idft_time_test.cpp

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

    Copyright 2004 Sandia Corporation and Argonne National
    Laboratory.  Under the terms of Contract DE-AC04-94AL85000
    with Sandia Corporation, the U.S. Government retains certain
    rights in 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

    [email protected]

  ***************************************************************** */
#include <iostream>
#include <sstream>
using std::cerr;
using std::cout;
using std::endl;

#include <cstdlib>

#include "Mesquite.hpp"
#include "MeshImpl.hpp"
#include "MsqError.hpp"
#include "InstructionQueue.hpp"
#include "TerminationCriterion.hpp"
#include "QualityAssessor.hpp"
#include "PlanarDomain.hpp"

#include "IdealWeightInverseMeanRatio.hpp"
#include "ElementPMeanP.hpp"
#include "TInverseMeanRatio.hpp"
#include "TQualityMetric.hpp"
#include "TOffset.hpp"
#include "TOffset.hpp"

#include "IdealShapeTarget.hpp"
#include "PMeanPTemplate.hpp"
#include "SteepestDescent.hpp"
#include "ConjugateGradient.hpp"
#include "QuasiNewton.hpp"

#include "MeshWriter.hpp"
#include "MsqTimer.hpp"
#include "TestUtil.hpp"

using namespace MBMesquite;

std::string DEFAULT_INPUT = TestDir + "unittest/mesquite/2D/vtk/tris/untangled/equil_tri2.vtk";

/* Print usage or help information: exits if err == true */
void usage( const char* argv0 = 0, bool err = true )
{
    std::ostream& s     = err ? cerr : cout;
    const char* defname = "main";
    if( !argv0 ) argv0 = defname;

    s << "Usage: " << defname << " [-n|-c|-q] [-e] [-t] [-a] [-N] [{-v|-g|-p} <output_file>] [<input_file>]" << endl
      << "       " << defname << " -h" << std::endl;

    if( err ) exit( 1 );

    s << "  -n : Use SteepestDescent solver (default)" << endl
      << "  -c : Use ConjugateGradient solver" << endl
      << "  -q : Use QuasiNewton solver" << endl
      << "  -e : Test IdealWeightInverseMeanRatio metric" << endl
      << "  -t : Test InverseMeanRatio3D target metric" << endl
      << "  -a : Test ElementPMeanP(InverseMeanRatio3D)" << endl
      << "  -N : Test InverseMeanRatio3D with finite difference derivatives" << endl
      << "  -C : Compare InverseMeanRatio3D and IdealWeightInverseMeanRatio" << endl
      << "  -v : Write output mesh to specified VTK file" << endl
      << "  -g : Write output mesh to specified GnuPlot file" << endl
      << "  -p : Write output mesh to specified EPS file" << endl
      << "  -P : Write solver plot data to specified file." << endl
      << "Default is all metrics if non specified." << endl
      << "Default input file: " << DEFAULT_INPUT << endl;
}

const char* vtk_file  = 0; /* vtk output file name */
const char* eps_file  = 0; /* eps output file name */
const char* gpt_file  = 0; /* GNUPlot output file name */
const char* plot_file = 0; /* Time-dependent plot of solver data */

enum Solver
{
    STEEP_DESCENT,
    CONJ_GRAD,
    QUASI_NEWT
};

/* Run an optimization: returns average quality of final mesh */
double run( QualityMetric* metric, Solver solver, const char* input_file, double& seconds_out, int& iterations_out );

/* Force finite difference approximation of derivatives for
 * an existing quality metric */
class NumericQM : public QualityMetric
{
  private:
    QualityMetric* realMetric;

  public:
    NumericQM( QualityMetric* real_metric ) : realMetric( real_metric ) {}
    virtual MetricType get_metric_type() const;
    virtual std::string get_name() const;
    virtual int get_negate_flag() const;
    virtual void get_evaluations( PatchData& pd,
                                  std::vector< size_t >& handles,
                                  bool free_vertices_only,
                                  MsqError& err );
    virtual bool evaluate( PatchData& pd, size_t handle, double& value, MsqError& err );
    virtual bool evaluate_with_indices( PatchData& pd,
                                        size_t handle,
                                        double& value,
                                        std::vector< size_t >& indices,
                                        MsqError& err );
};
QualityMetric::MetricType NumericQM::get_metric_type() const
{
    return realMetric->get_metric_type();
}
std::string NumericQM::get_name() const
{
    std::string r = realMetric->get_name();
    r += " (FD)";
    return r;
}

/* At each evaluation of this metric, compare the values resulting
 * from the evaluation of two other metrics: flag an error if they
 * differ or return the common result if the same */
class CompareMetric : public QualityMetric
{
  private:
    QualityMetric *metric1, *metric2;
    bool maskPlane;
    int maskAxis;
    std::vector< size_t > m2Handles;
    std::vector< Vector3D > m2Grad;
    std::vector< SymMatrix3D > m2Diag;
    std::vector< Matrix3D > m2Hess;
    static const double epsilon;

  public:
    CompareMetric( QualityMetric* qm1, QualityMetric* qm2, bool mask_qm2_coord = false )
        : metric1( qm1 ), metric2( qm2 ), maskPlane( mask_qm2_coord ), maskAxis( -1 )
    {
    }

    MetricType get_metric_type() const;

    std::string get_name() const;

    int get_negate_flag() const;

    void get_evaluations( PatchData& pd, std::vector< size_t >& handles, bool free_vertices_only, MsqError& err );

    bool evaluate( PatchData& pd, size_t handle, double& value, MsqError& err );

    bool evaluate_with_indices( PatchData& pd,
                                size_t handle,
                                double& value,
                                std::vector< size_t >& indices,
                                MsqError& err );

    bool evaluate_with_gradient( PatchData& pd,
                                 size_t handle,
                                 double& value,
                                 std::vector< size_t >& indices,
                                 std::vector< Vector3D >& gradient,
                                 MsqError& err );

    bool evaluate_with_Hessian_diagonal( PatchData& pd,
                                         size_t handle,
                                         double& value,
                                         std::vector< size_t >& indices,
                                         std::vector< Vector3D >& gradient,
                                         std::vector< SymMatrix3D >& Hessian_diagonal,
                                         MsqError& err );

    bool evaluate_with_Hessian( PatchData& pd,
                                size_t handle,
                                double& value,
                                std::vector< size_t >& indices,
                                std::vector< Vector3D >& gradient,
                                std::vector< Matrix3D >& Hessian,
                                MsqError& err );

    void get_mask_axis( PatchData& pd );
    bool equal( Vector3D grad1, const Vector3D& grad2 ) const;
    bool equal( SymMatrix3D hess1, const SymMatrix3D& hess2 ) const;
    bool equal( Matrix3D hess1, const Matrix3D& hess2 ) const;
};
const double CompareMetric::epsilon = 5e-2;

/* Parse command line options and call 'run' */
int main( int argc, char* argv[] )
{
    Solver solver              = STEEP_DESCENT;
    bool do_non_target_metric  = false;
    bool do_new_target_metric  = false;
    bool do_new_target_average = false;
    bool do_new_target_numeric = false;
    bool do_compare_metric     = false;
    const char* input_file     = DEFAULT_INPUT.c_str();
    bool no_more_flags         = false;

    std::list< const char** > exp_list;
    for( int i = 1; i < argc; ++i )
    {
        if( argv[i][0] == '-' && !no_more_flags )
        {
            for( int k = 1; argv[i][k]; ++k )
            {
                switch( argv[i][k] )
                {
                    case 'n':
                        solver = STEEP_DESCENT;
                        break;
                    case 'c':
                        solver = CONJ_GRAD;
                        break;
                    case 'q':
                        solver = QUASI_NEWT;
                        break;
                    case 'e':
                        do_non_target_metric = true;
                        break;
                    case 't':
                        do_new_target_metric = true;
                        break;
                    case 'a':
                        do_new_target_average = true;
                        break;
                    case 'N':
                        do_new_target_numeric = true;
                        break;
                    case 'C':
                        do_compare_metric = true;
                        break;
                    case 'v':
                        exp_list.push_back( &vtk_file );
                        break;
                    case 'g':
                        exp_list.push_back( &gpt_file );
                        break;
                    case 'p':
                        exp_list.push_back( &eps_file );
                        break;
                    case 'P':
                        exp_list.push_back( &plot_file );
                        break;
                    case 'h':
                        usage( argv[0], false );
                        return 0;
                    case '-':
                        no_more_flags = true;
                        break;
                    default:
                        cerr << "Invalid flag: '" << argv[i][k] << "'" << endl;
                        usage( argv[0] );
                }
            }
        }
        else if( !exp_list.empty() )
        {
            const char** ptr = exp_list.front();
            exp_list.pop_front();
            *ptr = argv[i];
        }
        else
        {
            if( !DEFAULT_INPUT.compare( input_file ) )
            {
                cerr << "Unexpected argument: \"" << argv[i] << '"' << endl;
                usage( argv[0] );
            }
            input_file = argv[i];
        }
    }

    int count = 0;
    if( do_non_target_metric ) ++count;
    if( do_new_target_metric ) ++count;
    if( do_new_target_average ) ++count;
    if( do_new_target_numeric ) ++count;
    if( do_compare_metric ) ++count;

    if( !count )
    {
        do_compare_metric = true;
        count             = 1;
    }

    if( ( vtk_file || gpt_file || eps_file ) && count != 1 )
    {
        cerr << "Error: Cannot write output file if running multiple tests" << endl;
        return 2;
    }

    IdealWeightInverseMeanRatio non_target_metric;
    IdealShapeTarget new_target;
    TInverseMeanRatio tmp;
    TOffset tmp_off( 1.0, &tmp );  // target metrics are zero-based
    TQualityMetric new_target_metric( &new_target, &tmp_off );
    ElementPMeanP new_target_average( 1.0, &new_target_metric );
    NumericQM new_target_numeric( &new_target_metric );
    CompareMetric comp_metric( &non_target_metric, &new_target_average, true );

    std::ostringstream os;
    double secs, qual;
    if( do_non_target_metric )
    {
        qual = run( &non_target_metric, solver, input_file, secs, count );
        os << "IdealWeightInverseMeanRatio: " << qual << " after " << count << " iterations in " << secs << " seconds"
           << endl;
    }
    if( do_new_target_metric )
    {
        qual = run( &new_target_metric, solver, input_file, secs, count );
        os << "TQualityMetric              : " << qual << " after " << count << " iterations in " << secs << " seconds"
           << endl;
    }
    if( do_new_target_average )
    {
        qual = run( &new_target_average, solver, input_file, secs, count );
        os << "ElementPMeanP              : " << qual << " after " << count << " iterations in " << secs << " seconds"
           << endl;
    }
    if( do_new_target_numeric )
    {
        qual = run( &new_target_numeric, solver, input_file, secs, count );
        os << "TQualityMetric (FD)         : " << qual << " after " << count << " iterations in " << secs << " seconds"
           << endl;
    }
    if( do_compare_metric )
    {
        qual = run( &comp_metric, solver, input_file, secs, count );
        os << "Metric comparison      : " << qual << " after " << count << " iterations in " << secs << " seconds"
           << endl;
    }

    cout << endl << os.str() << endl;
    return 0;
}

double run( QualityMetric* metric,
            Solver solver_type,
            const char* input_file,
            double& seconds_out,
            int& iterations_out )
{
    MsqPrintError err( cerr );
    IdealWeightInverseMeanRatio qa_metric;
    TerminationCriterion inner, outer;
    outer.add_iteration_limit( 1 );
    inner.add_absolute_vertex_movement( 1e-4 );
    inner.add_iteration_limit( 100 );
    PMeanPTemplate of( 1.0, metric );
    QualityAssessor qa( &qa_metric );
    qa.add_quality_assessment( metric );
    InstructionQueue q;
    SteepestDescent steep( &of );
    QuasiNewton quasi( &of );
    ConjugateGradient conj( &of );
    VertexMover* solver = 0;
    switch( solver_type )
    {
        case STEEP_DESCENT:
            solver = &steep;
            break;
        case QUASI_NEWT:
            solver = &quasi;
            break;
        case CONJ_GRAD:
            solver = &conj;
            break;
    }
    q.set_master_quality_improver( solver, err );
    q.add_quality_assessor( &qa, err );
    solver->set_inner_termination_criterion( &inner );
    solver->set_outer_termination_criterion( &outer );

    if( plot_file ) inner.write_iterations( plot_file, err );

    MeshImpl mesh;
    mesh.read_vtk( input_file, err );
    if( err )
    {
        cerr << "Failed to read input file: \"" << input_file << '"' << endl;
        exit( 1 );
    }

    std::vector< Mesh::VertexHandle > handles;
    mesh.get_all_vertices( handles, err );
    if( handles.empty() )
    {
        cerr << "no veritces in mesh" << endl;
        exit( 1 );
    }
    std::vector< MsqVertex > coords( handles.size() );
    mesh.vertices_get_coordinates( arrptr( handles ), arrptr( coords ), handles.size(), err );
    Vector3D min( HUGE_VAL ), max( -HUGE_VAL );
    for( size_t i = 0; i < coords.size(); ++i )
    {
        for( int j = 0; j < 3; ++j )
        {
            if( coords[i][j] < min[j] ) min[j] = coords[i][j];
            if( coords[i][j] > max[j] ) max[j] = coords[i][j];
        }
    }

    Vector3D size        = max - min;
    PlanarDomain* domain = 0;
    if( size[0] < 1e-4 )
        domain = new PlanarDomain( PlanarDomain::YZ, min[0] );
    else if( size[1] < 1e-4 )
        domain = new PlanarDomain( PlanarDomain::XZ, min[1] );
    else if( size[2] < 1e-4 )
        domain = new PlanarDomain( PlanarDomain::XY, min[2] );

    Timer timer;
    MeshDomainAssoc mesh_and_domain = MeshDomainAssoc( &mesh, domain );
    q.run_instructions( &mesh_and_domain, err );
    seconds_out = timer.since_birth();
    if( err )
    {
        cerr << "Optimization failed." << endl << err << endl;
        abort();
    }

    if( vtk_file )
    {
        MeshWriter::write_vtk( &mesh, vtk_file, err );
        if( err ) cerr << vtk_file << ": failed to write file." << endl;
    }
    if( gpt_file )
    {
        MeshWriter::write_gnuplot( &mesh, gpt_file, err );
        if( err ) cerr << gpt_file << ": failed to write file." << endl;
    }
    if( eps_file )
    {
        PlanarDomain xy( PlanarDomain::XY );
        MeshWriter::Projection proj( domain ? domain : &xy );
        MeshWriter::write_eps( &mesh, eps_file, proj, err );
        if( err ) cerr << eps_file << ": failed to write file." << endl;
    }
    delete domain;

    iterations_out = inner.get_iteration_count();

    const QualityAssessor::Assessor* a = qa.get_results( &qa_metric );
    return a->get_average();
}

int NumericQM::get_negate_flag() const
{
    return realMetric->get_negate_flag();
}

void NumericQM::get_evaluations( PatchData& pd, std::vector< size_t >& handles, bool free_vertices_only, MsqError& err )
{
    realMetric->get_evaluations( pd, handles, free_vertices_only, err );
}

bool NumericQM::evaluate( PatchData& pd, size_t handle, double& value, MsqError& err )
{
    return realMetric->evaluate( pd, handle, value, err );
}

bool NumericQM::evaluate_with_indices( PatchData& pd,
                                       size_t handle,
                                       double& value,
                                       std::vector< size_t >& indices,
                                       MsqError& err )
{
    return realMetric->evaluate_with_indices( pd, handle, value, indices, err );
}

QualityMetric::MetricType CompareMetric::get_metric_type() const
{
    MetricType t1 = metric1->get_metric_type();
    assert( metric2->get_metric_type() == t1 );
    return t1;
}

std::string CompareMetric::get_name() const
{
    std::string n = metric1->get_name();
    n += " =? ";
    n += metric2->get_name();
    return n;
}

int CompareMetric::get_negate_flag() const
{
    assert( metric1->get_negate_flag() == metric2->get_negate_flag() );
    return metric1->get_negate_flag();
}

void CompareMetric::get_evaluations( PatchData& pd,
                                     std::vector< size_t >& handles,
                                     bool free_vertices_only,
                                     MsqError& err )
{
    if( maskPlane ) get_mask_axis( pd );

    m2Handles.clear();
    metric1->get_evaluations( pd, handles, free_vertices_only, err );MSQ_ERRRTN( err );
    metric2->get_evaluations( pd, m2Handles, free_vertices_only, err );MSQ_ERRRTN( err );
    bool same = ( handles.size() == m2Handles.size() );
    std::sort( m2Handles.begin(), m2Handles.end() );
    for( std::vector< size_t >::iterator i = handles.begin(); i != handles.end(); ++i )
        if( !std::binary_search( m2Handles.begin(), m2Handles.end(), *i ) ) same = false;
    if( !same )
    {
        MSQ_SETERR( err )
        ( "Metrics have incompatible lists of evaluation handles.\n", MsqError::INVALID_STATE );
    }
}

bool CompareMetric::evaluate( PatchData& pd, size_t handle, double& value, MsqError& err )
{
    double m2val;
    bool r1, r2;
    r1 = metric1->evaluate( pd, handle, value, err );
    MSQ_ERRZERO( err );
    r2 = metric2->evaluate( pd, handle, m2val, err );
    MSQ_ERRZERO( err );
    if( r1 != r2 || ( r1 && fabs( value - m2val ) > epsilon ) )
    {
        MSQ_SETERR( err )
        ( MsqError::INVALID_STATE,
          "Metrics returned different values for handle %lu "
          "in evaluate:\n"
          "\t%s %f vs. %s %f\n",
          (unsigned long)handle, r1 ? "true" : "false", value, r2 ? "true" : "false", m2val );
    }

    return r1 && !err;
}

bool CompareMetric::evaluate_with_indices( PatchData& pd,
                                           size_t handle,
                                           double& value,
                                           std::vector< size_t >& indices,
                                           MsqError& err )
{
    double m2val;
    bool r1, r2;
    m2Handles.clear();
    r1 = metric1->evaluate_with_indices( pd, handle, value, indices, err );
    MSQ_ERRZERO( err );
    r2 = metric2->evaluate_with_indices( pd, handle, m2val, m2Handles, err );
    MSQ_ERRZERO( err );
    if( r1 != r2 || ( r1 && fabs( value - m2val ) > epsilon ) )
    {
        MSQ_SETERR( err )
        ( MsqError::INVALID_STATE,
          "Metrics returned different values for handle %lu "
          "in evaluate_with_indices:\n"
          "\t%s %f vs. %s %f\n",
          (unsigned long)handle, r1 ? "true" : "false", value, r2 ? "true" : "false", m2val );
    }
    else
    {
        bool same = ( indices.size() == m2Handles.size() );
        std::sort( m2Handles.begin(), m2Handles.end() );
        for( std::vector< size_t >::iterator i = indices.begin(); i != indices.end(); ++i )
            if( !std::binary_search( m2Handles.begin(), m2Handles.end(), *i ) ) same = false;
        if( !same )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned incompatible lists of vertex indices"
              " for handle %lu in evaluate_with_indices\n.",
              (unsigned long)handle );
        }
    }

    return r1 && !err;
}

bool CompareMetric::evaluate_with_gradient( PatchData& pd,
                                            size_t handle,
                                            double& value,
                                            std::vector< size_t >& indices,
                                            std::vector< Vector3D >& gradient,
                                            MsqError& err )
{
    double m2val;
    bool r1, r2;
    m2Handles.clear();
    m2Grad.clear();
    r1 = metric1->evaluate_with_gradient( pd, handle, value, indices, gradient, err );
    MSQ_ERRZERO( err );
    r2 = metric2->evaluate_with_gradient( pd, handle, m2val, m2Handles, m2Grad, err );
    MSQ_ERRZERO( err );
    if( r1 != r2 || ( r1 && fabs( value - m2val ) > epsilon ) )
    {
        MSQ_SETERR( err )
        ( MsqError::INVALID_STATE,
          "Metrics returned different values for handle %lu in "
          "evaluate_with_gradient:\n"
          "\t%s %f vs. %s %f\n",
          (unsigned long)handle, r1 ? "true" : "false", value, r2 ? "true" : "false", m2val );
    }
    else
    {
        std::vector< size_t >::const_iterator i, j;
        std::vector< Vector3D >::const_iterator r, s;
        int grad_diff = 0;
        bool same     = ( indices.size() == m2Handles.size() );
        std::sort( m2Handles.begin(), m2Handles.end() );
        for( i = indices.begin(); i != indices.end(); ++i )
        {
            j = std::lower_bound( m2Handles.begin(), m2Handles.end(), *i );
            if( j == m2Handles.end() || *j != *i )
            {
                same = false;
                continue;
            }

            r = gradient.begin() + ( i - indices.begin() );
            s = m2Grad.begin() + ( j - m2Handles.begin() );
            if( !equal( *r, *s ) ) ++grad_diff;
        }

        if( !same )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned incompatible lists of vertex indices"
              " for handle %lu in evaluate_with_gradient\n.",
              (unsigned long)handle );
        }
        else if( grad_diff )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned different gradient vectors for "
              " %d of %u vertices for handle %lu in "
              "evaluate_with_gradient\n.",
              grad_diff, (unsigned)gradient.size(), (unsigned long)handle );
        }
    }

    return r1 && !err;
}

bool CompareMetric::evaluate_with_Hessian_diagonal( PatchData& pd,
                                                    size_t handle,
                                                    double& value,
                                                    std::vector< size_t >& indices,
                                                    std::vector< Vector3D >& gradient,
                                                    std::vector< SymMatrix3D >& diagonal,
                                                    MsqError& err )
{
    double m2val;
    bool r1, r2;
    m2Handles.clear();
    m2Grad.clear();
    m2Diag.clear();
    r1 = metric1->evaluate_with_Hessian_diagonal( pd, handle, value, indices, gradient, diagonal, err );
    MSQ_ERRZERO( err );
    r2 = metric2->evaluate_with_Hessian_diagonal( pd, handle, m2val, m2Handles, m2Grad, m2Diag, err );
    MSQ_ERRZERO( err );
    if( r1 != r2 || ( r1 && fabs( value - m2val ) > epsilon ) )
    {
        MSQ_SETERR( err )
        ( MsqError::INVALID_STATE,
          "Metrics returned different values for handle %lu in "
          "evaluate_with_Hessian_diagonal:\n"
          "\t%s %f vs. %s %f\n",
          (unsigned long)handle, r1 ? "true" : "false", value, r2 ? "true" : "false", m2val );
    }
    else
    {
        std::vector< size_t >::const_iterator i, j;
        std::vector< Vector3D >::const_iterator r, s;
        std::vector< SymMatrix3D >::const_iterator u, v;
        int grad_diff = 0, hess_diff = 0;
        bool same = ( indices.size() == m2Handles.size() );
        std::sort( m2Handles.begin(), m2Handles.end() );
        for( i = indices.begin(); i != indices.end(); ++i )
        {
            j = std::lower_bound( m2Handles.begin(), m2Handles.end(), *i );
            if( j == m2Handles.end() || *j != *i )
            {
                same = false;
                continue;
            }

            r = gradient.begin() + ( i - indices.begin() );
            s = m2Grad.begin() + ( j - m2Handles.begin() );
            if( !equal( *r, *s ) ) ++grad_diff;

            u = diagonal.begin() + ( i - indices.begin() );
            v = m2Diag.begin() + ( j - m2Handles.begin() );
            if( !equal( *u, *v ) ) ++hess_diff;
        }

        if( !same )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned incompatible lists of vertex indices"
              " for handle %lu in evaluate_with_Hessian_diagonal\n.",
              (unsigned long)handle );
        }
        else if( grad_diff )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned different gradient vectors for "
              " %d of %u vertices for handle %lu in "
              "evaluate_with_Hessian_diagonal\n.",
              grad_diff, (unsigned)gradient.size(), (unsigned long)handle );
        }
        else if( hess_diff )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned different Hessian blocks for "
              " %d of %u vertices for handle %lu in "
              "evaluate_with_Hessian_diagonal\n.",
              hess_diff, (unsigned)diagonal.size(), (unsigned long)handle );
        }
    }

    return r1 && !err;
}

bool CompareMetric::evaluate_with_Hessian( PatchData& pd,
                                           size_t handle,
                                           double& value,
                                           std::vector< size_t >& indices,
                                           std::vector< Vector3D >& gradient,
                                           std::vector< Matrix3D >& Hessian,
                                           MsqError& err )
{
    double m2val;
    bool r1, r2;
    m2Handles.clear();
    m2Grad.clear();
    m2Hess.clear();
    r1 = metric1->evaluate_with_Hessian( pd, handle, value, indices, gradient, Hessian, err );
    MSQ_ERRZERO( err );
    r2 = metric2->evaluate_with_Hessian( pd, handle, m2val, m2Handles, m2Grad, m2Hess, err );
    MSQ_ERRZERO( err );
    if( r1 != r2 || fabs( value - m2val ) > epsilon )
    {
        MSQ_SETERR( err )
        ( MsqError::INVALID_STATE,
          "Metrics returned different values for handle %lu in "
          "evaluate_with_Hessian:\n"
          "\t%s %f vs. %s %f\n",
          (unsigned long)handle, r1 ? "true" : "false", value, r2 ? "true" : "false", m2val );
    }
    else
    {
        std::vector< size_t >::const_iterator i, j;
        std::vector< Vector3D >::const_iterator r, s;
        int grad_diff = 0, hess_diff = 0;
        bool same = ( indices.size() == m2Handles.size() );
        std::sort( m2Handles.begin(), m2Handles.end() );
        for( i = indices.begin(); i != indices.end(); ++i )
        {
            j = std::lower_bound( m2Handles.begin(), m2Handles.end(), *i );
            if( j == m2Handles.end() || *j != *i )
            {
                same = false;
                continue;
            }

            r = gradient.begin() + ( i - indices.begin() );
            s = m2Grad.begin() + ( j - m2Handles.begin() );
            if( !equal( *r, *s ) )
            {
                ++grad_diff;
                // call again for so debugger can step into it after failure is found
                std::vector< size_t > i2;
                std::vector< Vector3D > g2;
                std::vector< Matrix3D > h2;
                metric2->evaluate_with_Hessian( pd, handle, m2val, i2, g2, h2, err );
            }
        }

        if( !same )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned incompatible lists of vertex indices"
              " for handle %lu in evaluate_with_Hessian\n.",
              (unsigned long)handle );
        }
        else if( grad_diff )
        {
            MSQ_SETERR( err )
            ( MsqError::INVALID_STATE,
              "Metrics returned different gradient vectors for "
              " %d of %u vertices for handle %lu in "
              "evaluate_with_Hessian\n.",
              grad_diff, (unsigned)gradient.size(), (unsigned long)handle );
        }
        else
        {
            size_t row, col, row2, col2, idx, idx2;
            for( row = idx = 0; row < indices.size(); ++row )
            {
                row2 = std::lower_bound( m2Handles.begin(), m2Handles.end(), indices[row] ) - m2Handles.begin();
                for( col = row; col < indices.size(); ++col, ++idx )
                {
                    col2 = std::lower_bound( m2Handles.begin(), m2Handles.end(), indices[col] ) - m2Handles.begin();
                    if( row2 <= col2 )
                    {
                        idx2 = indices.size() * row2 - row2 * ( row2 + 1 ) / 2 + col2;
                        if( !equal( Hessian[idx], m2Hess[idx2] ) ) ++hess_diff;
                    }
                    else
                    {
                        idx2 = indices.size() * col2 - col2 * ( col2 + 1 ) / 2 + row2;
                        if( !equal( Hessian[idx], transpose( m2Hess[idx2] ) ) ) ++hess_diff;
                    }
                }
            }

            if( hess_diff )
            {
                MSQ_SETERR( err )
                ( MsqError::INVALID_STATE,
                  "Metrics returned different Hessian blocks for "
                  " %d of %u vertices for handle %lu in "
                  "evaluate_with_Hessian\n.",
                  hess_diff, (unsigned)Hessian.size(), (unsigned long)handle );
            }
        }
    }

    return r1 && !err;
}

void CompareMetric::get_mask_axis( PatchData& pd )
{
    maskAxis          = -1;
    PlanarDomain* dom = reinterpret_cast< PlanarDomain* >( pd.get_domain() );
    int bits          = 0;
    if( dom )
    {
        Vector3D n = dom->get_normal();
        for( int i = 0; i < 3; ++i )
            if( fabs( n[i] ) < epsilon ) bits |= ( 1 << i );
        switch( bits )
        {
            case 3:
                maskAxis = 2;
                break;
            case 5:
                maskAxis = 1;
                break;
            case 6:
                maskAxis = 0;
                break;
        }
    }
}

bool CompareMetric::equal( Vector3D grad1, const Vector3D& grad2 ) const
{
    if( maskAxis >= 0 ) grad1[maskAxis] = grad2[maskAxis];
    return ( grad1 - grad2 ).length_squared() <= epsilon * epsilon;
}

bool CompareMetric::equal( SymMatrix3D hess1, const SymMatrix3D& hess2 ) const
{
    if( maskAxis >= 0 )
    {
        for( unsigned i = 0; i < 3; ++i )
        {
            hess1( maskAxis, i ) = hess2( maskAxis, i );
            hess1( i, maskAxis ) = hess2( i, maskAxis );
        }
    }
    return Frobenius_2( hess1 - hess2 ) <= epsilon * epsilon;
}

bool CompareMetric::equal( Matrix3D hess1, const Matrix3D& hess2 ) const
{
    if( maskAxis >= 0 )
    {
        for( unsigned i = 0; i < 3; ++i )
        {
            hess1[maskAxis][i] = hess2[maskAxis][i];
            hess1[i][maskAxis] = hess2[i][maskAxis];
        }
    }
    return Frobenius_2( hess1 - hess2 ) <= epsilon * epsilon;
}