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TShapeOrientB2.hpp"
#include "MsqMatrix.hpp"
#include "MsqError.hpp"
#include "TMPDerivs.hpp"
#include "TMPCommon.hpp"

namespace MBMesquite
{

std::string TShapeOrientB2::get_name() const
{
    return "TShapeOrientB2";
}

TShapeOrientB2::~TShapeOrientB2() {}

bool TShapeOrientB2::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& err )
{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double tr = trace( T );
    result          = ( 0.5 / tau ) * ( sqr_Frobenius( T ) - 0.5 * tr * fabs( tr ) );
    return true;
}

bool TShapeOrientB2::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
                                         double& result,
                                         MsqMatrix< 2, 2 >& deriv_wrt_T,
                                         MsqError& err )
{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double b = 0.5 / tau;

    const double tr = trace( T );
    const double f  = 0.5 * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2 * tau;
    deriv_wrt_T -= result * transpose_adj( T );

    result *= b;
    deriv_wrt_T *= b / tau;

    return true;
}

bool TShapeOrientB2::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 )
{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double b = 0.5 / tau;

    // calculate non-barrier value (ShapeOrientAlt1)
    const double tr = trace( T );
    const double f  = 0.5 * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    // calculate non-barrier first derivatives
    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2;

    // calculate barrier second derivs
    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    set_scaled_sum_outer_product( second_wrt_T, -b / tau, deriv_wrt_T, adjt );
    pluseq_scaled_outer_product( second_wrt_T, result / ( tau * tau * tau ), adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -result * b / tau, T );
    // calculate non-barrier barrier portion of second derivs
    pluseq_scaled_I( second_wrt_T, 1 / tau );
    pluseq_scaled_outer_product_I_I( second_wrt_T, 0.5 / tau * ( tr < 0 ? 1 : -1 ) );

    // calculate barrier derivs from non-barrier
    deriv_wrt_T *= tau;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= b / tau;

    // barrier value from non-barrier
    result *= b;
    return true;
}

bool TShapeOrientB2::evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err )
{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double tr = trace( T );
    result          = ( 0.5 / tau ) * ( sqr_Frobenius( T ) - MSQ_ONE_THIRD * tr * fabs( tr ) );
    return true;
}

bool TShapeOrientB2::evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
                                         double& result,
                                         MsqMatrix< 3, 3 >& deriv_wrt_T,
                                         MsqError& err )
{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double b = 0.5 / tau;

    const double tr = trace( T );
    const double f  = MSQ_ONE_THIRD * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2 * tau;
    deriv_wrt_T -= result * transpose_adj( T );

    result *= b;
    deriv_wrt_T *= b / tau;

    return true;
}

bool TShapeOrientB2::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 )
{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        result = 0.0;
        return false;
    }
    const double b = 0.5 / tau;

    // calculate non-barrier value (ShapeOrientAlt1)
    const double tr = trace( T );
    const double f  = MSQ_ONE_THIRD * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    // calculate non-barrier first derivatives
    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2;

    // calculate barrier second derivs
    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    set_scaled_sum_outer_product( second_wrt_T, -b / tau, deriv_wrt_T, adjt );
    pluseq_scaled_outer_product( second_wrt_T, result / ( tau * tau * tau ), adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -result * b / tau, T );
    // calculate non-barrier barrier portion of second derivs
    pluseq_scaled_I( second_wrt_T, 1 / tau );
    pluseq_scaled_outer_product_I_I( second_wrt_T, MSQ_ONE_THIRD / tau * ( tr < 0 ? 1 : -1 ) );

    // calculate barrier derivs from non-barrier
    deriv_wrt_T *= tau;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= b / tau;

    // barrier value from non-barrier
    result *= b;
    return true;
}

}  // namespace MBMesquite