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

#undef PRINT_INFO

#include "Mesquite.hpp"
#include "TQualityMetric.hpp"
#include "MsqMatrix.hpp"
#include "ElementQM.hpp"
#include "MsqError.hpp"
#include "Vector3D.hpp"
#include "PatchData.hpp"
#include "MappingFunction.hpp"
#include "WeightCalculator.hpp"
#include "TargetCalculator.hpp"
#include "TMetric.hpp"
#include "TMetricBarrier.hpp"
#include "TargetMetricUtil.hpp"
#include "TMPDerivs.hpp"

#ifdef PRINT_INFO
#include <iostream>
#endif

#include <functional>
#include <algorithm>

#define NUMERICAL_2D_HESSIAN

namespace MBMesquite
{

std::string TQualityMetric::get_name() const
{
    return targetMetric->get_name();
}

bool TQualityMetric::evaluate_internal( PatchData& pd, size_t p_handle, double& value, size_t* indices,
                                        size_t& num_indices, MsqError& err )
{
    const Sample s        = ElemSampleQM::sample( p_handle );
    const size_t e        = ElemSampleQM::elem( p_handle );
    MsqMeshEntity& p_elem = pd.element_by_index( e );
    EntityTopology type   = p_elem.get_element_type();
    unsigned edim         = TopologyInfo::dimension( type );
    const NodeSet bits    = pd.non_slave_node_set( e );

    bool rval;
    if( edim == 3 )
    {  // 3x3 or 3x2 targets ?
        const MappingFunction3D* mf = pd.get_mapping_function_3D( type );
        if( !mf )
        {
            MSQ_SETERR( err )
            ( "No mapping function for element type", MsqError::UNSUPPORTED_ELEMENT );
            return false;
        }

        MsqMatrix< 3, 3 > A, W;
        mf->jacobian( pd, e, bits, s, indices, mDerivs3D, num_indices, A, err );
        MSQ_ERRZERO( err );
        targetCalc->get_3D_target( pd, e, s, W, err );
        MSQ_ERRZERO( err );
        const MsqMatrix< 3, 3 > Winv = inverse( W );
        const MsqMatrix< 3, 3 > T    = A * Winv;
        rval                         = targetMetric->evaluate( T, value, err );
        MSQ_ERRZERO( err );
#ifdef PRINT_INFO
        print_info< 3 >( e, s, A, W, A * inverse( W ) );
#endif
    }
    else if( edim == 2 )
    {
        MsqMatrix< 2, 2 > W, A;
        MsqMatrix< 3, 2 > S_a_transpose_Theta;
        rval =
            evaluate_surface_common( pd, s, e, bits, indices, num_indices, mDerivs2D, W, A, S_a_transpose_Theta, err );
        if( MSQ_CHKERR( err ) || !rval ) return false;
        const MsqMatrix< 2, 2 > Winv = inverse( W );
        const MsqMatrix< 2, 2 > T    = A * Winv;
        rval                         = targetMetric->evaluate( T, value, err );
        MSQ_ERRZERO( err );

#ifdef PRINT_INFO
        print_info< 2 >( e, s, J, Wp, A * inverse( W ) );
#endif
    }
    else
    {
        assert( false );
        return false;
    }

    return rval;
}

bool TQualityMetric::evaluate_with_gradient( PatchData& pd, size_t p_handle, double& value,
                                             std::vector< size_t >& indices, std::vector< Vector3D >& grad,
                                             MsqError& err )
{
    const Sample s        = ElemSampleQM::sample( p_handle );
    const size_t e        = ElemSampleQM::elem( p_handle );
    MsqMeshEntity& p_elem = pd.element_by_index( e );
    EntityTopology type   = p_elem.get_element_type();
    unsigned edim         = TopologyInfo::dimension( type );
    size_t num_idx        = 0;
    const NodeSet bits    = pd.non_slave_node_set( e );

    bool rval;
    if( edim == 3 )
    {  // 3x3 or 3x2 targets ?
        const MappingFunction3D* mf = pd.get_mapping_function_3D( type );
        if( !mf )
        {
            MSQ_SETERR( err )
            ( "No mapping function for element type", MsqError::UNSUPPORTED_ELEMENT );
            return false;
        }

        MsqMatrix< 3, 3 > A, W, dmdT;
        mf->jacobian( pd, e, bits, s, mIndices, mDerivs3D, num_idx, A, err );
        MSQ_ERRZERO( err );
        targetCalc->get_3D_target( pd, e, s, W, err );
        MSQ_ERRZERO( err );
        const MsqMatrix< 3, 3 > Winv = inverse( W );
        const MsqMatrix< 3, 3 > T    = A * Winv;
        rval                         = targetMetric->evaluate_with_grad( T, value, dmdT, err );
        MSQ_ERRZERO( err );
        gradient< 3 >( num_idx, mDerivs3D, dmdT * transpose( Winv ), grad );
#ifdef PRINT_INFO
        print_info< 3 >( e, s, A, W, A * inverse( W ) );
#endif
    }
    else if( edim == 2 )
    {
        MsqMatrix< 2, 2 > W, A, dmdT;
        MsqMatrix< 3, 2 > S_a_transpose_Theta;
        rval = evaluate_surface_common( pd, s, e, bits, mIndices, num_idx, mDerivs2D, W, A, S_a_transpose_Theta, err );
        if( MSQ_CHKERR( err ) || !rval ) return false;
        const MsqMatrix< 2, 2 > Winv = inverse( W );
        const MsqMatrix< 2, 2 > T    = A * Winv;
        rval                         = targetMetric->evaluate_with_grad( T, value, dmdT, err );
        MSQ_ERRZERO( err );
        gradient< 2 >( num_idx, mDerivs2D, S_a_transpose_Theta * dmdT * transpose( Winv ), grad );
#ifdef PRINT_INFO
        print_info< 2 >( e, s, J, Wp, A * inverse( W ) );
#endif
    }
    else
    {
        assert( false );
        return false;
    }

    // pass back index list
    indices.resize( num_idx );
    std::copy( mIndices, mIndices + num_idx, indices.begin() );

    // apply target weight to value
    weight( pd, s, e, num_idx, value, grad.empty() ? 0 : arrptr( grad ), 0, 0, err );
    MSQ_ERRZERO( err );
    return rval;
}

bool TQualityMetric::evaluate_with_Hessian( PatchData& pd, size_t p_handle, double& value,
                                            std::vector< size_t >& indices, std::vector< Vector3D >& grad,
                                            std::vector< Matrix3D >& Hessian, MsqError& err )
{
    const Sample s        = ElemSampleQM::sample( p_handle );
    const size_t e        = ElemSampleQM::elem( p_handle );
    MsqMeshEntity& p_elem = pd.element_by_index( e );
    EntityTopology type   = p_elem.get_element_type();
    unsigned edim         = TopologyInfo::dimension( type );
    size_t num_idx        = 0;
    const NodeSet bits    = pd.non_slave_node_set( e );

    bool rval;
    if( edim == 3 )
    {  // 3x3 or 3x2 targets ?
        const MappingFunction3D* mf = pd.get_mapping_function_3D( type );
        if( !mf )
        {
            MSQ_SETERR( err )
            ( "No mapping function for element type", MsqError::UNSUPPORTED_ELEMENT );
            return false;
        }

        MsqMatrix< 3, 3 > A, W, dmdT, d2mdT2[6];
        mf->jacobian( pd, e, bits, s, mIndices, mDerivs3D, num_idx, A, err );
        MSQ_ERRZERO( err );
        targetCalc->get_3D_target( pd, e, s, W, err );
        MSQ_ERRZERO( err );
        const MsqMatrix< 3, 3 > Winv = inverse( W );
        const MsqMatrix< 3, 3 > T    = A * Winv;
        rval                         = targetMetric->evaluate_with_hess( T, value, dmdT, d2mdT2, err );
        MSQ_ERRZERO( err );
        gradient< 3 >( num_idx, mDerivs3D, dmdT * transpose( Winv ), grad );
        second_deriv_wrt_product_factor( d2mdT2, Winv );
        Hessian.resize( num_idx * ( num_idx + 1 ) / 2 );
        if( num_idx ) hessian< 3 >( num_idx, mDerivs3D, d2mdT2, arrptr( Hessian ) );

#ifdef PRINT_INFO
        print_info< 3 >( e, s, A, W, A * inverse( W ) );
#endif
    }
    else if( edim == 2 )
    {
#ifdef NUMERICAL_2D_HESSIAN
        // return finite difference approximation for now

        return QualityMetric::evaluate_with_Hessian( pd, p_handle, value, indices, grad, Hessian, err );
#else
        MsqMatrix< 2, 2 > W, A, dmdT, d2mdT2[3];
        MsqMatrix< 3, 2 > M;
        rval = evaluate_surface_common( pd, s, e, bits, mIndices, num_idx, mDerivs2D, W, A, M, err );
        if( MSQ_CHKERR( err ) || !rval ) return false;
        const MsqMatrix< 2, 2 > Winv = inverse( W );
        const MsqMatrix< 2, 2 > T    = A * Winv;
        rval                         = targetMetric->evaluate_with_hess( T, value, dmdT, d2mdT2, err );
        MSQ_ERRZERO( err );
        gradient< 2 >( num_idx, mDerivs2D, M * dmdT * transpose( Winv ), grad );
        // calculate 2D hessian
        second_deriv_wrt_product_factor( d2mdT2, Winv );
        const size_t n = num_idx * ( num_idx + 1 ) / 2;
        hess2d.resize( n );
        if( n ) hessian< 2 >( num_idx, mDerivs2D, d2mdT2, arrptr( hess2d ) );
        // calculate surface hessian as transform of 2D hessian
        Hessian.resize( n );
        for( size_t i = 0; i < n; ++i )
            Hessian[i] = Matrix3D( ( M * hess2d[i] * transpose( M ) ).data() );
#ifdef PRINT_INFO
        print_info< 2 >( e, s, J, Wp, A * inverse( W ) );
#endif
#endif
    }
    else
    {
        assert( 0 );
        return false;
    }

    // pass back index list
    indices.resize( num_idx );
    std::copy( mIndices, mIndices + num_idx, indices.begin() );

    // apply target weight to value
    if( !num_idx )
        weight( pd, s, e, num_idx, value, 0, 0, 0, err );
    else
        weight( pd, s, e, num_idx, value, arrptr( grad ), 0, arrptr( Hessian ), err );
    MSQ_ERRZERO( err );
    return rval;
}

bool TQualityMetric::evaluate_with_Hessian_diagonal( PatchData& pd, size_t p_handle, double& value,
                                                     std::vector< size_t >& indices, std::vector< Vector3D >& grad,
                                                     std::vector< SymMatrix3D >& diagonal, MsqError& err )
{
    const Sample s        = ElemSampleQM::sample( p_handle );
    const size_t e        = ElemSampleQM::elem( p_handle );
    MsqMeshEntity& p_elem = pd.element_by_index( e );
    EntityTopology type   = p_elem.get_element_type();
    unsigned edim         = TopologyInfo::dimension( type );
    size_t num_idx        = 0;
    const NodeSet bits    = pd.non_slave_node_set( e );

    bool rval;
    if( edim == 3 )
    {  // 3x3 or 3x2 targets ?
        const MappingFunction3D* mf = pd.get_mapping_function_3D( type );
        if( !mf )
        {
            MSQ_SETERR( err )
            ( "No mapping function for element type", MsqError::UNSUPPORTED_ELEMENT );
            return false;
        }

        MsqMatrix< 3, 3 > A, W, dmdT, d2mdT2[6];
        mf->jacobian( pd, e, bits, s, mIndices, mDerivs3D, num_idx, A, err );
        MSQ_ERRZERO( err );
        targetCalc->get_3D_target( pd, e, s, W, err );
        MSQ_ERRZERO( err );
        const MsqMatrix< 3, 3 > Winv = inverse( W );
        const MsqMatrix< 3, 3 > T    = A * Winv;
        rval                         = targetMetric->evaluate_with_hess( T, value, dmdT, d2mdT2, err );
        MSQ_ERRZERO( err );
        gradient< 3 >( num_idx, mDerivs3D, dmdT * transpose( Winv ), grad );
        second_deriv_wrt_product_factor( d2mdT2, Winv );

        diagonal.resize( num_idx );
        hessian_diagonal< 3 >( num_idx, mDerivs3D, d2mdT2, arrptr( diagonal ) );
#ifdef PRINT_INFO
        print_info< 3 >( e, s, A, W, A * inverse( W ) );
#endif
    }
    else if( edim == 2 )
    {
#ifdef NUMERICAL_2D_HESSIAN
        // use finite diference approximation for now
        return QualityMetric::evaluate_with_Hessian_diagonal( pd, p_handle, value, indices, grad, diagonal, err );
#else
        MsqMatrix< 2, 2 > W, A, dmdT, d2mdT2[3];
        MsqMatrix< 3, 2 > M;
        rval = evaluate_surface_common( pd, s, e, bits, mIndices, num_idx, mDerivs2D, W, A, M, err );
        if( MSQ_CHKERR( err ) || !rval ) return false;
        const MsqMatrix< 2, 2 > Winv = inverse( W );
        const MsqMatrix< 2, 2 > T    = A * Winv;
        rval                         = targetMetric->evaluate_with_hess( T, value, dmdT, d2mdT2, err );
        MSQ_ERRZERO( err );
        gradient< 2 >( num_idx, mDerivs2D, M * dmdT * transpose( Winv ), grad );
        second_deriv_wrt_product_factor( d2mdT2, Winv );

        diagonal.resize( num_idx );
        for( size_t i = 0; i < num_idx; ++i )
        {
            MsqMatrix< 2, 2 > block2d;
            block2d( 0, 0 )     = transpose( mDerivs2D[i] ) * d2mdT2[0] * mDerivs2D[i];
            block2d( 0, 1 )     = transpose( mDerivs2D[i] ) * d2mdT2[1] * mDerivs2D[i];
            block2d( 1, 0 )     = block2d( 0, 1 );
            block2d( 1, 1 )     = transpose( mDerivs2D[i] ) * d2mdT2[2] * mDerivs2D[i];
            MsqMatrix< 3, 2 > p = M * block2d;

            SymMatrix3D& H = diagonal[i];
            H[0]           = p.row( 0 ) * transpose( M.row( 0 ) );
            H[1]           = p.row( 0 ) * transpose( M.row( 1 ) );
            H[2]           = p.row( 0 ) * transpose( M.row( 2 ) );
            H[3]           = p.row( 1 ) * transpose( M.row( 1 ) );
            H[4]           = p.row( 1 ) * transpose( M.row( 2 ) );
            H[5]           = p.row( 2 ) * transpose( M.row( 2 ) );
        }
#ifdef PRINT_INFO
        print_info< 2 >( e, s, J, Wp, A * inverse( W ) );
#endif
#endif
    }
    else
    {
        assert( 0 );
        return false;
    }

    // pass back index list
    indices.resize( num_idx );
    std::copy( mIndices, mIndices + num_idx, indices.begin() );

    // apply target weight to value
    if( !num_idx )
        weight( pd, s, e, num_idx, value, 0, 0, 0, err );
    else
        weight( pd, s, e, num_idx, value, arrptr( grad ), arrptr( diagonal ), 0, err );
    MSQ_ERRZERO( err );
    return rval;
}

}  // namespace MBMesquite