AveragingQM.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], [email protected], [email protected],
    [email protected], [email protected], [email protected]

    (2006) [email protected]

  ***************************************************************** */
/*!
  \file   AveragingQM.cpp
  \brief

  \author Michael Brewer
  \author Thomas Leurent
  \author Jason Kraftcheck
  \date   2002-05-14
*/

#include "AveragingQM.hpp"
#include "MsqVertex.hpp"
#include "MsqMeshEntity.hpp"
#include "MsqDebug.hpp"
#include "MsqTimer.hpp"
#include "PatchData.hpp"

namespace MBMesquite
{

double AveragingQM::average_corner_gradients( EntityTopology type,
                                              uint32_t fixed_vertices,
                                              unsigned num_corner,
                                              double corner_values[],
                                              const Vector3D corner_grads[],
                                              Vector3D vertex_grads[],
                                              MsqError& err )
{
    const unsigned num_vertex = TopologyInfo::corners( type );
    const unsigned dim        = TopologyInfo::dimension( type );
    const unsigned per_vertex = dim + 1;

    unsigned i, j, num_adj;
    const unsigned *adj_idx, *rev_idx;

    // NOTE: This function changes the corner_values array such that
    //       it contains the gradient coefficients.
    double avg = average_metric_and_weights( corner_values, num_corner, err );
    MSQ_ERRZERO( err );

    for( i = 0; i < num_vertex; ++i )
    {
        if( fixed_vertices & ( 1 << i ) )  // skip fixed vertices
            continue;

        adj_idx = TopologyInfo::adjacent_vertices( type, i, num_adj );
        rev_idx = TopologyInfo::reverse_vertex_adjacency_offsets( type, i, num_adj );
        if( i < num_corner )  // not all vertices are corners (e.g. pyramid)
            vertex_grads[i] = corner_values[i] * corner_grads[per_vertex * i];
        else
            vertex_grads[i] = 0;
        for( j = 0; j < num_adj; ++j )
        {
            const unsigned v = adj_idx[j], c = rev_idx[j] + 1;
            if( v >= num_corner )  // if less corners than vertices (e.g. pyramid apex)
                continue;
            vertex_grads[i] += corner_values[v] * corner_grads[per_vertex * v + c];
        }
    }

    return avg;
}

/**\brief Iterate over only diagonal blocks of element corner Hessian data
 *
 * Given concatenation of corner Hessian data for an element, iterate
 * over only the diagonal terms for each corner.  This class allows
 * common code to be used to generate Hessian diagonal blocks from either
 * the diagonal blocks for each corner or the full Hessian data for each
 * corner, where this class is used for the latter.
 */
class CornerHessDiagIterator
{
  private:
    const Matrix3D* cornerHess;     //!< Current location in concatenated Hessian data.
    const EntityTopology elemType;  //!< Element topology for Hessian data
    unsigned mCorner;               //!< The element corner for which cornerHess
                                    //!< is pointing into the corresponding Hessian data.
    unsigned mStep;                 //!< Amount to step to reach next diagonal block.
  public:
    CornerHessDiagIterator( const Matrix3D* corner_hessians, EntityTopology elem_type )
        : cornerHess( corner_hessians ), elemType( elem_type ), mCorner( 0 )
    {
        TopologyInfo::adjacent_vertices( elemType, mCorner, mStep );
        ++mStep;
    }

    SymMatrix3D operator*() const
    {
        return cornerHess->upper();
    }

    CornerHessDiagIterator& operator++()
    {
        cornerHess += mStep;
        if( !--mStep )
        {
            TopologyInfo::adjacent_vertices( elemType, ++mCorner, mStep );
            ++mStep;
        }
        return *this;
    }

    CornerHessDiagIterator operator++( int )
    {
        CornerHessDiagIterator copy( *this );
        operator++();
        return copy;
    }
};

template < typename HessIter >
static inline double sum_corner_diagonals( EntityTopology type,
                                           unsigned num_corner,
                                           const double corner_values[],
                                           const Vector3D corner_grads[],
                                           HessIter corner_diag_blocks,
                                           Vector3D vertex_grads[],
                                           SymMatrix3D vertex_hessians[] )
{
    unsigned i, n, r, R, idx[4];
    const unsigned* adj_list;
    double avg = 0.0;

    // calculate mean
    for( i = 0; i < num_corner; ++i )
        avg += corner_values[i];

    const Vector3D* grad = corner_grads;
    HessIter hess        = corner_diag_blocks;
    for( i = 0; i < num_corner; ++i )
    {
        adj_list = TopologyInfo::adjacent_vertices( type, i, n );
        idx[0]   = i;
        idx[1]   = adj_list[0];
        idx[2]   = adj_list[1];
        idx[3]   = adj_list[2 % n];  // %n so don't read off end if 2D

        for( r = 0; r <= n; ++r )
        {
            R = idx[r];
            vertex_grads[R] += *grad;
            vertex_hessians[R] += *hess;
            ++grad;
            ++hess;
        }
    }
    return avg;
}

template < typename HessIter >
static inline double sum_sqr_corner_diagonals( EntityTopology type,
                                               unsigned num_corner,
                                               const double corner_values[],
                                               const Vector3D corner_grads[],
                                               HessIter corner_diag_blocks,
                                               Vector3D vertex_grads[],
                                               SymMatrix3D vertex_hessians[] )
{
    unsigned i, n, r, R, idx[4];
    const unsigned* adj_list;
    double v, avg = 0.0;

    // calculate mean
    for( i = 0; i < num_corner; ++i )
        avg += corner_values[i] * corner_values[i];

    const Vector3D* grad = corner_grads;
    HessIter hess        = corner_diag_blocks;
    for( i = 0; i < num_corner; ++i )
    {
        adj_list = TopologyInfo::adjacent_vertices( type, i, n );
        idx[0]   = i;
        idx[1]   = adj_list[0];
        idx[2]   = adj_list[1];
        idx[3]   = adj_list[2 % n];  // %n so don't read off end if 2D
        ++n;

        v = 2.0 * corner_values[i];
        for( r = 0; r < n; ++r )
        {
            R = idx[r];
            vertex_grads[R] += v * *grad;
            vertex_hessians[R] += 2.0 * outer( *grad );
            vertex_hessians[R] += v * *hess;
            ++grad;
            ++hess;
        }
    }
    return avg;
}

template < typename HessIter >
static inline double pmean_corner_diagonals( EntityTopology type,
                                             unsigned num_corner,
                                             const double corner_values[],
                                             const Vector3D corner_grads[],
                                             HessIter corner_diag_blocks,
                                             Vector3D vertex_grads[],
                                             SymMatrix3D vertex_hessians[],
                                             double p )
{
    const unsigned N = TopologyInfo::corners( type );
    unsigned i, n, r, R, idx[4];
    const unsigned* adj_list;
    double m = 0.0, nm;
    double gf[8], hf[8];
    double inv = 1.0 / num_corner;
    assert( num_corner <= 8 );

    // calculate mean
    for( i = 0; i < num_corner; ++i )
    {
        nm = pow( corner_values[i], p );
        m += nm;

        gf[i] = inv * p * nm / corner_values[i];
        hf[i] = ( p - 1 ) * gf[i] / corner_values[i];
    }
    nm = inv * m;

    const Vector3D* grad = corner_grads;
    HessIter hess        = corner_diag_blocks;
    for( i = 0; i < num_corner; ++i )
    {
        adj_list = TopologyInfo::adjacent_vertices( type, i, n );
        idx[0]   = i;
        idx[1]   = adj_list[0];
        idx[2]   = adj_list[1];
        idx[3]   = adj_list[2 % n];  // %n so don't read off end if 2D
        ++n;

        for( r = 0; r < n; ++r )
        {
            R = idx[r];
            vertex_grads[R] += gf[i] * *grad;
            vertex_hessians[R] += hf[i] * outer( *grad );
            vertex_hessians[R] += gf[i] * *hess;
            ++grad;
            ++hess;
        }
    }

    m     = pow( nm, 1.0 / p );
    gf[0] = m / ( p * nm );
    hf[0] = ( 1.0 / p - 1 ) * gf[0] / nm;
    for( r = 0; r < N; ++r )
    {
        vertex_hessians[r] *= gf[0];
        vertex_hessians[r] += hf[0] * outer( vertex_grads[r] );
        vertex_grads[r] *= gf[0];
    }

    return m;
}

template < typename HessIter >
static inline double average_corner_diagonals( EntityTopology type,
                                               QualityMetric::AveragingMethod method,
                                               unsigned num_corner,
                                               const double corner_values[],
                                               const Vector3D corner_grads[],
                                               HessIter corner_diag_blocks,
                                               Vector3D vertex_grads[],
                                               SymMatrix3D vertex_hessians[],
                                               MsqError& err )
{
    unsigned i;
    double avg, inv;

    // Zero gradients and Hessians
    const unsigned num_vertex = TopologyInfo::corners( type );
    for( i = 0; i < num_vertex; ++i )
    {
        vertex_grads[i].set( 0.0 );
        vertex_hessians[i] = SymMatrix3D( 0.0 );
    }

    switch( method )
    {
        case QualityMetric::SUM:
            avg = sum_corner_diagonals( type, num_corner, corner_values, corner_grads, corner_diag_blocks, vertex_grads,
                                        vertex_hessians );
            break;

        case QualityMetric::LINEAR:
            avg = sum_corner_diagonals( type, num_corner, corner_values, corner_grads, corner_diag_blocks, vertex_grads,
                                        vertex_hessians );
            inv = 1.0 / num_corner;
            avg *= inv;
            for( i = 0; i < num_vertex; ++i )
            {
                vertex_grads[i] *= inv;
                vertex_hessians[i] *= inv;
            }
            break;

        case QualityMetric::SUM_SQUARED:
            avg = sum_sqr_corner_diagonals( type, num_corner, corner_values, corner_grads, corner_diag_blocks,
                                            vertex_grads, vertex_hessians );
            break;

        case QualityMetric::RMS:
            avg = pmean_corner_diagonals( type, num_corner, corner_values, corner_grads, corner_diag_blocks,
                                          vertex_grads, vertex_hessians, 2.0 );
            break;

        case QualityMetric::HARMONIC:
            avg = pmean_corner_diagonals( type, num_corner, corner_values, corner_grads, corner_diag_blocks,
                                          vertex_grads, vertex_hessians, -1.0 );
            break;

        case QualityMetric::HMS:
            avg = pmean_corner_diagonals( type, num_corner, corner_values, corner_grads, corner_diag_blocks,
                                          vertex_grads, vertex_hessians, -2.0 );
            break;

        default:
            MSQ_SETERR( err )( "averaging method not available.", MsqError::INVALID_STATE );
            return 0.0;
    }

    return avg;
}

double AveragingQM::average_corner_hessian_diagonals( EntityTopology element_type,
                                                      uint32_t,
                                                      unsigned num_corners,
                                                      const double corner_values[],
                                                      const Vector3D corner_grads[],
                                                      const Matrix3D corner_hessians[],
                                                      Vector3D vertex_grads[],
                                                      SymMatrix3D vertex_hessians[],
                                                      MsqError& err )
{
    return average_corner_diagonals( element_type, avgMethod, num_corners, corner_values, corner_grads,
                                     CornerHessDiagIterator( corner_hessians, element_type ), vertex_grads,
                                     vertex_hessians, err );
}

double AveragingQM::average_corner_hessian_diagonals( EntityTopology element_type,
                                                      uint32_t,
                                                      unsigned num_corners,
                                                      const double corner_values[],
                                                      const Vector3D corner_grads[],
                                                      const SymMatrix3D corner_hess_diag[],
                                                      Vector3D vertex_grads[],
                                                      SymMatrix3D vertex_hessians[],
                                                      MsqError& err )
{
    return average_corner_diagonals( element_type, avgMethod, num_corners, corner_values, corner_grads,
                                     corner_hess_diag, vertex_grads, vertex_hessians, err );
}

static inline double sum_corner_hessians( EntityTopology type,
                                          unsigned num_corner,
                                          const double corner_values[],
                                          const Vector3D corner_grads[],
                                          const Matrix3D corner_hessians[],
                                          Vector3D vertex_grads[],
                                          Matrix3D vertex_hessians[] )
{
    const unsigned N = TopologyInfo::corners( type );
    unsigned i, n, r, c, R, C, idx[4];
    const unsigned* adj_list;
    double avg = 0.0;

    // calculate mean
    for( i = 0; i < num_corner; ++i )
        avg += corner_values[i];

    const Vector3D* grad = corner_grads;
    const Matrix3D* hess = corner_hessians;
    for( i = 0; i < num_corner; ++i )
    {
        adj_list = TopologyInfo::adjacent_vertices( type, i, n );
        idx[0]   = i;
        idx[1]   = adj_list[0];
        idx[2]   = adj_list[1];
        idx[3]   = adj_list[2 % n];  // %n so don't read off end if 2D

        for( r = 0; r <= n; ++r )
        {
            R = idx[r];
            vertex_grads[R] += *grad;
            ++grad;
            for( c = r; c <= n; ++c )
            {
                C = idx[c];
                if( R <= C )
                    vertex_hessians[N * R - R * ( R + 1 ) / 2 + C] += *hess;
                else
                    vertex_hessians[N * C - C * ( C + 1 ) / 2 + R].plus_transpose_equal( *hess );
                ++hess;
            }
        }
    }
    return avg;
}

static inline double sum_sqr_corner_hessians( EntityTopology type,
                                              unsigned num_corner,
                                              const double corner_values[],
                                              const Vector3D corner_grads[],
                                              const Matrix3D corner_hessians[],
                                              Vector3D vertex_grads[],
                                              Matrix3D vertex_hessians[] )
{
    const unsigned N = TopologyInfo::corners( type );
    unsigned i, n, r, c, R, C, idx[4];
    const unsigned* adj_list;
    double v, avg = 0.0;
    Matrix3D op;

    // calculate mean
    for( i = 0; i < num_corner; ++i )
        avg += corner_values[i] * corner_values[i];

    const Vector3D* grad = corner_grads;
    const Matrix3D* hess = corner_hessians;
    for( i = 0; i < num_corner; ++i )
    {
        adj_list = TopologyInfo::adjacent_vertices( type, i, n );
        idx[0]   = i;
        idx[1]   = adj_list[0];
        idx[2]   = adj_list[1];
        idx[3]   = adj_list[2 % n];  // %n so don't read off end if 2D
        ++n;

        v = 2.0 * corner_values[i];
        for( r = 0; r < n; ++r )
        {
            R = idx[r];
            vertex_grads[R] += v * grad[r];
            for( c = r; c < n; ++c )
            {
                C = idx[c];
                op.outer_product( 2.0 * grad[r], grad[c] );
                op += v * *hess;
                if( R <= C )
                    vertex_hessians[N * R - R * ( R + 1 ) / 2 + C] += op;
                else
                    vertex_hessians[N * C - C * ( C + 1 ) / 2 + R].plus_transpose_equal( op );
                ++hess;
            }
        }
        grad += n;
    }
    return avg;
}

static inline double pmean_corner_hessians( EntityTopology type,
                                            unsigned num_corner,
                                            const double corner_values[],
                                            const Vector3D corner_grads[],
                                            const Matrix3D corner_hessians[],
                                            Vector3D vertex_grads[],
                                            Matrix3D vertex_hessians[],
                                            double p )
{
    const unsigned N = TopologyInfo::corners( type );
    unsigned i, n, r, c, R, C, idx[4];
    const unsigned* adj_list;
    double m = 0.0, nm;
    Matrix3D op;
    double gf[8], hf[8];
    double inv = 1.0 / num_corner;
    assert( num_corner <= 8 );

    // calculate mean
    for( i = 0; i < num_corner; ++i )
    {
        nm = pow( corner_values[i], p );
        m += nm;

        gf[i] = inv * p * nm / corner_values[i];
        hf[i] = ( p - 1 ) * gf[i] / corner_values[i];
    }
    nm = inv * m;

    const Vector3D* grad = corner_grads;
    const Matrix3D* hess = corner_hessians;
    for( i = 0; i < num_corner; ++i )
    {
        adj_list = TopologyInfo::adjacent_vertices( type, i, n );
        idx[0]   = i;
        idx[1]   = adj_list[0];
        idx[2]   = adj_list[1];
        idx[3]   = adj_list[2 % n];  // %n so don't read off end if 2D
        ++n;

        for( r = 0; r < n; ++r )
        {
            R = idx[r];
            vertex_grads[R] += gf[i] * grad[r];
            for( c = r; c < n; ++c )
            {
                C = idx[c];
                op.outer_product( grad[r], grad[c] );
                op *= hf[i];
                op += gf[i] * *hess;
                if( R <= C )
                    vertex_hessians[N * R - R * ( R + 1 ) / 2 + C] += op;
                else
                    vertex_hessians[N * C - C * ( C + 1 ) / 2 + R].plus_transpose_equal( op );
                ++hess;
            }
        }
        grad += n;
    }

    m     = pow( nm, 1.0 / p );
    gf[0] = m / ( p * nm );
    hf[0] = ( 1.0 / p - 1 ) * gf[0] / nm;
    for( r = 0; r < N; ++r )
    {
        for( c = r; c < N; ++c )
        {
            op.outer_product( vertex_grads[r], vertex_grads[c] );
            op *= hf[0];
            *vertex_hessians *= gf[0];
            *vertex_hessians += op;
            ++vertex_hessians;
        }
        vertex_grads[r] *= gf[0];
    }

    return m;
}

double AveragingQM::average_corner_hessians( EntityTopology type,
                                             uint32_t,
                                             unsigned num_corner,
                                             const double corner_values[],
                                             const Vector3D corner_grads[],
                                             const Matrix3D corner_hessians[],
                                             Vector3D vertex_grads[],
                                             Matrix3D vertex_hessians[],
                                             MsqError& err )
{
    unsigned i;
    double avg, inv;

    // Zero gradients and Hessians
    const unsigned num_vertex = TopologyInfo::corners( type );
    for( i = 0; i < num_vertex; ++i )
        vertex_grads[i].set( 0.0 );
    const unsigned num_hess = num_vertex * ( num_vertex + 1 ) / 2;
    for( i = 0; i < num_hess; ++i )
        vertex_hessians[i].zero();

    switch( avgMethod )
    {
        case QualityMetric::SUM:
            avg = sum_corner_hessians( type, num_corner, corner_values, corner_grads, corner_hessians, vertex_grads,
                                       vertex_hessians );
            break;

        case QualityMetric::LINEAR:
            avg = sum_corner_hessians( type, num_corner, corner_values, corner_grads, corner_hessians, vertex_grads,
                                       vertex_hessians );
            inv = 1.0 / num_corner;
            avg *= inv;
            for( i = 0; i < num_vertex; ++i )
                vertex_grads[i] *= inv;
            for( i = 0; i < num_hess; ++i )
                vertex_hessians[i] *= inv;
            break;

        case QualityMetric::SUM_SQUARED:
            avg = sum_sqr_corner_hessians( type, num_corner, corner_values, corner_grads, corner_hessians, vertex_grads,
                                           vertex_hessians );
            break;

        case QualityMetric::RMS:
            avg = pmean_corner_hessians( type, num_corner, corner_values, corner_grads, corner_hessians, vertex_grads,
                                         vertex_hessians, 2.0 );
            break;

        case QualityMetric::HARMONIC:
            avg = pmean_corner_hessians( type, num_corner, corner_values, corner_grads, corner_hessians, vertex_grads,
                                         vertex_hessians, -1.0 );
            break;

        case QualityMetric::HMS:
            avg = pmean_corner_hessians( type, num_corner, corner_values, corner_grads, corner_hessians, vertex_grads,
                                         vertex_hessians, -2.0 );
            break;

        default:
            MSQ_SETERR( err )( "averaging method not available.", MsqError::INVALID_STATE );
            return 0.0;
    }

    return avg;
}

double AveragingQM::average_metric_and_weights( double metrics[], int count, MsqError& err )
{
    static bool min_max_warning = false;
    double avg                  = 0.0;
    int i, tmp_count;
    double f;

    switch( avgMethod )
    {

        case QualityMetric::MINIMUM:
            if( !min_max_warning )
            {
                MSQ_DBGOUT( 1 ) << "Minimum and maximum not continuously differentiable.\n"
                                   "Element of subdifferential will be returned.\n";
                min_max_warning = true;
            }

            avg = metrics[0];
            for( i = 1; i < count; ++i )
                if( metrics[i] < avg ) avg = metrics[i];

            tmp_count = 0;
            for( i = 0; i < count; ++i )
            {
                if( metrics[i] - avg <= MSQ_MIN )
                {
                    metrics[i] = 1.0;
                    ++tmp_count;
                }
                else
                {
                    metrics[i] = 0.0;
                }
            }

            f = 1.0 / tmp_count;
            for( i = 0; i < count; ++i )
                metrics[i] *= f;

            break;

        case QualityMetric::MAXIMUM:
            if( !min_max_warning )
            {
                MSQ_DBGOUT( 1 ) << "Minimum and maximum not continuously differentiable.\n"
                                   "Element of subdifferential will be returned.\n";
                min_max_warning = true;
            }

            avg = metrics[0];
            for( i = 1; i < count; ++i )
                if( metrics[i] > avg ) avg = metrics[i];

            tmp_count = 0;
            for( i = 0; i < count; ++i )
            {
                if( avg - metrics[i] <= MSQ_MIN )
                {
                    metrics[i] = 1.0;
                    ++tmp_count;
                }
                else
                {
                    metrics[i] = 0.0;
                }
            }

            f = 1.0 / tmp_count;
            for( i = 0; i < count; ++i )
                metrics[i] *= f;

            break;

        case QualityMetric::SUM:
            for( i = 0; i < count; ++i )
            {
                avg += metrics[i];
                metrics[i] = 1.0;
            }

            break;

        case QualityMetric::SUM_SQUARED:
            for( i = 0; i < count; ++i )
            {
                avg += ( metrics[i] * metrics[i] );
                metrics[i] *= 2;
            }

            break;

        case QualityMetric::LINEAR:
            f = 1.0 / count;
            for( i = 0; i < count; ++i )
            {
                avg += metrics[i];
                metrics[i] = f;
            }
            avg *= f;

            break;

        case QualityMetric::GEOMETRIC:
            avg = 1.0;
            for( i = 0; i < count; ++i )
                avg *= metrics[i];
            avg = pow( avg, 1.0 / count );

            f = avg / count;
            for( i = 0; i < count; ++i )
                metrics[i] = f / metrics[i];

            break;

        case QualityMetric::RMS:
            for( i = 0; i < count; ++i )
                avg += metrics[i] * metrics[i];
            avg = sqrt( avg / count );

            f = 1. / ( avg * count );
            for( i = 0; i < count; ++i )
                metrics[i] *= f;

            break;

        case QualityMetric::HARMONIC:
            for( i = 0; i < count; ++i )
                avg += 1.0 / metrics[i];
            avg = count / avg;

            for( i = 0; i < count; ++i )
                metrics[i] = ( avg * avg ) / ( count * metrics[i] * metrics[i] );

            break;

        case QualityMetric::HMS:
            for( i = 0; i < count; ++i )
                avg += 1. / ( metrics[i] * metrics[i] );
            avg = sqrt( count / avg );

            f = avg * avg * avg / count;
            for( i = 0; i < count; ++i )
                metrics[i] = f / ( metrics[i] * metrics[i] * metrics[i] );

            break;

        default:
            MSQ_SETERR( err )( "averaging method not available.", MsqError::INVALID_STATE );
    }

    return avg;
}

/*!
  average_metrics takes an array of length num_value and averages the
  contents using averaging method 'method'.
*/
double AveragingQM::average_metrics( const double metric_values[], int num_values, MsqError& err )
{
    // MSQ_MAX needs to be made global?
    // double MSQ_MAX=1e10;
    double total_value = 0.0;
    double temp_value  = 0.0;
    int i              = 0;
    int j              = 0;
    // if no values, return zero
    if( num_values <= 0 )
    {
        return 0.0;
    }

    switch( avgMethod )
    {
        case QualityMetric::GEOMETRIC:
            total_value = 1.0;
            for( i = 0; i < num_values; ++i )
            {
                total_value *= ( metric_values[i] );
            }
            total_value = pow( total_value, 1.0 / num_values );
            break;

        case QualityMetric::HARMONIC:
            // ensure no divide by zero, return zero
            for( i = 0; i < num_values; ++i )
            {
                if( metric_values[i] < MSQ_MIN )
                {
                    if( metric_values[i] > MSQ_MIN )
                    {
                        return 0.0;
                    }
                }
                total_value += ( 1 / metric_values[i] );
            }
            // ensure no divide by zero, return MSQ_MAX_CAP
            if( total_value < MSQ_MIN )
            {
                if( total_value > MSQ_MIN )
                {
                    return MSQ_MAX_CAP;
                }
            }
            total_value = num_values / total_value;
            break;

        case QualityMetric::LINEAR:
            for( i = 0; i < num_values; ++i )
            {
                total_value += metric_values[i];
            }
            total_value /= (double)num_values;
            break;

        case QualityMetric::MAXIMUM:
            total_value = metric_values[0];
            for( i = 1; i < num_values; ++i )
            {
                if( metric_values[i] > total_value )
                {
                    total_value = metric_values[i];
                }
            }
            break;

        case QualityMetric::MINIMUM:
            total_value = metric_values[0];
            for( i = 1; i < num_values; ++i )
            {
                if( metric_values[i] < total_value )
                {
                    total_value = metric_values[i];
                }
            }
            break;

        case QualityMetric::RMS:
            for( i = 0; i < num_values; ++i )
            {
                total_value += ( metric_values[i] * metric_values[i] );
            }
            total_value /= (double)num_values;
            total_value = sqrt( total_value );
            break;

        case QualityMetric::HMS:
            // ensure no divide by zero, return zero
            for( i = 0; i < num_values; ++i )
            {
                if( metric_values[i] * metric_values[i] < MSQ_MIN )
                {
                    return 0.0;
                }
                total_value += ( 1.0 / ( metric_values[i] * metric_values[i] ) );
            }

            // ensure no divide by zero, return MSQ_MAX_CAP
            if( total_value < MSQ_MIN )
            {
                return MSQ_MAX_CAP;
            }
            total_value = sqrt( num_values / total_value );
            break;

        case QualityMetric::STANDARD_DEVIATION:
            total_value = 0;
            temp_value  = 0;
            for( i = 0; i < num_values; ++i )
            {
                temp_value += metric_values[i];
                total_value += ( metric_values[i] * metric_values[i] );
            }
            temp_value /= (double)num_values;
            temp_value *= temp_value;
            total_value /= (double)num_values;
            total_value = total_value - temp_value;
            break;

        case QualityMetric::SUM:
            for( i = 0; i < num_values; ++i )
            {
                total_value += metric_values[i];
            }
            break;

        case QualityMetric::SUM_SQUARED:
            for( i = 0; i < num_values; ++i )
            {
                total_value += ( metric_values[i] * metric_values[i] );
            }
            break;

        case QualityMetric::MAX_MINUS_MIN:
            // total_value used to store the maximum
            // temp_value used to store the minimum
            temp_value = MSQ_MAX_CAP;
            for( i = 0; i < num_values; ++i )
            {
                if( metric_values[i] < temp_value )
                {
                    temp_value = metric_values[i];
                }
                if( metric_values[i] > total_value )
                {
                    total_value = metric_values[i];
                }
            }

            total_value -= temp_value;
            break;

        case QualityMetric::MAX_OVER_MIN:
            // total_value used to store the maximum
            // temp_value used to store the minimum
            temp_value = MSQ_MAX_CAP;
            for( i = 0; i < num_values; ++i )
            {
                if( metric_values[i] < temp_value )
                {
                    temp_value = metric_values[i];
                }
                if( metric_values[i] > total_value )
                {
                    total_value = metric_values[i];
                }
            }

            // ensure no divide by zero, return MSQ_MAX_CAP
            if( fabs( temp_value ) < MSQ_MIN )
            {
                return MSQ_MAX_CAP;
            }
            total_value /= temp_value;
            break;

        case QualityMetric::SUM_OF_RATIOS_SQUARED:
            for( j = 0; j < num_values; ++j )
            {
                // ensure no divide by zero, return MSQ_MAX_CAP
                if( fabs( metric_values[j] ) < MSQ_MIN )
                {
                    return MSQ_MAX_CAP;
                }
                for( i = 0; i < num_values; ++i )
                {
                    total_value +=
                        ( ( metric_values[i] / metric_values[j] ) * ( metric_values[i] / metric_values[j] ) );
                }
            }
            total_value /= (double)( num_values * num_values );
            break;

        default:
            // Return error saying Averaging Method mode not implemented
            MSQ_SETERR( err )
            ( "Requested Averaging Method Not Implemented", MsqError::NOT_IMPLEMENTED );
            return 0;
    }
    return total_value;
}

}  // namespace MBMesquite