kmeans.cpp

# include <cstdlib>
# include <iostream>
# include <fstream>
# include <iomanip>
# include <cmath>
# include <ctime>
# include <cstring>

using namespace std;

# include "kmeans.hpp"

//****************************************************************************80

char ch_cap ( char ch )

//****************************************************************************80
//
//  Purpose:
//
//    CH_CAP capitalizes a single character.
//
//  Discussion:
//
//    This routine should be equivalent to the library "toupper" function.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    19 July 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH, the character to capitalize.
//
//    Output, char CH_CAP, the capitalized character.
//
{
  if ( 97 <= ch && ch <= 122 )
  {
    ch = ch - 32;
  }

  return ch;
}
//****************************************************************************80

bool ch_eqi ( char ch1, char ch2 )

//****************************************************************************80
//
//  Purpose:
//
//    CH_EQI is true if two characters are equal, disregarding case.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH1, CH2, the characters to compare.
//
//    Output, bool CH_EQI, is true if the two characters are equal,
//    disregarding case.
//
{
  if ( 97 <= ch1 && ch1 <= 122 )
  {
    ch1 = ch1 - 32;
  }
  if ( 97 <= ch2 && ch2 <= 122 )
  {
    ch2 = ch2 - 32;
  }

  return ( ch1 == ch2 );
}
//****************************************************************************80

int ch_to_digit ( char ch )

//****************************************************************************80
//
//  Purpose:
//
//    CH_TO_DIGIT returns the integer value of a base 10 digit.
//
//  Example:
//
//     CH  DIGIT
//    ---  -----
//    '0'    0
//    '1'    1
//    ...  ...
//    '9'    9
//    ' '    0
//    'X'   -1
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH, the decimal digit, '0' through '9' or blank are legal.
//
//    Output, int CH_TO_DIGIT, the corresponding integer value.  If the
//    character was 'illegal', then DIGIT is -1.
//
{
  int digit;

  if ( '0' <= ch && ch <= '9' )
  {
    digit = ch - '0';
  }
  else if ( ch == ' ' )
  {
    digit = 0;
  }
  else
  {
    digit = -1;
  }

  return digit;
}
//****************************************************************************80

double *cluster_energy_compute ( int dim_num, int point_num, int cluster_num, 
  double point[], int cluster[], double cluster_center[] )

//****************************************************************************80
//
//  Purpose:
//
//    CLUSTER_ENERGY_COMPUTE computes the energy of the clusters.
//
//  Discussion:
//
//    The cluster energy is defined as the sum of the distance
//    squared from each point to its cluster center.  It is the goal
//    of the H-means and K-means algorithms to find, for a fixed number
//    of clusters, a clustering that minimizes this energy
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    07 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of data points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the data points.
//
//    Input, int CLUSTER[POINT_NUM], the cluster to which each
//    data point belongs.  These values are 0-based.
//
//    Input, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], the 
//    centers associated with the minimal energy clustering.
//
//    Output, double CLUSTER_ENERGY_COMPUTE[CLUSTER_NUM], the energy
//    associated with each cluster.
//
{
  double *cluster_energy;
  int i;
  int j;
  int k;
  double point_energy;

  cluster_energy = r8vec_zero_new ( cluster_num );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[i];
    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy 
        + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + point_energy;
  }

  return cluster_energy;
}
//****************************************************************************80

double *cluster_initialize_1 ( int dim_num, int point_num, int cluster_num, 
  double point[] )

//****************************************************************************80
//
//  Purpose:
//
//    CLUSTER_INITIALIZE_1 initializes the clusters to data points.
//
//  Discussion:
//
//    The cluster centers are simply chosen to be the first data points.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Output, double CLUSTER_INITIALIZE_1[DIM_NUM*CLUSTER_NUM],
//    the coordinates of the cluster centers.
//
{
  double *cluster_center;
  int i;
  int j;

  cluster_center = new double[dim_num*cluster_num];

  for ( j = 0; j < cluster_num; j++ )
  {
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+j*dim_num] = point[i+j*dim_num];
    }
  }

  return cluster_center;
}
//****************************************************************************80

double *cluster_initialize_2 ( int dim_num, int point_num, int cluster_num, 
  double point[], int *seed )

//****************************************************************************80
//
//  Purpose:
//
//    CLUSTER_INITIALIZE_2 initializes the cluster centers to random values.
//
//  Discussion:
//
//    In this case, the hyperbox containing the data is computed.
//
//    Then the cluster centers are chosen uniformly at random within
//    this hyperbox.
//
//    Of course, if the data is not smoothly distributed throughout
//    the box, many cluster centers will be isolated.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input/output, int *SEED, a seed for the random 
//    number generator.
//
//    Output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], 
//    the coordinates of the cluster centers.
//
{
  double *cluster_center;
  int i;
  int j;
  double *r;
  double *r_max;
  double *r_min;

  cluster_center = new double[dim_num*cluster_num];

  r = new double[dim_num];
  r_min = new double[dim_num];
  r_max = new double[dim_num];

  j = 0;
  for ( i = 0; i < dim_num; i++ )
  {
    r_max[i] = point[i+j*dim_num];
    r_min[i] = point[i+j*dim_num];
  }

  for ( j = 1; j < point_num; j++ )
  {
    for ( i = 0; i < dim_num; i++ )
    {
      r_max[i] = r8_max ( r_max[i], point[i+j*dim_num] );
      r_min[i] = r8_min ( r_min[i], point[i+j*dim_num] );
    }
  }

  for ( j = 0; j < cluster_num; j++ )
  {
    r8vec_uniform_01 ( dim_num, seed, r );
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+j*dim_num] = ( 1.0 - r[i] ) * r_min[i] + r[i] * r_max[i];
    }
  }
  delete [] r;
  delete [] r_max;
  delete [] r_min;

  return cluster_center;
}
//****************************************************************************80

double *cluster_initialize_3 ( int dim_num, int point_num, int cluster_num, 
  double point[], int *seed )

//****************************************************************************80
//
//  Purpose:
//
//   CLUSTER_INITIALIZE_3 initializes the cluster centers to random values.
//
//  Discussion:
//
//    In this case, each point is randomly assigned to a cluster, and
//    the cluster centers are then computed as the centroids of the points 
//    in the cluster.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input/output, int SEED, a seed for the random 
//    number generator.
//
//    Output, double CLUSTER_INITIALIZE_3[DIM_NUM*CLUSTER_NUM], 
//    the coordinates of the cluster centers.
//
{
  double *cluster_center;
  int *cluster_population;
  int i;
  int j;
  int k;
//
//  Assign one point to each cluster center.
//
  cluster_center = new double[dim_num*cluster_num];

  for ( k = 0; k < cluster_num; k++ )
  {
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = point[i+k*dim_num];
    }
  }

  cluster_population = new int[cluster_num];

  for ( k = 0; k < cluster_num; k++ )
  {
    cluster_population[k] = 1;
  }
//
//  The rest of the points get assigned randomly.
//
  for ( j = cluster_num; j < point_num; j++ )
  {
    k = i4_uniform ( 1, cluster_num, seed );
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        + point[i+j*dim_num];
    }
    cluster_population[k] = cluster_population[k] + 1;
  }
//
//  Now average the points to get the centroid.
//
  for ( k = 0; k < cluster_num; k++ )
  {
    if ( cluster_population[k] != 0 )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] / 
          ( double ) ( cluster_population[k] );
      }
    }
  }

  delete [] cluster_population;

  return cluster_center;
}
//****************************************************************************80

double *cluster_initialize_4 ( int dim_num, int point_num, int cluster_num, 
  double point[], int *seed )

//****************************************************************************80
//
//  Purpose:
//
//   CLUSTER_INITIALIZE_4 initializes the cluster centers to random values.
//
//  Discussion:
//
//    In this case, each data point is divided randomly among the
//    the cluster centers.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input/output, int SEED, a seed for the random 
//    number generator.
//
//    Output, double CLUSTER_INITIALIZE_4[DIM_NUM*CLUSTER_NUM], 
//    the coordinates of the cluster centers.
//
{
  double *cluster_center;
  double *cluster_factor;
  double *cluster_weight;
  double divisor;
  int i;
  int j;
  int k;

  cluster_center = r8vec_zero_new ( dim_num * cluster_num );

  cluster_factor = new double[cluster_num];

  cluster_weight = r8vec_zero_new ( cluster_num );

  for ( j = 0; j < point_num; j++ )
  {
    r8vec_uniform_01 ( cluster_num, seed, cluster_factor );

    divisor = r8vec_sum ( cluster_num, cluster_factor );

    for ( k = 0; k < cluster_num; k++ )
    {
      cluster_factor[k] = cluster_factor[k] / divisor;
    }

    for ( k = 0; k < cluster_num; k++ )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num]
          + cluster_factor[k] * point[i+j*dim_num];
      }
    }

    for ( k = 0; k < cluster_num; k++ )
    {
      cluster_weight[k] = cluster_weight[k] + cluster_factor[k];
    }
  }
//
//  Now normalize,  so that each cluster center is now a convex 
//  combination of the points.
//
  for ( k = 0; k < cluster_num; k++ )
  {
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        / cluster_weight[k];
    }
  }

  delete [] cluster_factor;
  delete [] cluster_weight;

  return cluster_center;
}
//****************************************************************************80

double *cluster_initialize_5 ( int dim_num, int point_num, int cluster_num, 
  double point[], int *seed )

//****************************************************************************80
//
//  Purpose:
//
//   CLUSTER_INITIALIZE_5 initializes the cluster centers to random values.
//
//  Discussion:
//
//    In this case, each cluster center is a random convex combination 
//    of the data points.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input/output, int *SEED, a seed for the random 
//    number generator.
//
//    Output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the coordinates of the cluster centers.
//
{
  double *cluster_center;
  double column_sum;
  double *factor;
  int j;
  int k;
//
//  Get a PxC block of random factors.
//
  factor = r8mat_uniform_01_new ( point_num, cluster_num, seed );
//
//  Make each column of factors have unit sum.
//
  for ( k = 0; k < cluster_num; k++ )
  {
    column_sum = 0.0;
    for ( j = 0; j < point_num; j++ )
    {
      column_sum = column_sum + factor[j+k*point_num];
    }
    for ( j = 0; j < point_num; j++ )
    {
      factor[j+k*point_num] = factor[j+k*point_num] / column_sum;
    }
  }
//
//  Set centers = points * factors.
//
  cluster_center = r8mat_mm_new ( dim_num, point_num, cluster_num, point, 
    factor );

  delete [] factor;

  return cluster_center;
}
//****************************************************************************80

void cluster_print_summary ( int point_num, int cluster_num, 
  int cluster_population[], double cluster_energy[], double cluster_variance[] )

//****************************************************************************80
//
//  Purpose:
//
//   CLUSTER_PRINT_SUMMARY prints a summary of data about a clustering.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int CLUSTER_POPULATION[CLUSTER_NUM], the number of
//    points assigned to each cluster.
//
//    Input, double CLUSTER_ENERGY[CLUSTER_NUM], the energy of 
//    the clusters.
//
//    Input, double CLUSTER_VARIANCE[CLUSTER_NUM], the variance of 
//    the clusters.
//
{
  double ce;
  int cep;
  double ce_total;
  int cp;
  int cpp;
  double cv;
  int k;

  ce_total = r8vec_sum ( cluster_num, cluster_energy );

  cout << "\n";
  cout << "  Clustering statistics:\n";
  cout << "\n";
  cout << "    Number of clusters is " << cluster_num << "\n";
  cout << "    Number of points is   " << point_num << "\n";
  cout << "    Total energy is       " << ce_total << "\n";
  cout << "\n";
  cout << "    Cluster   Population        Energy          Variance\n";
  cout << "    -------  -----------  -----------------  --------------\n";
  cout << "                  #    %     value        %\n";
  cout << "\n";

  for ( k = 0; k < cluster_num; k++ )
  {
    cp = cluster_population[k];
    cpp = ( int ) ( ( double ) ( 100 * cp ) / ( double ) ( point_num ) );
    ce = cluster_energy[k];
    cep = ( int ) ( ( ce * 100.0 ) / ce_total );
    cv = cluster_variance[k];
    cout << "  " << setw(7) << k
         << "  " << setw(8) << cp
         << "  " << setw(3) << cpp
         << "  " << setw(12) << ce
         << "  " << setw(3) << cep
         << "  " << setw(12) << cv << "\n";
  }

  cp = i4vec_sum ( cluster_num, cluster_population );
  cpp = 100;
  ce = r8vec_sum ( cluster_num, cluster_energy );
  cep = 100;
  cv = r8vec_i4vec_dot_product ( cluster_num, cluster_variance, 
    cluster_population ) / cp;

  cout << "\n";
  cout << "  " << "  Total"
       << "  " << setw(8) << cp
       << "  " << setw(3) << cpp
       << "  " << setw(12) << ce
       << "  " << setw(3) << cep
       << "  " << setw(12) << cv << "\n";

  return;
}
//****************************************************************************80

double *cluster_variance_compute ( int dim_num, int point_num, int cluster_num, 
  double point[], int cluster[], double cluster_center[] )

//****************************************************************************80
//
//  Purpose:
//
//   CLUSTER_VARIANCE_COMPUTE computes the variance of the clusters.
//
//  Discussion:
//
//    The cluster variance (from the cluster center) is the average of the 
//    sum of the squares of the distances of each point in the cluster to the 
//    cluster center.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    06 October 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of data points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the data points.
//
//    Input, int CLUSTER[POINT_NUM], the cluster to which each
//    data point belongs.
//
//    Input, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], the 
//    centers associated with the minimal energy clustering.
//
//    Output, double CLUSTER_VARIANCE_COMPUTE[CLUSTER_NUM], the variance
//    associated with each cluster.
//
{
  int *cluster_population;
  double *cluster_variance;
  int i;
  int j;
  int k;
  double point_variance;

  cluster_population = i4vec_zero_new ( cluster_num );
  cluster_variance = r8vec_zero_new ( cluster_num );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_variance = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_variance = point_variance +
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_variance[k] = cluster_variance[k] + point_variance;
    cluster_population[k] = cluster_population[k] + 1;
  }

  for ( k = 0; k < cluster_num; k++ )
  {
    if ( 0 < cluster_population[k] )
    {
      cluster_variance[k] = cluster_variance[k] / cluster_population[k];
    }
  }

  delete [] cluster_population;

  return cluster_variance;
}
//****************************************************************************80

int file_column_count ( string filename )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_COLUMN_COUNT counts the columns in the first line of a file.
//
//  Discussion:
//
//    The file is assumed to be a simple text file.
//
//    Most lines of the file are presumed to consist of COLUMN_NUM words,
//    separated by spaces.  There may also be some blank lines, and some
//    comment lines, which have a "#" in column 1.
//
//    The routine tries to find the first non-comment non-blank line and
//    counts the number of words in that line.
//
//    If all lines are blanks or comments, it goes back and tries to analyze
//    a comment line.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string FILENAME, the name of the file.
//
//    Output, int FILE_COLUMN_COUNT, the number of columns assumed
//    to be in the file.
//
{
  int column_num;
  ifstream input;
  bool got_one;
  string text;
//
//  Open the file.
//
  input.open ( filename.c_str ( ) );

  if ( !input )
  {
    column_num = -1;
    cerr << "\n";
    cerr << "FILE_COLUMN_COUNT - Fatal error!\n";
    cerr << "  Could not open the file:\n";
    cerr << "  \"" << filename << "\"\n";
    exit ( 1 );
  }
//
//  Read one line, but skip blank lines and comment lines.
//
  got_one = false;

  for ( ; ; )
  {
    getline ( input, text );

    if ( input.eof ( ) )
    {
      break;
    }

    if ( s_len_trim ( text ) <= 0 )
    {
      continue;
    }

    if ( text[0] == '#' )
    {
      continue;
    }
    got_one = true;
    break;
  }

  if ( !got_one )
  {
    input.close ( );

    input.open ( filename.c_str ( ) );

    for ( ; ; )
    {
      input >> text;

      if ( input.eof ( ) )
      {
        break;
      }

      if ( s_len_trim ( text ) == 0 )
      {
        continue;
      }
      got_one = true;
      break;
    }
  }

  input.close ( );

  if ( !got_one )
  {
    cerr << "\n";
    cerr << "FILE_COLUMN_COUNT - Warning!\n";
    cerr << "  The file does not seem to contain any data.\n";
    return -1;
  }

  column_num = s_word_count ( text );

  return column_num;
}
//****************************************************************************80

int file_row_count ( string input_filename )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_ROW_COUNT counts the number of row records in a file.
//
//  Discussion:
//
//    It does not count lines that are blank, or that begin with a
//    comment symbol '#'.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string INPUT_FILENAME, the name of the input file.
//
//    Output, int FILE_ROW_COUNT, the number of rows found.
//
{
  int bad_num;
  int comment_num;
  ifstream input;
  int i;
  string line;
  int record_num;
  int row_num;

  row_num = 0;
  comment_num = 0;
  record_num = 0;
  bad_num = 0;

  input.open ( input_filename.c_str ( ) );

  if ( !input )
  {
    cerr << "\n";
    cerr << "FILE_ROW_COUNT - Fatal error!\n";
    cerr << "  Could not open the input file: \"" << input_filename << "\"\n";
    exit ( 1 );
  }

  for ( ; ; )
  {
    getline ( input, line );

    if ( input.eof ( ) )
    {
      break;
    }

    record_num = record_num + 1;

    if ( line[0] == '#' )
    {
      comment_num = comment_num + 1;
      continue;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      comment_num = comment_num + 1;
      continue;
    }

    row_num = row_num + 1;

  }

  input.close ( );

  return row_num;
}
//****************************************************************************80

void hmeans_01 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], int cluster[], double cluster_center[], 
  int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   HMEANS_01 applies the H-Means algorithm.
//
//  Discussion:
//
//    The data for the H-Means problem is a set of N points X in
//    M-dimensions, and a desired number of clusters K.
//
//    The goal is to determine K points Z, called cluster centers, so that
//    if we associate each point X with its nearest Z value, we minimize
//    the standard deviation or cluster energy.  Writing CLUSTER(I) to
//    indicate the index of the nearest cluster center to point X(I), the
//    energy can be written as:
//
//      Energy = Sum ( 1 <= I <= N ) || X(I) - Z(CLUSTER(I)) ||^2
//
//    where
//
//      || X - Z ||^2 = Sum ( 1 <= J <= M ) ( X(J) - Z(J) )^2
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Wendy Martinez, Angel Martinez,
//    Computational Statistics Handbook with MATLAB,
//    pages 373-376,
//    Chapman and Hall / CRC, 2002.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of data points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int &IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the data points.
//
//    Input/output, int CLUSTER[POINT_NUM].  On input, the user 
//    may specify an initial cluster for each point, or leave all entrie of
//    CLUSTER set to 0.  On output, CLUSTER contains the index of the
//    cluster to which each data point belongs.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], the 
//    centers associated with the minimal energy clustering.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM],
//    the populuation of each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the energy
//    associated with each cluster.
//
{
  int c;
  double *centroid;
  bool debug = true;
  int i;
  int j;
  int k;
  int k2;
  int missed;
  double point_energy;
  double point_energy_min;
  int swap;
//
//  Data checks.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_01 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_01 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_01 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "HMEANS_01 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }
//
//  On input, legal entries in CLUSTER are preserved, but
//  otherwise, each point is assigned to its nearest cluster.
//
  for ( j = 0; j < point_num; j++ )
  {
    if ( cluster[j] < 0 || cluster_num <= cluster[j] )
    {
      point_energy_min = r8_huge ( );

      for ( k = 0; k < cluster_num; k++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
        }

        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k;
        }
      }
    }
  }
  it_num = 0;

  while ( it_num < it_max )
  {
    it_num = it_num + 1;
//
//  #1:
//  Assign each point to the cluster of its nearest center.
//
    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      point_energy_min = r8_huge ( );
      k = cluster[j];

      for ( k2 = 0; k2 < cluster_num; k2++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k2*dim_num], 2 );
        }

        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k2;
        }
      }

      if ( k != cluster[j] )
      {
        swap = swap + 1;
      }
    }
//
//  Terminate if no points were swapped.
//
    if ( 1 < it_num )
    {
      if ( swap == 0 )
      {
        break;
      }
    }
//
//  #2:
//  Determine the total energy of the new clustering with current centroids.
//
    r8vec_zero ( cluster_num, cluster_energy );

    for ( j = 0; j < point_num; j++ )
    {
      k = cluster[j];

      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }
      cluster_energy[k] = cluster_energy[k] + point_energy;
    }
//
//  #3:
//  Determine the centroids of the clusters.
//
    centroid = r8vec_zero_new ( dim_num * cluster_num );
    i4vec_zero ( cluster_num, cluster_population );

    for ( j = 0; j < point_num; j++ )
    {
      k = cluster[j];
      cluster_population[k] = cluster_population[k] + 1;
      for ( i = 0; i < dim_num; i++ )
      {
        centroid[i+k*dim_num] = centroid[i+k*dim_num] + point[i+j*dim_num];
      }
    }
//
//  Now divide by the population to get the centroid.
//  But if a center has no population, pick a point at random.
//
    missed = 0;

    for ( k = 0; k < cluster_num; k++ )
    {
      if ( cluster_population[k] != 0 )
      {
        for ( i = 0; i < dim_num; i++ )
        {
          centroid[i+k*dim_num] = centroid[i+k*dim_num]
          / ( double ) ( cluster_population[k] );
        }
      }
      else
      {
        for ( i = 0; i < dim_num; i++ )
        {
          centroid[i+k*dim_num] = point[i+missed*dim_num];
        }
        missed = missed + 1;
      }
    }

    for ( k = 0; k < cluster_num; k++ )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = centroid[i+k*dim_num];
      }
    }

    delete [] centroid;
//
//  #4:
//  Determine the total energy of the current clustering with new centroids.
//
    r8vec_zero ( cluster_num, cluster_energy );

    for ( j = 0; j < point_num; j++ )
    {
      k = cluster[j];

      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }
      cluster_energy[k] = cluster_energy[k] + point_energy;
    }
  }
  return;
}
//****************************************************************************80

void hmeans_02 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], int cluster[], double cluster_center[], 
  int cluster_population[], double cluster_energy[], int *seed )

//****************************************************************************80
//
//  Purpose:
//
//   HMEANS_02 applies the H-Means algorithm.
//
//  Discussion:
//
//    This is a simple routine to group a set of points into K clusters,
//    each with a center point, in such a way that the total cluster 
//    energy is minimized.  The total cluster energy is the sum of the
//    squares of the distances of each point to the center of its cluster.
//
//    The algorithm begins with an initial estimate for the cluster centers:
//
//    1. The points are assigned to the nearest cluster centers.
//
//    2. The iteration exit ( 1 );s if the total energy has not changed 
//        significantly, or we have reached the maximum number of iterations.
//
//    3. Each cluster center is replaced by the centroid of the points
//       in the cluster.
//
//    4. Return to step 1.
//
//    The algorithm may fail to find the best solution.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input/output, int CLUSTER[POINT_NUM].  On input, the user 
//    may specify an initial cluster for each point, or leave all entrie of
//    CLUSTER set to 0.  On output, CLUSTER contains the index of the
//    cluster to which each data point belongs.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the coordinates of the cluster centers.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number of
//    points assigned to each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the energy of 
//    the clusters.
//
//    Input/output, int *SEED, a seed for the random
//    number generator.
//
{
  int c;
  bool debug = false;
  int i;
  int j;
  int k;
  int k2;
  double point_energy;
  double point_energy_min;
  int swap;
//
//  Data checks.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_02 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_02 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_02 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "HMEANS_02 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }
//
//  On input, legal entries in CLUSTER are preserved, but
//  otherwise, each point is assigned to its nearest cluster.
//
  for ( j = 0; j < point_num; j++ )
  {
    if ( cluster[j] < 0 || cluster_num <= cluster[j] )
    {
      point_energy_min = r8_huge ( );
      for ( k = 0; k < cluster_num; k++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
            pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
        }
        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k;
        }
      }
    }
  }

  it_num = 0;

  for ( ; ; )
  {
//
//  Given centers, assign points to nearest center.
//
    i4vec_zero ( cluster_num, cluster_population );
    r8vec_zero ( cluster_num, cluster_energy );

    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      point_energy_min = r8_huge ( );
      k = cluster[j];

      for ( k2 = 0; k2 < cluster_num; k2++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
            pow ( point[i+j*dim_num] - cluster_center[i+k2*dim_num], 2 );
        }

        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k2;
        }
      }
      if ( k != cluster[j] )
      {
        swap = swap + 1;
      }
      k = cluster[j];
      cluster_energy[k] = cluster_energy[k] + point_energy_min;
      cluster_population[k] = cluster_population[k] + 1;
    }

    if ( debug )
    {
      cout << "  " << setw(3) << it_num
           << "  " << setw(14) << r8vec_sum ( cluster_num, cluster_energy ) << "\n";
    }

    if ( 0 < it_num )
    {
      if ( swap == 0 )
      {
        break;
      }
    }

    if ( it_max <= it_num )
    {
      break;
    }

    it_num = it_num + 1;
//
//  Given points in cluster, replace center by centroid.
//
    r8vec_zero ( dim_num * cluster_num, cluster_center );
  
    for ( j = 0; j < point_num; j++ )
    {
      k = cluster[j];
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
          + point[i+j*dim_num];
      }
    }

    for ( k = 0; k < cluster_num; k++ )
    {
      if ( cluster_population[k] != 0 )
      {
        for ( i = 0; i < dim_num; i++ )
        {
          cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] / 
            ( double ) ( cluster_population[k] );
        }
      }
      else
      {
        j = i4_uniform ( 0, point_num - 1, seed );
        for ( i = 0; i < dim_num; i++ )
        {
          cluster_center[i+k*dim_num] = point[i+j*dim_num];
        }
      }
    }
  }
//
//  Compute the energy based on the final value of the cluster centers.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
      pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + point_energy;
  }
  return;
}
//****************************************************************************80

void hmeans_w_01 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], double weight[], int cluster[], 
  double cluster_center[], int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   HMEANS_W_01 applies the weighted H-Means algorithm. 
//
//  Discussion:
//
//    The input data for the weight H-Means problem includes:
//    * a set of N data points X in M dimensions, 
//    * a set of N nonnegative weights W,
//    * a desired number of clusters K.
//    * an initial set of cluster centers Z,
//    * an (optional) initial set of cluster assignments.
//
//    The goal is to determine K points Z, called cluster centers, and
//    to assign each point X(I) to some cluster Z(J), so that we minimize
//    the weighted standard deviation of the distance of each data point
//    to the center of its cluster.  Writing J = CLUSTER(I) to
//    indicate the index of the nearest cluster center Z(J) to the 
//    point X(I), the quantity we are trying to minimize is the sum
//    of the weighted cluster energies E(J), where:
//
//      E(J) = Sum ( 1 <= I <= N ) W(I) * || X(I) - Z(J) ||^2
//
//    Here, we assume that we are using the Euclidean norm, so that
//    
//      || X(I) - Z(J) ||^2 = Sum ( 1 <= K <= M )
//        ( X(I)(K) - Z(J)(K) )^2
//
//    In this notation, X(I)(K) is the K-th spatial component of the
//    I-th data point.
//
//    Note that this routine should give the same results as HMEANS_01
//    in any case in which all the entries of the WEIGHT vector are equal.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Wendy Martinez, Angel Martinez,
//    Computational Statistics Handbook with MATLAB,
//    pages 373-376,
//    Chapman and Hall / CRC, 2002.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of data points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int &IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the data points.
//
//    Input, double WEIGHT[POINT_NUM], the weights
//    assigned to the data points.  These must be nonnegative, and
//    at least one must be strictly positive.
//
//    Input/output, int CLUSTER[POINT_NUM].  On input, the user 
//    may specify an initial cluster for each point, or leave all entrie of
//    CLUSTER set to 0.  On output, CLUSTER contains the index of the
//    cluster to which each data point belongs.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], the
//    centers associated with the minimal energy clustering.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the energy
//    associated with each cluster.
//
{
  int c;
  double *centroid;
  double *cluster_weight;
  bool debug = true;
  double energy;
  int i;
  int j;
  int k;
  int k2;
  int missed;
  double point_energy;
  double point_energy_min;
  int swap;
//
//  Data checks.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_W_01 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_W_01 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_W_01 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "HMEANS_W_01 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }

  if ( r8vec_any_negative ( point_num, weight ) )
  {
    cout << "\n";
    cout << "HMEANS_W_01 - Fatal error!\n";
    cout << "  Some weight entry is negative.\n";
    exit ( 1 );
  }

  if ( r8vec_all_nonpositive ( point_num, weight ) )
  {
    cout << "\n";
    cout << "HMEANS_W_01 - Fatal error!\n";
    cout << "  No weight entry is positive.\n";
    exit ( 1 );
  }
//
//  On input, legal entries in CLUSTER are preserved, but
//  otherwise, each point is assigned to its nearest cluster.
//
  for ( j = 0; j < point_num; j++ )
  {
    if ( cluster[j] < 0 || cluster_num <= cluster[j] )
    {
      point_energy_min = r8_huge ( );

      for ( k = 0; k < cluster_num; k++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
            pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
        }

        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k;
        }
      }
    }
  }
  it_num = 0;

  while ( it_num < it_max )
  {
    it_num = it_num + 1;
//
//  #1:
//  Reassign points to clusters:
//  Assign each point to the cluster whose center is nearest;
//  Count the number of points whose cluster assignment is changed.
//
    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      point_energy_min = r8_huge ( );
      k = cluster[j];

      for ( k2 = 0; k2 < cluster_num; k2++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
            pow ( point[i+j*dim_num] - cluster_center[i+k2*dim_num], 2 );
        }

        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k2;
        }
      }

      if ( k != cluster[j] )
      {
        swap = swap + 1;
      }
    }
//
//  If no point changed its cluster assignment, the algorithm can make no 
//  more improvements, so terminate.
//
    if ( 1 < it_num )
    {
      if ( swap == 0 )
      {
        break;
      }
    }
//
//  Determine the current energy.
//
    energy = 0.0;
    for ( j = 0; j < point_num; j++ )
    {
      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k2*dim_num], 2 );
      }
      energy = energy + weight[j] * point_energy;
    }
    cout << "  " << setw(4) << it_num
         << "  " << setw(14) << energy << "\n";
//
//  #2:
//  Determine the centroids of the clusters, and set the 
//  cluster center to the cluster centroid.
//
    centroid = r8vec_zero_new ( dim_num * cluster_num );
    cluster_weight = r8vec_zero_new ( cluster_num );

    for ( j = 0; j < point_num; j++ )
    {
      k = cluster[j];
      cluster_population[k] = cluster_population[k] + 1;
      cluster_weight[k] = cluster_weight[k] + weight[j];
      for ( i = 0; i < dim_num; i++ )
      {
        centroid[i+k*dim_num] = centroid[i+k*dim_num] 
          + weight[j] * point[i+j*dim_num];
      }
    }

    missed = 0;

    for ( k = 0; k < cluster_num; k++ )
    {
      if ( cluster_weight[k] != 0.0 )
      {
        for ( i = 0; i < dim_num; i++ )
        {
          centroid[i+k*dim_num] = centroid[i+k*dim_num] / cluster_weight[k];
        }
      }
      else
      {
        for ( i = 0; i < dim_num; i++ )
        {
          centroid[i+k*dim_num] = point[i+missed*dim_num];
        }
        missed = missed + 1;
      }
    }

    for ( k = 0; k < cluster_num; k++ )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = centroid[i+k*dim_num];
      }
    }

    delete [] centroid;
    delete [] cluster_weight;
  }
//
//  Compute the energy based on the final value of the cluster centers.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
      pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + weight[j] * point_energy;
  }
  return;
}
//****************************************************************************80

void hmeans_w_02 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], double weight[], int cluster[], 
  double cluster_center[], int cluster_population[], double cluster_energy[], 
  int *seed )

//****************************************************************************80
//
//  Purpose:
//
//   HMEANS_W_02 applies the weighted H-Means algorithm.
//
//  Discussion:
//
//    The input data for the weight H-Means problem includes:
//    * a set of N data points X in M dimensions, 
//    * a set of N nonnegative weights W,
//    * a desired number of clusters K.
//    * an initial set of cluster centers Z,
//    * an (optional) initial set of cluster assignments.
//
//    The goal is to determine K points Z, called cluster centers, and
//    to assign each point X(I) to some cluster Z(J), so that we minimize
//    the weighted standard deviation of the distance of each data point
//    to the center of its cluster.  Writing J = CLUSTER(I) to
//    indicate the index of the nearest cluster center Z(J) to the 
//    point X(I), the quantity we are trying to minimize is the sum
//    of the weighted cluster energies E(J), where:
//
//      E(J) = Sum ( 1 <= I <= N ) W(I) * || X(I) - Z(J) ||^2
//
//    Here, we assume that we are using the Euclidean norm, so that
//    
//      || X(I) - Z(J) ||^2 = Sum ( 1 <= K <= M )
//        ( X(I)(K) - Z(J)(K) )^2
//
//    In this notation, X(I)(K) is the K-th spatial component of the
//    I-th data point.
//
//    Note that this routine should give the same results as HMEANS_02
//    in any case in which all the entries of the WEIGHT vector are equal.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    09 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int &IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input, double WEIGHT[POINT_NUM], the weights
//    assigned to the data points.  These must be nonnegative, and
//    at least one must be strictly positive.
//
//    Input/output, int CLUSTER[POINT_NUM].  On input, the user 
//    may specify an initial cluster for each point, or leave all entrie of
//    CLUSTER set to 0.  On output, CLUSTER contains the index of the
//    cluster to which each data point belongs.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the coordinates of the cluster centers.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number of
//    points assigned to each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the energy of 
//    the clusters.
//
//    Input/output, int *SEED, a seed for the random 
//    number generator.
//
{
  double *cluster_weight;
  int i;
  int j;
  int k;
  int k2;
  double point_energy;
  double point_energy_min;
  int swap;
//
//  Data checks.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_W_02 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_W_02 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "HMEANS_W_02 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "HMEANS_W_02 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }

  if ( r8vec_any_negative ( point_num, weight ) )
  {
    cout << "\n";
    cout << "HMEANS_W_02 - Fatal error!\n";
    cout << "  Some weight entry is negative.\n";
    exit ( 1 );
  }

  if ( r8vec_all_nonpositive ( point_num, weight ) )
  {
    cout << "\n";
    cout << "HMEANS_W_02 - Fatal error!\n";
    cout << "  No weight entry is positive.\n";
    exit ( 1 );
  }
//
//  On input, legal entries in CLUSTER are preserved, but
//  otherwise, each point is assigned to its nearest cluster.
//
  for ( j = 0; j < point_num; j++ )
  {
    if ( cluster[j] < 0 || cluster_num <= cluster[j] )
    {
      point_energy_min = r8_huge ( );
      for ( k = 0; k < cluster_num; k++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
            pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
        }
        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k;
        }
      }
    }
  }
  it_num = 0;

  for ( ; ; )
  {
//
//  Given centers, assign points to nearest center.
//
    i4vec_zero ( cluster_num, cluster_population );
    r8vec_zero ( cluster_num, cluster_energy );
    cluster_weight = r8vec_zero_new ( cluster_num );

    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      point_energy_min = r8_huge ( );
      k = cluster[j];

      for ( k2 = 0; k2 < cluster_num; k2++ )
      {
        point_energy = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          point_energy = point_energy + 
            pow ( point[i+j*dim_num] - cluster_center[i+k2*dim_num], 2 );
        }

        if ( point_energy < point_energy_min )
        {
          point_energy_min = point_energy;
          cluster[j] = k2;
        }
      }

      if ( k != cluster[j] )
      {
        swap = swap + 1;
      }
      k = cluster[j];
      cluster_energy[k] = cluster_energy[k] + weight[j] * point_energy_min;
      cluster_population[k] = cluster_population[k] + 1;
      cluster_weight[k] = cluster_weight[k] + weight[j];
    }

    if ( 0 < it_num )
    {
      if ( swap == 0 )
      {
        break;
      }
    }

    if ( it_max <= it_num )
    {
      break;
    }

    it_num = it_num + 1;
//
//  Given points in cluster, replace center by weighted centroid.
//
    r8vec_zero ( dim_num * cluster_num, cluster_center );
  
    for ( j = 0; j < point_num; j++ )
    {
      k = cluster[j];
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
          + weight[j] * point[i+j*dim_num];
      }
    }

    for ( k = 0; k < cluster_num; k++ )
    {
      if ( cluster_weight[k] != 0.0 )
      {
        for ( i = 0; i < dim_num; i++ )
        {
          cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] / 
            cluster_weight[k];
        }
      }
      else
      {
        j = i4_uniform ( 0, point_num - 1, seed );
        for ( i = 0; i < dim_num; i++ )
        {
          cluster_center[i+k*dim_num] = point[i+j*dim_num];
        }
      }
    }
    delete [] cluster_weight;
  }
//
//  Compute the energy based on the final value of the cluster centers.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + weight[j] * point_energy;
  }

  return;
}
//****************************************************************************80

int i4_max ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MAX returns the maximum of two I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, are two integers to be compared.
//
//    Output, int I4_MAX, the larger of I1 and I2.
//
{
  int value;

  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int i4_min ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MIN returns the minimum of two I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, two integers to be compared.
//
//    Output, int I4_MIN, the smaller of I1 and I2.
//
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int i4_uniform ( int a, int b, int *seed )

//****************************************************************************80
//
//  Purpose:
//
//    I4_UNIFORM returns a scaled pseudorandom I4.
//
//  Discussion:
//
//    The pseudorandom number should be uniformly distributed
//    between A and B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    12 November 2006
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley Interscience, page 95, 1998.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, pages 362-376, 1986.
//
//    Peter Lewis, Allen Goodman, James Miller
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, pages 136-143, 1969.
//
//  Parameters:
//
//    Input, int A, B, the limits of the interval.
//
//    Input/output, int *SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, int I4_UNIFORM, a number between A and B.
//
{
  int k;
  float r;
  int value;

  if ( *seed == 0 )
  {
    cerr << "\n";
    cerr << "I4_UNIFORM - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  k = *seed / 127773;

  *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

  if ( *seed < 0 )
  {
    *seed = *seed + 2147483647;
  }

  r = ( float ) ( *seed ) * 4.656612875E-10;
//
//  Scale R to lie between A-0.5 and B+0.5.
//
  r = ( 1.0 - r ) * ( ( float ) ( i4_min ( a, b ) ) - 0.5 )
    +         r   * ( ( float ) ( i4_max ( a, b ) ) + 0.5 );
//
//  Use rounding to convert R to an integer between A and B.
//
  value = r4_nint ( r );

  value = i4_max ( value, i4_min ( a, b ) );
  value = i4_min ( value, i4_max ( a, b ) );

  return value;
}
//****************************************************************************80

void i4mat_write ( string output_filename, int m, int n, int table[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_WRITE writes an I4MAT file with no header.
//
//  Discussion:
//
//    An I4MAT is an array of I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    01 June 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string OUTPUT_FILENAME, the output filename.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, int TABLE[M*N], the data.
//
{
  int i;
  int j;
  ofstream output;
//
//  Open the file.
//
  output.open ( output_filename.c_str ( ) );

  if ( !output )
  {
    cerr << "\n";
    cerr << "I4MAT_WRITE - Fatal error!\n";
    cerr << "  Could not open the output file.\n";
    exit ( 1 );
  }
//
//  Write the data.
//
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << "  " << setw(10) << table[i+j*m];
    }
    output << "\n";
  }
//
//  Close the file.
//
  output.close ( );

  return;
}
//****************************************************************************80

void i4vec_negone ( int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_NEGONE sets an I4VEC to -1.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    12 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Output, int A[N], a vector of -1's.
//
{
  int i;

  for ( i = 0; i < n; i++ )
  {
    a[i] = -1;
  }
  return;
}
//****************************************************************************80

int *i4vec_negone_new ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_NEGONE_NEW creates an I4VEC and sets it to -1.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    12 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Output, int I4VEC_NEGONE_NEW[N], a vector of -1's.
//
{
  int *a;
  int i;

  a = new int[n];

  for ( i = 0; i < n; i++ )
  {
    a[i] = -1;
  }
  return a;
}
//****************************************************************************80

int i4vec_sum ( int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_SUM sums the entries of an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Example:
//
//    Input:
//
//      A = ( 1, 2, 3, 4 )
//
//    Output:
//
//      I4VEC_SUM = 10
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    26 May 1999
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, int A[N], the vector to be summed.
//
//    Output, int I4VEC_SUM, the sum of the entries of A.
//
{
  int i;
  int sum;

  sum = 0;
  for ( i = 0; i < n; i++ )
  {
    sum = sum + a[i];
  }

  return sum;
}
//****************************************************************************80

void i4vec_zero ( int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_ZERO zeroes an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    01 August 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Output, int A[N], a vector of zeroes.
//
{
  int i;

  for ( i = 0; i < n; i++ )
  {
    a[i] = 0;
  }
  return;
}
//****************************************************************************80

int *i4vec_zero_new ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_ZERO_NEW creates and zeroes an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    11 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Output, int I4VEC_ZERO_NEW[N], a vector of zeroes.
//
{
  int *a;
  int i;

  a = new int[n];

  for ( i = 0; i < n; i++ )
  {
    a[i] = 0;
  }
  return a;
}
//****************************************************************************80

void kmeans_01 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], int cluster[], double cluster_center[], 
  int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_01 applies the K-Means algorithm.
//
//  Discussion:
//
//    Given a matrix of POINT_NUM observations on DIM_NUM variables, the
//    observations are to be allocated to CLUSTER_NUM clusters in such 
//    a way that the within-cluster sum of squares is minimized.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    09 October 2011
//
//  Author:
//
//    Original FORTRAN77 version by David Sparks.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    David Sparks,
//    Algorithm AS 58: 
//    Euclidean Cluster Analysis,
//    Applied Statistics,
//    Volume 22, Number 1, 1973, pages 126-130.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the points.
//
//    Output, int CLUSTER[POINT_NUM], indicates which cluster
//    each point belongs to.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the cluster centers.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number 
//    of points in each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the 
//    cluster energies.
//
{
  double dc;
  double de;
  double *f;
  int i;
  int il;
  int ir;
  int j;
  int j2;
  int k;
  double point_energy;
  double point_energy_min;
  int swap;

  it_num = 0;
//
//  Idiot checks.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_01 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_01 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_01 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }
//
//  For each observation, calculate the distance from each cluster
//  center, and assign to the nearest.
//
  for ( j = 0; j < point_num; j++ )
  {
    point_energy_min = r8_huge ( );
    cluster[j] = -1;

    for ( k = 0; k < cluster_num; k++ )
    {
      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }

      if ( point_energy < point_energy_min )
      {
        point_energy_min = point_energy;
        cluster[j] = k;
      }
    }
  }
//
//  Determine the cluster population counts.
//
  i4vec_zero ( cluster_num, cluster_population );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_population[k] = cluster_population[k] + 1;
  }
//
//  Calculate the mean and sum of squares for each cluster.
//
  r8vec_zero ( dim_num * cluster_num, cluster_center );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        + point[i+j*dim_num];
    }
  }

  for ( k = 0; k < cluster_num; k++ )
  {
    if ( 0 < cluster_population[k] )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] / 
         ( double ) cluster_population[k];
      }
    }
  }
//
//  Set the point energies.
//
  f = r8vec_zero_new ( point_num );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      f[j] = f[j] + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
  }
//
//  Set the cluster energies.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_energy[k] = cluster_energy[k] + f[j];
  }
//
//  Adjust the point energies by a weight factor.
//
  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    if ( 1 < cluster_population[k] )
    {
      f[j] = f[j] * ( double ) ( cluster_population[k] ) 
        / ( double ) ( cluster_population[k] - 1 );
    }
  }
//
//  Examine each observation in turn to see if it should be
//  reassigned to a different cluster.
//
  it_num = 0;

  while ( it_num < it_max )
  {
    it_num = it_num + 1;

    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      il = cluster[j];
      ir = il;

      if ( cluster_population[il] <= 1 )
      {
        continue;
      }

      dc = f[j];

      for ( k = 0; k < cluster_num; k++ )
      {
        if ( k != il )
        {
          de = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            de = de + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
          }
          de = de * ( double ) cluster_population[k] 
             / ( double ) ( cluster_population[k] + 1 );

          if ( de < dc )
          {
            dc = de;
            ir = k;
          }
        }
      }
//
//  If the lowest value was obtained by staying in the current cluster,
//  then cycle.
//
      if ( ir == il )
      {
        continue;
      }
//
//  Reassign the point from cluster IL to cluster IR.
//
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+il*dim_num] = ( cluster_center[i+il*dim_num]
          * ( double ) ( cluster_population[il] ) - point[i+j*dim_num] )
          / ( double ) ( cluster_population[il] - 1 );

        cluster_center[i+ir*dim_num] = ( cluster_center[i+ir*dim_num]
          * ( double ) ( cluster_population[ir] ) + point[i+j*dim_num] )
          / ( double ) ( cluster_population[ir] + 1 );
      }
      cluster_energy[il] = cluster_energy[il] - f[j];
      cluster_energy[ir] = cluster_energy[ir] + dc;
      cluster_population[ir] = cluster_population[ir] + 1;
      cluster_population[il] = cluster_population[il] - 1;

      cluster[j] = ir;
//
//  Adjust the value of F for points in clusters IL and IR.
//  
      for ( j2 = 0; j2 < point_num; j2++ )
      {
        k = cluster[j2];

        if ( k == il || k == ir )
        {
          f[j2] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            f[j2] = f[j2] + pow ( point[i+j2*dim_num] - cluster_center[i+k*dim_num], 2 );
          }

          if ( 1 < cluster_population[k] )
          {
            f[j2] = f[j2] * ( double ) ( cluster_population[k] ) 
              / ( ( double ) ( cluster_population[k] - 1 ) );
          }
        }
      }
      swap = swap + 1;
    }
//
//  Exit if no reassignments were made during this iteration.
//
    if ( swap == 0 )
    {
      break;
    }
  }
//
//  Compute the cluster energies.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + point_energy;
  }

  delete [] f;

  return;
}
//****************************************************************************80

void kmeans_02 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], int cluster[], double cluster_center[], 
  int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_02 applies the K-Means algorithm.
//
//  Discussion:
//
//    The routine attempts to divide POINT_NUM points in 
//    DIM_NUM-dimensional space into CLUSTER_NUM clusters so that the within 
//    cluster sum of squares is minimized.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    13 October 2011
//
//  Author:
//
//    Original FORTRAN77 by John Hartigan, Manchek Wong.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    John Hartigan, Manchek Wong,
//    Algorithm AS 136:
//    A K-Means Clustering Algorithm,
//    Applied Statistics,
//    Volume 28, Number 1, 1979, pages 100-108.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int &IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Output, int CLUSTER[POINT_NUM], the cluster each 
//    point belongs to.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the cluster centers.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number 
//    of points in each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the 
//    within-cluster sum of squares.
//
{
  double *an1;
  double *an2;
  int *cluster2;
  double *d;
  double db;
  double dt[2];
  int i;
  int ifault;
  int il;
  int indx;
  int *itran;
  int j;
  int k;
  int l;
  int *live;
  int *ncp;
  double point_energy;
  double temp;

  it_num = 0;

  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_02 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num <= cluster_num )
  {
    cout << "\n";
    cout << "KMEANS_02 - Fatal error!\n";
    cout << "  POINT_NUM <= CLUSTER_NUM.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_02 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_02 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }
//
//  For each point I, find its two closest centers, CLUSTER(I) and CLUSTER2(I).
//  Assign it to CLUSTER(I).
//
  cluster2 = new int[point_num];

  for ( j = 0; j < point_num; j++ )
  {
    cluster[j] = 0;
    cluster2[j] = 1;

    for ( il = 0; il < 2; il++ )
    {
      dt[il] = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        dt[il] = dt[il] + pow ( point[i+j*dim_num] - cluster_center[i+il*dim_num], 2 );
      }
    }

    if ( dt[1] < dt[0] )
    {
      cluster[j] = 1;
      cluster2[j] = 0;
      temp = dt[0];
      dt[0] = dt[1];
      dt[1] = temp;
    }

    for ( k = 2; k < cluster_num; k++ )
    {
      db = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        db = db + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }

      if ( db < dt[0] )
      {
        dt[1] = dt[0];
        cluster2[j] = cluster[j];
        dt[0] = db;
        cluster[j] = k;
      }
      else if ( db < dt[1] )
      {
        dt[1] = db;
        cluster2[j] = k;
      }
    }
  }
//
//  Update cluster centers to be the average of points contained
//  within them.
//
  i4vec_zero ( cluster_num, cluster_population );
  r8vec_zero ( dim_num * cluster_num, cluster_center );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_population[k] = cluster_population[k] + 1;
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        + point[i+j*dim_num];
    }
  }
//
//  Check to see if there is any empty cluster.
//
  an1 = new double[cluster_num];
  an2 = new double[cluster_num];
  itran = new int[cluster_num];
  ncp = new int[cluster_num];

  for ( k = 0; k < cluster_num; k++ )
  {
    if ( cluster_population[k] == 0 )
    {
      cout << "\n";
      cout << "KMEANS_02 - Fatal error!\n";
      cout << "  Cluster " << k << " has zero population.\n";
      exit ( 1 );
    }

    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num]
      / ( double ) ( cluster_population[k] );
    }
//
//  Initialize AN1, AN2, ITRAN and NCP
//  AN1(K) = CLUSTER_POPULATION(K) / (CLUSTER_POPULATION(K) - 1)
//  AN2(K) = CLUSTER_POPULATION(K) / (CLUSTER_POPULATION(K) + 1)
//  ITRAN(K) = 1 if cluster K is updated in the quick-transfer stage,
//           = 0 otherwise
//  In the optimal-transfer stage, NCP(K) stores the step at which
//  cluster K is last updated.
//  In the quick-transfer stage, NCP(K) stores the step at which
//  cluster K is last updated plus POINT_NUM.
//
    an2[k] = ( double ) ( cluster_population[k] ) 
      / ( double ) ( cluster_population[k] + 1 );

    if ( 1 < cluster_population[k] )
    {
      an1[k] = ( double ) ( cluster_population[k] ) 
        / ( double ) ( cluster_population[k] - 1 );
    }
    else
    {
      an1[k] = r8_huge ( );
    }
    itran[k] = 1;
    ncp[k] = -1;
  }

  indx = 0;
  ifault = 2;
  it_num = 0;

  d = new double[point_num];
  live = new int[cluster_num];

  while ( it_num < it_max )
  {
    it_num = it_num + 1;
//
//  In this stage, there is only one pass through the data.   Each
//  point is re-allocated, if necessary, to the cluster that will
//  induce the maximum reduction in within-cluster sum of squares.
//
    kmeans_02_optra ( dim_num, point_num, cluster_num, point, 
      cluster_center, cluster, cluster2, cluster_population, an1, an2, 
      ncp, d, itran, live, indx );
//
//  Stop if no transfer took place in the last POINT_NUM optimal transfer steps.
//
    if ( indx == point_num )
    {
      ifault = 0;
      break;
    }
//
//  Each point is tested in turn to see if it should be re-allocated
//  to the cluster to which it is most likely to be transferred,
//  CLUSTER2(I), from its present cluster, CLUSTER(I).   Loop through the
//  data until no further change is to take place.
//
    kmeans_02_qtran ( dim_num, point_num, cluster_num, point, 
      cluster_center, cluster, cluster2, cluster_population, an1, an2, 
      ncp, d, itran, indx );
//
//  If there are only two clusters, there is no need to re-enter the
//  optimal transfer stage.
//
    if ( cluster_num == 2 )
    {
      ifault = 0;
      break;
    }
//
//  NCP has to be set to 0 before entering OPTRA.
//
    i4vec_zero ( cluster_num, ncp );
  }
  if ( ifault == 2 )
  {
    cout << "\n";
    cout << "KMEANS_02 - Warning!\n";
    cout << "  Maximum number of iterations reached\n";
    cout << "  without convergence.\n";
  }
//
//  Compute the within-cluster sum of squares for each cluster.
//
  r8vec_zero ( dim_num * cluster_num, cluster_center );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num]
        + point[i+j*dim_num];
    }
  }

  for ( k = 0; k < cluster_num; k++ )
  {
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        / ( double ) cluster_population[k];
    }
  }
//
//  Compute the cluster energies.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + point_energy;
  }

  delete [] an1;
  delete [] an2;
  delete [] cluster2;
  delete [] d;
  delete [] itran;
  delete [] live;
  delete [] ncp;

  return;
}
//****************************************************************************80

void kmeans_02_optra ( int dim_num, int point_num, int cluster_num, 
  double point[], double cluster_center[], int cluster[], int cluster2[], 
  int cluster_population[], double an1[], double an2[], int ncp[], 
  double d[], int itran[], int live[], int &indx )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_02_OPTRA carries out the optimal transfer stage.
//
//  Discussion:
//
//    Each point is re-allocated, if necessary, to the cluster that
//    will induce a maximum reduction in the within-cluster sum of
//    squares.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    09 October 2011
//
//  Author:
//
//    Original FORTRAN77 by John Hartigan, Manchek Wong.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    John Hartigan, Manchek Wong,
//    Algorithm AS 136:
//    A K-Means Clustering Algorithm,
//    Applied Statistics,
//    Volume 28, Number 1, 1979, pages 100-108.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates of 
//    the points.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the cluster centers.
//
//    Input/output, int CLUSTER[POINT_NUM], the cluster 
//    each point belongs to.
//
//    Input/output, int CLUSTER2[POINT_NUM], the cluster 
//    to which each point is most likely to be transferred to.
//
//    Input/output, int CLUSTER_POPULATION[CLUSTER_NUM], 
//    the number of points in each cluster.
//
//    Input/output, double AN1[CLUSTER_NUM], 
//    CLUSTER_POPULATION(L) / (CLUSTER_POPULATION(L) - 1)
//
//    Input/output, double AN2[CLUSTER_NUM], 
//    CLUSTER_POPULATION(L) / (CLUSTER_POPULATION(L) + 1)
//
//    Input/output, int NCP[CLUSTER_NUM], ?
//
//    Input/output, double D[POINT_NUM], ?
//
//    Input/output, int ITRAN[CLUSTER_NUM], 
//    1 if cluster L is updated in the quick-transfer stage,
//    0 otherwise.  Reset to zero on output.
//
//    Input/output, int LIVE[CLUSTER_NUM], ?
//
//    Input/output, int INDX, ?
//
{
  double al1;
  double al2;
  double alt;
  double alw;
  double dc;
  int i;
  int j;
  int k;
  int l;
  int l1;
  int l2;
  int ll;
  double r2;
  double rr;
//
//  If cluster L is updated in the last quick-transfer stage, it
//  belongs to the live set throughout this stage.   Otherwise, at
//  each step, it is not in the live set if it has not been updated
//  in the last POINT_NUM optimal transfer steps.
//
  for ( k = 0; k < cluster_num; k++ )
  {
    if ( itran[k] == 1 )
    {
      live[k] = point_num + 1;
    }
  }

  for ( j = 0; j < point_num; j++ )
  {
    indx = indx + 1;
    l1 = cluster[j];
    l2 = cluster2[j];
    ll = l2;
//
//  If point J is the only member of cluster L1, no transfer.
//
    if ( 1 < cluster_population[l1] )
    {
//
//  If L1 has been updated in this stage, re-compute D(I).
//
      if ( ncp[l1] != 0 )
      {
        d[j] = 0.0;
        for ( i = 0; i < dim_num; i++ )
        {
          d[j] = d[j] + pow ( point[i+j*dim_num] - cluster_center[i+l1*dim_num], 2 );
        }
        d[j] = an1[l1] * d[j];
      }
//
//  Find the cluster with minimum R2.
//
      r2 = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        r2 = r2 + pow ( point[i+j*dim_num] - cluster_center[i+l2*dim_num], 2 );
      }
      r2 = an2[l2] * r2;

      for ( l = 0; l < cluster_num; l++ )
      {
//
//  If LIVE(L1) <= J, then L1 is not in the live set.   If this is
//  true, we only need to consider clusters that are in the live set
//  for possible transfer of point J.   
//
//  Otherwise, we need to consider all possible clusters.
//
        if ( ( j < live[l1] || j < live[l] ) && l != l1 && l != ll )
        {
          rr = r2 / an2[l];

          dc = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            dc = dc + pow ( point[i+j*dim_num] - cluster_center[i+l*dim_num], 2 );
          }

          if ( dc < rr )
          {
            r2 = dc * an2[l];
            l2 = l;
          }
        }
      }
//
//  If no transfer is necessary, L2 is the new CLUSTER2(J).
// 
      if ( d[j] <= r2 )
      {
        cluster2[j] = l2;
      }
//
//  Update cluster centers, LIVE, NCP, AN1 and AN2 for clusters L1 and
//  L2, and update CLUSTER(J) and CLUSTER2(J).
//
      else
      {
        indx = 0;
        live[l1] = point_num + j;
        live[l2] = point_num + j;
        ncp[l1] = j;
        ncp[l2] = j;
        al1 = cluster_population[l1];
        alw = al1 - 1.0;
        al2 = cluster_population[l2];
        alt = al2 + 1.0;

        for ( i = 0; i < dim_num; i++ )
        {
          cluster_center[i+l1*dim_num] = ( cluster_center[i+l1*dim_num] * al1 
            - point[i+j*dim_num] ) / alw;

          cluster_center[i+l2*dim_num] = ( cluster_center[i+l2*dim_num] * al2 
            + point[i+j*dim_num] ) / alt;
        }

        cluster_population[l1] = cluster_population[l1] - 1;
        cluster_population[l2] = cluster_population[l2] + 1;
        an2[l1] = alw / al1;

        if ( 1.0 < alw )
        {
          an1[l1] = alw / ( alw - 1.0 );
        }
        else
        {
          an1[l1] = r8_huge ( );
        }

        an1[l2] = alt / al2;
        an2[l2] = alt / ( alt + 1.0 );
        cluster[j] = l2;
        cluster2[j] = l1;
      }
    }

    if ( indx == point_num )
    {
      return;
    }

  }
//
//  ITRAN(L) = 0 before entering QTRAN.
//
  i4vec_zero ( cluster_num, itran );
//
//  LIVE(L) has to be decreased by POINT_NUM before re-entering OPTRA.
//
  for ( k = 0; k < cluster_num; k++ )
  {
    live[k] = live[k] - point_num;
  }

  return;
}
//****************************************************************************80

void kmeans_02_qtran ( int dim_num, int point_num, int cluster_num, 
  double point[], double cluster_center[], int cluster[], int cluster2[], 
  int cluster_population[], double an1[], double an2[], int ncp[], double d[], 
  int itran[], int &indx )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_02_QTRAN carries out the quick transfer stage.
//
//  Discussion:
//
//    For each point I, CLUSTER(I) and CLUSTER2(I) are switched, if necessary, 
//    to reduce within-cluster sum of squares.  The cluster centers are
//    updated after each step.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    13 October 2011
//
//  Author:
//
//    Original FORTRAN77 by John Hartigan, Manchek Wong.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    John Hartigan, Manchek Wong,
//    Algorithm AS 136:
//    A K-Means Clustering Algorithm,
//    Applied Statistics,
//    Volume 28, Number 1, 1979, pages 100-108.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the coordinates 
//    of the points.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the cluster centers.
//
//    Input/output, int CLUSTER[POINT_NUM], the cluster 
//    each point belongs to.
//
//    Input/output, int CLUSTER2[POINT_NUM], the cluster to 
//    which each point is most likely to be transferred to.
//
//    Input/output, int CLUSTER_POPULATION[CLUSTER_NUM], 
//    the number of points in each cluster.
//
//    Input/output, double AN1[CLUSTER_NUM], 
//    CLUSTER_POPULATION(L) / (CLUSTER_POPULATION(L) - 1).
//
//    Input/output, double AN2[CLUSTER_NUM], 
//    CLUSTER_POPULATION(L) / (CLUSTER_POPULATION(L) + 1).
//
//    Input/output, int NCP[CLUSTER_NUM], ?
//
//    Input/output, double D[POINT_NUM], ?
//
//    Input/output, int ITRAN[CLUSTER_NUM], 
//    1 if cluster L is updated in the quick-transfer stage,
//    0 otherwise.
//
//    Input/output, int INDX, is set to 0 if any 
//    updating occurs.
//
{
  double al1;
  double al2;
  double alt;
  double alw;
  int count;
  double dd;
  int i;
  int j;
  int l1;
  int l2;
  double r2;
  int step;
//
//  In the optimal transfer stage, NCP(L) indicates the step at which
//  cluster L is last updated.   In the quick transfer stage, NCP(L)
//  is equal to the step at which cluster L is last updated plus POINT_NUM.
//
  count = 0;
  step = 0;

  for ( ; ; )
  {
    for ( j = 0; j < point_num; j++ )
    {
      count = count + 1;
      step = step + 1;
      l1 = cluster[j];
      l2 = cluster2[j];
//
//  If point I is the only member of cluster L1, no transfer.
//
      if ( 1 < cluster_population[l1] )
      {
//
//  If NCP(L1) < STEP, no need to re-compute distance from point I to
//  cluster L1.   Note that if cluster L1 is last updated exactly POINT_NUM
//  steps ago, we still need to compute the distance from point I to
//  cluster L1.
//
        if ( step <= ncp[l1] )
        {
          d[j] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            d[j] = d[j] + pow ( point[i+j*dim_num] - cluster_center[i+l1*dim_num], 2 );
          }
          d[j] = an1[l1] * d[j];
        }
//
//  If STEP >= both NCP(L1) and NCP(L2) there will be no transfer of
//  point I at this step.
//
        if ( step < ncp[l1] || step < ncp[l2] )
        {
          r2 = d[j] / an2[l2];

          dd = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            dd = dd + pow ( point[i+j*dim_num] - cluster_center[i+l2*dim_num], 2 );
          }
//
//  Update cluster centers, NCP, CLUSTER_POPULATION, ITRAN, AN1 and AN2 
//  for clusters L1 and L2.   Also update CLUSTER(J) and CLUSTER2(J).   
//
//  Note that if any updating occurs in this stage, INDX is set back to 0.
//
          if ( dd < r2 )
          {
            count = 0;
            indx = 0;
            itran[l1] = 1;
            itran[l2] = 1;
            ncp[l1] = step + point_num;
            ncp[l2] = step + point_num;
            al1 = cluster_population[l1];
            alw = al1 - 1.0;
            al2 = cluster_population[l2];
            alt = al2 + 1.0;

            for ( i = 0; i < dim_num; i++ )
            {
              cluster_center[i+l1*dim_num] = ( cluster_center[i+l1*dim_num] * al1 
                - point[i+j*dim_num] ) / alw;

              cluster_center[i+l2*dim_num] = ( cluster_center[i+l2*dim_num] * al2 
                + point[i+j*dim_num] ) / alt;
            }

            cluster_population[l1] = cluster_population[l1] - 1;
            cluster_population[l2] = cluster_population[l2] + 1;
            an2[l1] = alw / al1;

            if ( 1.0 < alw )
            {
              an1[l1] = alw / ( alw - 1.0 );
            }
            else
            {
              an1[l1] = r8_huge ( );
            }
            an1[l2] = alt / al2;
            an2[l2] = alt / ( alt + 1.0 );
            cluster[j] = l2;
            cluster2[j] = l1;
          }
        }
      }
//
//  If no re-allocation took place in the last POINT_NUM steps, return.
//
      if ( count == point_num )
      {
        return;
      }
    }
  }
  return;
}
//****************************************************************************80

void kmeans_03 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], int cluster[], double cluster_center[], 
  int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_03 applies the K-Means algorithm.
//
//  Discussion:
//
//    It is possible for a straightforward K-Means algorithm to
//    halt at a non-optimal partition of the points.  This routine
//    tries to improve the input partition if possible.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    10 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Wendy Martinez, Angel Martinez,
//    Computational Statistics Handbook with MATLAB,
//    pages 373-376,
//    Chapman and Hall / CRC, 2002.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of data points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the data points.
//
//    Output, int CLUSTER[POINT_NUM], the cluster to which
//    each point belongs.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], the 
//    centers associated with the clustering.  On output, these may 
//    have been altered.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number
//    of points in each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the energy of 
//    the clusters.
//
{
  int ci;
  int cj;
  bool debug = true;
  double *distsq;
  int i;
  int j;
  int k;
  double point_energy;
  double point_energy_min;
  int swap;
//
//  Check the input.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_03 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_03 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_03 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "KMEANS_03 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }
//
//  Assign each point to the nearest cluster center.
//
  for ( j = 0; j < point_num; j++ )
  {
    point_energy_min = r8_huge ( );
    cluster[j] = -1;

    for ( k = 0; k < cluster_num; k++ )
    {
      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }

      if ( point_energy < point_energy_min )
      {
        point_energy_min = point_energy;
        cluster[j] = k;
      }
    }
  }
//
//  Determine the cluster populations.
//
  i4vec_zero ( cluster_num, cluster_population );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_population[k] = cluster_population[k] + 1;
  }
//
//  Average the points in each cluster to get a new cluster center.
//
  r8vec_zero ( dim_num * cluster_num, cluster_center );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num]
        + point[i+j*dim_num];
    }
  }

  for ( k = 0; k < cluster_num; k++ )
  {
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num]
        / ( double ) ( cluster_population[k] );
    }
  }
//
//  Carry out the iteration.
//
  it_num = 0;
  distsq = new double[cluster_num];

  while ( it_num < it_max )
  {
    it_num = it_num + 1;

    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      ci = cluster[j];

      if ( cluster_population[ci] <= 1 )
      {
        continue;
      }

      for ( cj = 0; cj < cluster_num; cj++ )
      {
        if ( cj == ci )
        {
          distsq[cj] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            distsq[cj] = distsq[cj] 
              + pow ( point[i+j*dim_num] - cluster_center[i+cj*dim_num], 2 );
          }
          distsq[cj] = distsq[cj] * ( double ) ( cluster_population[cj] ) 
            / ( double ) ( cluster_population[cj] - 1 );
        }
        else if ( cluster_population[cj] == 0 )
        {
          for ( i = 0; i < dim_num; i++ )
          {
            cluster_center[i+cj*dim_num] = point[i+j*dim_num];
          }
          distsq[cj] = 0.0;
        }
        else
        {
          distsq[cj] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            distsq[cj] = distsq[cj] 
              + pow ( point[i+j*dim_num] - cluster_center[i+cj*dim_num], 2 );
          }
          distsq[cj] = distsq[cj] * ( double ) ( cluster_population[cj] ) 
            / ( double ) ( cluster_population[cj] + 1 );
        }
      }
//
//  Find the index of the minimum value of DISTSQ.
//
      k = r8vec_min_index ( cluster_num, distsq );
//
//  If that is not the cluster to which point I now belongs, move it there.
//
      if ( k == ci )
      {
        continue;
      }

      cj = k;

      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+ci*dim_num] = ( ( double ) ( cluster_population[ci] ) 
          * cluster_center[i+ci*dim_num] - point[i+j*dim_num] ) 
          / ( double ) ( cluster_population[ci] - 1 );

        cluster_center[i+cj*dim_num] = ( ( double ) ( cluster_population[cj] )
          * cluster_center[i+cj*dim_num] + point[i+j*dim_num] ) 
          / ( double ) ( cluster_population[cj] + 1 );
      }
      cluster_population[ci] = cluster_population[ci] - 1;
      cluster_population[cj] = cluster_population[cj] + 1;

      cluster[j] = cj;
      swap = swap + 1;
    }
//
//  Exit if no reassignments were made during this iteration.
//
    if ( swap == 0 )
    {
      break;
    }
  }
//
//  Compute the cluster energies.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + point_energy;
  }

  delete [] distsq;

  return;
}
//****************************************************************************80

void kmeans_w_01 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], double weight[], int cluster[], 
  double cluster_center[], int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_W_01 applies the weighted K-Means algorithm.
//
//  Discussion:
//
//    The input data for the weight K-Means problem includes:
//    * a set of N data points X in M dimensions, 
//    * a set of N nonnegative weights W,
//    * a desired number of clusters K.
//    * an initial set of cluster centers Z,
//    * an (optional) initial set of cluster assignments.
//
//    The goal is to determine K points Z, called cluster centers, and
//    to assign each point X(I) to some cluster Z(J), so that we minimize
//    the weighted standard deviation of the distance of each data point
//    to the center of its cluster.  Writing J = CLUSTER(I) to
//    indicate the index of the nearest cluster center Z(J) to the 
//    point X(I), the quantity we are trying to minimize is the sum
//    of the weighted cluster energies E(J), where:
//
//      E(J) = Sum ( 1 <= I <= N ) W(I) * || X(I) - Z(J) ||^2
//
//    Here, we assume that we are using the Euclidean norm, so that
//    
//      || X(I) - Z(J) ||^2 = Sum ( 1 <= K <= M )
//         ( X(I)(K) - Z(J)(K) )^2
//
//    In this notation, X(I)(K) is the K-th spatial component of the
//    I-th data point.
//
//    Note that this routine should give the same results as KMEANS_01
//    in any case in which all the entries of the WEIGHT vector are equal.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    10 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    David Sparks,
//    Algorithm AS 58: Euclidean Cluster Analysis,
//    Applied Statistics,
//    Volume 22, Number 1, 1973, pages 126-130.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int &IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the points.
//
//    Input, double WEIGHT[POINT_NUM], the weights.
//
//    Output, int CLUSTER[POINT_NUM], indicates which cluster
//    each point belongs to.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM],
//    the cluster centers.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number 
//    of points in each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the 
//    cluster energies.
//
{
  int c;
  double *cluster_weight;
  double dc;
  double de;
  double *f;
  int i;
  int il;
  int ir;
  int j;
  int k;
  double point_energy;
  double point_energy_min;
  int swap;

  it_num = 0;
//
//  Idiot checks.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_W_01 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_W_01 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_W_01 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "KMEANS_W_01 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }

  if ( r8vec_any_negative ( point_num, weight ) )
  {
    cout << "\n";
    cout << "KMEANS_W_01 - Fatal error!\n";
    cout << "  Some weight entry is negative.\n";
    exit ( 1 );
  }

  if ( r8vec_all_nonpositive ( point_num, weight ) )
  {
    cout << "\n";
    cout << "KMEANS_W_01 - Fatal error!\n";
    cout << "  No weight entry is positive.\n";
    exit ( 1 );
  }
//
//  Assign each point to the nearest cluster.
//
  for ( j = 0; j < point_num; j++ )
  {
    point_energy_min = r8_huge ( );
    cluster[j] = -1;

    for ( k = 0; k < cluster_num; k++ )
    {
      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }

      if ( point_energy < point_energy_min )
      {
        point_energy_min = point_energy;
        cluster[j] = k;
      }
    }
  }
//
//  Determine the cluster populations and weights.
//
  i4vec_zero ( cluster_num, cluster_population );
  cluster_weight = r8vec_zero_new ( cluster_num );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_population[k] = cluster_population[k] + 1;
    cluster_weight[k] = cluster_weight[k] + weight[j];
  }
//
//  Calculate the mean and sum of squares for each cluster.
//
  r8vec_zero ( dim_num * cluster_num, cluster_center );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        + weight[j] * point[i+j*dim_num];
    }
  }

  for ( k = 0; k < cluster_num; k++ )
  {
    if ( 0.0 < cluster_weight[k] )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num]
          / cluster_weight[k];
      }
    }
  }
//
//  Set the point energies.
//
  f = r8vec_zero_new ( point_num );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      f[j] = f[j] + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
  }
//
//  Set the cluster energies.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_energy[k] = cluster_energy[k] + weight[j] * f[j];
  }
//
//  Adjust the point energies by a weight factor.
//
  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    if ( weight[j] < cluster_weight[k] )
    {
      f[j] = f[j] * cluster_weight[k] / ( cluster_weight[k] - weight[j] );
    }
  }
//
//  Examine each observation in turn to see if it should be
//  reassigned to a different cluster.
//
  it_num = 0;

  while ( it_num < it_max )
  {
    it_num = it_num + 1;

    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      il = cluster[j];
      ir = il;

      if ( cluster_population[il] <= 1 )
      {
        continue;
      }

      dc = f[j];

      for ( k = 0; k < cluster_num; k++ )
      {
        if ( k != il )
        {
          de = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            de = de + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 )
              * cluster_weight[k] / ( cluster_weight[k] + weight[j] );
          }

          if ( de < dc )
          {
            dc = de;
            ir = k;
          }
        }
      }
//
//  If the lowest value was obtained by staying in the current cluster,
//  then cycle.
//
      if ( ir == il )
      {
        continue;
      }
//
//  Reassign the point from cluster IL to cluster IR.
//
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+il*dim_num] = 
          ( cluster_weight[il] * cluster_center[i+il*dim_num] 
          - weight[j] * point[i+j*dim_num] ) 
          / ( cluster_weight[il] - weight[j] );

        cluster_center[i+ir*dim_num] = 
          ( cluster_weight[ir] * cluster_center[i+ir*dim_num]
          + weight[j] * point[i+j*dim_num] ) 
          / ( cluster_weight[ir] + weight[j] );
      }
      cluster_weight[il] = cluster_weight[il] - weight[j];
      cluster_weight[ir] = cluster_weight[ir] + weight[j];

      cluster_energy[il] = cluster_energy[il] - f[j];
      cluster_energy[ir] = cluster_energy[ir] + dc;

      cluster_population[ir] = cluster_population[ir] + 1;
      cluster_population[il] = cluster_population[il] - 1;

      cluster[j] = ir;
//
//  Adjust the value of F for all points in clusters IL and IR.
//
      for ( j = 0; j < point_num; j++ )
      {
        k = cluster[j];

        if ( k == il || k == ir )
        {
          f[j] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            f[j] = f[j] + pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
          }
          if ( weight[j] < cluster_weight[k] )
          {
            f[j] = f[j] * cluster_weight[k] / ( cluster_weight[k] - weight[j] );
          }
        }
      }
      swap = swap + 1;
    }
//
//  Exit if no reassignments were made during this iteration.
//
    if ( swap == 0 )
    {
      break;
    }
  }
//
//  Compute the energy based on the final value of the cluster centers.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + weight[j] * point_energy;
  }

  delete [] cluster_weight;
  delete [] f;

  return;
}
//****************************************************************************80

void kmeans_w_03 ( int dim_num, int point_num, int cluster_num, int it_max, 
  int &it_num, double point[], double weight[], int cluster[], 
  double cluster_center[], int cluster_population[], double cluster_energy[] )

//****************************************************************************80
//
//  Purpose:
//
//   KMEANS_W_03 applies the weighted K-Means algorithm.
//
//  Discussion:
//
//    The input data for the weight K-Means problem includes:
//    * a set of N data points X in M dimensions, 
//    * a set of N nonnegative weights W,
//    * a desired number of clusters K.
//    * an initial set of cluster centers Z,
//    * an (optional) initial set of cluster assignments.
//
//    The goal is to determine K points Z, called cluster centers, and
//    to assign each point X(I) to some cluster Z(J), so that we minimize
//    the weighted standard deviation of the distance of each data point
//    to the center of its cluster.  Writing J = CLUSTER(I) to
//    indicate the index of the nearest cluster center Z(J) to the 
//    point X(I), the quantity we are trying to minimize is the sum
//    of the weighted cluster energies E(J), where:
//
//      E(J) = Sum ( 1 <= I <= N ) W(I) * || X(I) - Z(J) ||^2
//
//    Here, we assume that we are using the Euclidean norm, so that
//    
//      || X(I) - Z(J) ||^2 = Sum ( 1 <= K <= M )
//        ( X(I)(K) - Z(J)(K) )^2
//
//    In this notation, X(I)(K) is the K-th spatial component of the
//    I-th data point.
//
//    Note that this routine should give the same results as KMEANS_01
//    in any case in which all the entries of the WEIGHT vector are equal.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    10 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Wendy Martinez, Angel Martinez,
//    Computational Statistics Handbook with MATLAB,
//    pages 373-376,
//    Chapman and Hall / CRC, 2002.
//
//  Parameters:
//
//    Input, int DIM_NUM, the number of spatial dimensions.
//
//    Input, int POINT_NUM, the number of data points.
//
//    Input, int CLUSTER_NUM, the number of clusters.
//
//    Input, int IT_MAX, the maximum number of iterations.
//
//    Output, int IT_NUM, the number of iterations taken.
//
//    Input, double POINT[DIM_NUM*POINT_NUM], the data points.
//
//    Input, double WEIGHT[POINT_NUM], the weights.
//
//    Input/output, int CLUSTER[POINT_NUM], the cluster 
//    to which each point belongs.  On output, these may have been altered.
//
//    Input/output, double CLUSTER_CENTER[DIM_NUM*CLUSTER_NUM], the
//    centers associated with the clustering.  On output, these may
//    have been altered.
//
//    Output, int CLUSTER_POPULATION[CLUSTER_NUM], the number
//    of points in each cluster.
//
//    Output, double CLUSTER_ENERGY[CLUSTER_NUM], the energy of
//    the clusters.
//
{
  int ci;
  int cj;
  double *cluster_weight;
  bool debug = true;
  double *distsq;
  int i;
  int j;
  int k;
  double point_energy;
  double point_energy_min;
  int swap;
//
//  Check the input.
//
  if ( cluster_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_W_03 - Fatal error!\n";
    cout << "  CLUSTER_NUM < 1.\n";
    exit ( 1 );
  }

  if ( dim_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_W_03 - Fatal error!\n";
    cout << "  DIM_NUM < 1.\n";
    exit ( 1 );
  }

  if ( point_num < 1 )
  {
    cout << "\n";
    cout << "KMEANS_W_03 - Fatal error!\n";
    cout << "  POINT_NUM < 1.\n";
    exit ( 1 );
  }

  if ( it_max < 0 )
  {
    cout << "\n";
    cout << "KMEANS_W_03 - Fatal error!\n";
    cout << "  IT_MAX < 0.\n";
    exit ( 1 );
  }

  if ( r8vec_any_negative ( point_num, weight ) )
  {
    cout << "\n";
    cout << "KMEANS_W_03 - Fatal error!\n";
    cout << "  Some weight entry is negative.\n";
    exit ( 1 );
  }

  if ( r8vec_all_nonpositive ( point_num, weight ) )
  {
    cout << "\n";
    cout << "KMEANS_W_03 - Fatal error!\n";
    cout << "  No weight entry is positive.\n";
    exit ( 1 );
  }
//
//  Assign each observation to the nearest cluster center.
//
  for ( j = 0; j < point_num; j++ )
  {
    point_energy_min = r8_huge ( );
    cluster[j] = -1;

    for ( k = 0; k < cluster_num; k++ )
    {
      point_energy = 0.0;
      for ( i = 0; i < dim_num; i++ )
      {
        point_energy = point_energy + 
          pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
      }

      if ( point_energy < point_energy_min )
      {
        point_energy_min = point_energy;
        cluster[j] = k;
      }
    }
  }
//
//  Determine the cluster populations and weights.
//
  i4vec_zero ( cluster_num, cluster_population );
  cluster_weight = r8vec_zero_new ( cluster_num );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    cluster_population[k] = cluster_population[k] + 1;
    cluster_weight[k] = cluster_weight[k] + weight[j];
  }
//
//  Average the points in each cluster to get a new cluster center.
//
  r8vec_zero ( dim_num * cluster_num, cluster_center );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];
    for ( i = 0; i < dim_num; i++ )
    {
      cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] 
        + weight[j] * point[i+j*dim_num];
    }
  }

  for ( k = 0; k < cluster_num; k++ )
  {
    if ( cluster_weight[k] != 0.0 )
    {
      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+k*dim_num] = cluster_center[i+k*dim_num] / 
          cluster_weight[k];
      }
    }
  }
//
//  Carry out the iteration.
//
  it_num = 0;
  distsq = new double[cluster_num];

  while ( it_num < it_max )
  {
    it_num = it_num + 1;

    swap = 0;

    for ( j = 0; j < point_num; j++ )
    {
      ci = cluster[j];

      if ( cluster_population[ci] <= 1 )
      {
        continue;
      }

      for ( cj = 0; cj < cluster_num; cj++ )
      {
        if ( cj == ci )
        {
          distsq[cj] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            distsq[cj] = distsq[cj] 
              + pow ( point[i+j*dim_num] - cluster_center[i+cj*dim_num], 2 );
          }
          distsq[cj] = distsq[cj] * cluster_weight[cj]  
            / ( cluster_weight[cj] - weight[j] );
        }
        else if ( cluster_population[cj] == 0 )
        {
          for ( i = 0; i < dim_num; i++ )
          {
            cluster_center[i+cj*dim_num] = point[i+j*dim_num];
          }
          distsq[cj] = 0.0;
        }
        else
        {
          distsq[cj] = 0.0;
          for ( i = 0; i < dim_num; i++ )
          {
            distsq[cj] = distsq[cj] 
              + pow ( point[i+j*dim_num] - cluster_center[i+cj*dim_num], 2 );
          }
          distsq[cj] = distsq[cj] * cluster_weight[cj] 
            / ( cluster_weight[cj] + weight[j] );
        }
      }
//
//  Find the index of the minimum value of DISTSQ.
//
      k = r8vec_min_index ( cluster_num, distsq );
//
//  If that is not the cluster to which point I now belongs, move it there.
//
      if ( k == ci )
      {
        continue;
      }

      cj = k;

      for ( i = 0; i < dim_num; i++ )
      {
        cluster_center[i+ci*dim_num] = 
          ( cluster_weight[ci] * cluster_center[i+ci*dim_num] 
          - weight[j] * point[i+j*dim_num] ) 
          / ( cluster_weight[ci] - weight[j] );

        cluster_center[i+cj*dim_num] = 
          ( cluster_weight[cj] * cluster_center[i+cj*dim_num]
          + weight[j] * point[i+j*dim_num] ) 
          / ( cluster_weight[cj] + weight[j] );
      }
      cluster_population[ci] = cluster_population[ci] - 1;
      cluster_population[cj] = cluster_population[cj] + 1;

      cluster_weight[ci] = cluster_weight[ci] - weight[j];
      cluster_weight[cj] = cluster_weight[cj] + weight[j];

      cluster[j] = cj;

      swap = swap + 1;
    }
//
//  Exit if no reassignments were made during this iteration.
//
    if ( swap == 0 )
    {
      break;
    }
  }
//
//  Compute the energy based on the final value of the cluster centers.
//
  r8vec_zero ( cluster_num, cluster_energy );

  for ( j = 0; j < point_num; j++ )
  {
    k = cluster[j];

    point_energy = 0.0;
    for ( i = 0; i < dim_num; i++ )
    {
      point_energy = point_energy + 
        pow ( point[i+j*dim_num] - cluster_center[i+k*dim_num], 2 );
    }
    cluster_energy[k] = cluster_energy[k] + weight[j] * point_energy;
  }

  delete [] cluster_weight;
  delete [] distsq;

  return;
}
//****************************************************************************80

int r4_nint ( float x )

//****************************************************************************80
//
//  Purpose:
//
//    R4_NINT returns the nearest integer to an R4.
//
//  Example:
//
//        X         R4_NINT
//
//      1.3         1
//      1.4         1
//      1.5         1 or 2
//      1.6         2
//      0.0         0
//     -0.7        -1
//     -1.1        -1
//     -1.6        -2
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    14 November 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, float X, the value.
//
//    Output, int R4_NINT, the nearest integer to X.
//
{
  int value;

  if ( x < 0.0 )
  {
    value = - ( int ) ( - x + 0.5 );
  }
  else
  {
    value =   ( int ) (  x + 0.5 );
  }
  return value;
}
//****************************************************************************80

double r8_huge ( )

//****************************************************************************80
//
//  Purpose:
//
//    R8_HUGE returns a "huge" R8.
//
//  Discussion:
//
//    The value returned by this function is NOT required to be the
//    maximum representable R8.  This value varies from machine to machine,
//    from compiler to compiler, and may cause problems when being printed.
//    We simply want a "very large" but non-infinite number.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 October 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_HUGE, a "huge" R8 value.
//
{
  double value;

  value = 1.0E+30;

  return value;
}
//****************************************************************************80

double r8_max ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MAX returns the maximum of two R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    18 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MAX, the maximum of X and Y.
//
{
  double value;

  if ( y < x )
  {
    value = x;
  }
  else
  {
    value = y;
  }
  return value;
}
//****************************************************************************80

double r8_min ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MIN returns the minimum of two R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    31 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MIN, the minimum of X and Y.
//
{
  double value;

  if ( y < x )
  {
    value = y;
  }
  else
  {
    value = x;
  }
  return value;
}
//****************************************************************************80

double r8_uniform_01 ( int *seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8_UNIFORM_01 returns a unit pseudorandom R8.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//    If the initial seed is 12345, then the first three computations are
//
//      Input     Output      R8_UNIFORM_01
//      SEED      SEED
//
//         12345   207482415  0.096616
//     207482415  1790989824  0.833995
//    1790989824  2035175616  0.947702
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    11 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Second Edition,
//    Springer, 1987,
//    ISBN: 0387964673,
//    LC: QA76.9.C65.B73.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, December 1986, pages 362-376.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998,
//    ISBN: 0471134031,
//    LC: T57.62.H37.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, Number 2, 1969, pages 136-143.
//
//  Parameters:
//
//    Input/output, int *SEED, the "seed" value.  Normally, this
//    value should not be 0.  On output, SEED has been updated.
//
//    Output, double R8_UNIFORM_01, a new pseudorandom variate,
//    strictly between 0 and 1.
//
{
  int i4_huge = 2147483647;
  int k;
  double r;

  if ( *seed == 0 )
  {
    cerr << "\n";
    cerr << "R8_UNIFORM_01 - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  k = *seed / 127773;

  *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

  if ( *seed < 0 )
  {
    *seed = *seed + i4_huge;
  }
  r = ( double ) ( *seed ) * 4.656612875E-10;

  return r;
}
//****************************************************************************80

double *r8mat_data_read ( string input_filename, int m, int n )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_DATA_READ reads the data from an R8MAT file.
//
//  Discussion:
//
//    An R8MAT is an array of R8's.
//
//    The file is assumed to contain one record per line.
//
//    Records beginning with '#' are comments, and are ignored.
//    Blank lines are also ignored.
//
//    Each line that is not ignored is assumed to contain exactly (or at least)
//    M real numbers, representing the coordinates of a point.
//
//    There are assumed to be exactly (or at least) N such records.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string INPUT_FILENAME, the name of the input file.
//
//    Input, int M, the number of spatial dimensions.
//
//    Input, int N, the number of points.  The program
//    will stop reading data once N values have been read.
//
//    Output, double R8MAT_DATA_READ[M*N], the data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  string line;
  double *table;
  double *x;

  input.open ( input_filename.c_str ( ) );

  if ( !input )
  {
    cerr << "\n";
    cerr << "R8MAT_DATA_READ - Fatal error!\n";
    cerr << "  Could not open the input file: \"" << input_filename << "\"\n";
    exit ( 1 );
  }

  table = new double[m*n];

  x = new double[m];

  j = 0;

  while ( j < n )
  {
    getline ( input, line );

    if ( input.eof ( ) )
    {
      break;
    }

    if ( line[0] == '#' || s_len_trim ( line ) == 0 )
    {
      continue;
    }

    error = s_to_r8vec ( line, m, x );

    if ( error )
    {
      continue;
    }

    for ( i = 0; i < m; i++ )
    {
      table[i+j*m] = x[i];
    }
    j = j + 1;

  }

  input.close ( );

  delete [] x;

  return table;
}
//****************************************************************************80

void r8mat_header_read ( string input_filename, int *m, int *n )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_HEADER_READ reads the header from an R8MAT file.
//
//  Discussion:
//
//    An R8MAT is an array of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string INPUT_FILENAME, the name of the input file.
//
//    Output, int *M, the number of spatial dimensions.
//
//    Output, int *N, the number of points.
//
{
  *m = file_column_count ( input_filename );

  if ( *m <= 0 )
  {
    cerr << "\n";
    cerr << "R8MAT_HEADER_READ - Fatal error!\n";
    cerr << "  FILE_COLUMN_COUNT failed.\n";
    exit ( 1 );
  }

  *n = file_row_count ( input_filename );

  if ( *n <= 0 )
  {
    cerr << "\n";
    cerr << "R8MAT_HEADER_READ - Fatal error!\n";
    cerr << "  FILE_ROW_COUNT failed.\n";
    exit ( 1 );
  }

  return;
}
//****************************************************************************80

double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_MM_NEW multiplies two matrices.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
//    in column-major order.
//
//    For this routine, the result is returned as the function value.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    18 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N1, N2, N3, the order of the matrices.
//
//    Input, double A[N1*N2], double B[N2*N3], the matrices to multiply.
//
//    Output, double R8MAT_MM[N1*N3], the product matrix C = A * B.
//
{
  double *c;
  int i;
  int j;
  int k;

  c = new double[n1*n3];

  for ( i = 0; i < n1; i++ )
  {
    for ( j = 0; j < n3; j++ )
    {
      c[i+j*n1] = 0.0;
      for ( k = 0; k < n2; k++ )
      {
        c[i+j*n1] = c[i+j*n1] + a[i+k*n1] * b[k+j*n2];
      }
    }
  }

  return c;
}
//****************************************************************************80

void r8mat_uniform_01 ( int m, int n, int *seed, double r[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.
//
//  Discussion:
//
//    An R8MAT is an array of R8's.
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Second Edition,
//    Springer, 1987,
//    ISBN: 0387964673,
//    LC: QA76.9.C65.B73.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, December 1986, pages 362-376.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998,
//    ISBN: 0471134031,
//    LC: T57.62.H37.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, Number 2, 1969, pages 136-143.
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input/output, int *SEED, the "seed" value.  Normally, this
//    value should not be 0.  On output, SEED has
//    been updated.
//
//    Output, double R[M*N], a matrix of pseudorandom values.
//
{
  int i;
  int i4_huge = 2147483647;
  int j;
  int k;

  if ( *seed == 0 )
  {
    cerr << "\n";
    cerr << "R8MAT_UNIFORM_01 - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      k = *seed / 127773;

      *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

      if ( *seed < 0 )
      {
        *seed = *seed + i4_huge;
      }

      r[i+j*m] = ( double ) ( *seed ) * 4.656612875E-10;
    }
  }
  return;
}
//****************************************************************************80

double *r8mat_uniform_01_new ( int m, int n, int *seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_UNIFORM_01_NEW returns a unit pseudorandom R8MAT.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8's,  stored as a vector
//    in column-major order.
//
//    This routine implements the recursion
//
//      seed = 16807 * seed mod ( 2^31 - 1 )
//      unif = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, pages 362-376, 1986.
//
//    Philip Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, pages 136-143, 1969.
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input/output, int *SEED, the "seed" value.  Normally, this
//    value should not be 0, otherwise the output value of SEED
//    will still be 0, and R8_UNIFORM will be 0.  On output, SEED has
//    been updated.
//
//    Output, double R8MAT_UNIFORM_01_NEW[M*N], a matrix of pseudorandom values.
//
{
  int i;
  int j;
  int k;
  double *r;

  r = new double[m*n];

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      k = *seed / 127773;

      *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

      if ( *seed < 0 )
      {
        *seed = *seed + 2147483647;
      }
      r[i+j*m] = ( double ) ( *seed ) * 4.656612875E-10;
    }
  }

  return r;
}
//****************************************************************************80

void r8mat_write ( string output_filename, int m, int n, double table[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_WRITE writes an R8MAT file.
//
//  Discussion:
//
//    An R8MAT is an array of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    29 June 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string OUTPUT_FILENAME, the output filename.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, double TABLE[M*N], the data.
//
{
  int i;
  int j;
  ofstream output;
//
//  Open the file.
//
  output.open ( output_filename.c_str ( ) );

  if ( !output )
  {
    cerr << "\n";
    cerr << "R8MAT_WRITE - Fatal error!\n";
    cerr << "  Could not open the output file.\n";
    exit ( 1 );
  }
//
//  Write the data.
//
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << "  " << setw(24) << setprecision(16) << table[i+j*m];
    }
    output << "\n";
  }
//
//  Close the file.
//
  output.close ( );

  return;
}
//****************************************************************************80

bool r8vec_all_nonpositive ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_ALL_NONPOSITIVE: ( all ( A <= 0 ) ) for R8VEC's.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries.
//
//    Input, double A[N], the vector to check.
//
//    Output, bool R8VEC_ALL_NONPOSITIVE is TRUE if all entries
//    of A are less than or equal to zero.
//
{
  int i;
  bool value;

  for ( i = 0; i < n; i++ )
  {
    if ( 0.0 < a[i] )
    {
      value = false;
      return value;
    }
  }
  value = true;

  return value;
}
//****************************************************************************80

bool r8vec_any_negative ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_ANY_NEGATIVE: ( any ( A < 0 ) ) for R8VEC's.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 October 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries.
//
//    Input, double A[N], the vector to check.
//
//    Output, bool R8VEC_ANY_NEGATIVE is TRUE if any entry
//    of A is less than zero.
//
{
  int i;
  bool value;

  for ( i = 0; i < n; i++ )
  {
    if ( a[i] < 0.0 )
    {
      value = true;
      return value;
    }
  }
  value = false;

  return value;
}
//****************************************************************************80

double r8vec_i4vec_dot_product ( int n, double r8vec[], int i4vec[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_I4VEC_DOT_PRODUCT computes the dot product of an R8VEC and an I4VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    30 June 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vectors.
//
//    Input, double R8VEC[N], the first vector.
//
//    Input, int I4VEC[N], the second vector.
//
//    Output, double R8VEC_I4VEC_DOT_PRODUCT, the dot product of the vectors.
//
{
  int i;
  double value;

  value = 0.0;
  for ( i = 0; i < n; i++ )
  {
    value = value + r8vec[i] * ( double ) ( i4vec[i] );
  }
  return value;
}
//****************************************************************************80

int r8vec_min_index ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_MIN_INDEX returns the index of the minimum value in an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    02 August 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input, double A[N], the array.
//
//    Output, int R8VEC_MIN_INDEX, the index of the smallest entry.
//
{
  int i;
  int min_index;

  if ( n <= 0 )
  {
    min_index = -1;
  }
  else
  {
    min_index = 0;

    for ( i = 1; i < n; i++ )
    {
      if ( a[i] < a[min_index] )
      {
        min_index = i;
      }
    }
  }

  return min_index;
}
//****************************************************************************80

double r8vec_sum ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_SUM returns the sum of an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    15 October 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, double A[N], the vector.
//
//    Output, double R8VEC_SUM, the sum of the vector.
//
{
  int i;
  double value;

  value = 0.0;
  for ( i = 0; i < n; i++ )
  {
    value = value + a[i];
  }
  return value;
}
//****************************************************************************80

void r8vec_uniform_01 ( int n, int *seed, double r[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    19 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Second Edition,
//    Springer, 1987,
//    ISBN: 0387964673,
//    LC: QA76.9.C65.B73.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, December 1986, pages 362-376.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998,
//    ISBN: 0471134031,
//    LC: T57.62.H37.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, Number 2, 1969, pages 136-143.
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input/output, int *SEED, a seed for the random number generator.
//
//    Output, double R[N], the vector of pseudorandom values.
//
{
  int i;
  int i4_huge = 2147483647;
  int k;

  if ( *seed == 0 )
  {
    cerr << "\n";
    cerr << "R8VEC_UNIFORM_01 - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  for ( i = 0; i < n; i++ )
  {
    k = *seed / 127773;

    *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

    if ( *seed < 0 )
    {
      *seed = *seed + i4_huge;
    }

    r[i] = ( double ) ( *seed ) * 4.656612875E-10;
  }

  return;
}
//****************************************************************************80

void r8vec_zero ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_ZERO zeroes an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 July 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Output, double A[N], a vector of zeroes.
//
{
  int i;

  for ( i = 0; i < n; i++ )
  {
    a[i] = 0.0;
  }
  return;
}
//****************************************************************************80

double *r8vec_zero_new ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_ZERO_NEW creates and zeroes an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    10 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Output, double R8VEC_ZERO_NEW[N], a vector of zeroes.
//
{
  double *a;
  int i;

  a = new double[n];

  for ( i = 0; i < n; i++ )
  {
    a[i] = 0.0;
  }
  return a;
}
//****************************************************************************80

int s_len_trim ( string s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, a string.
//
//    Output, int S_LEN_TRIM, the length of the string to the last nonblank.
//    If S_LEN_TRIM is 0, then the string is entirely blank.
//
{
  int n;

  n = s.length ( );

  while ( 0 < n )
  {
    if ( s[n-1] != ' ' )
    {
      return n;
    }
    n = n - 1;
  }

  return n;
}
//****************************************************************************80

double s_to_r8 ( string s, int *lchar, bool *error )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8 reads an R8 from a string.
//
//  Discussion:
//
//    This routine will read as many characters as possible until it reaches
//    the end of the string, or encounters a character which cannot be
//    part of the real number.
//
//    Legal input is:
//
//       1 blanks,
//       2 '+' or '-' sign,
//       2.5 spaces
//       3 integer part,
//       4 decimal point,
//       5 fraction part,
//       6 'E' or 'e' or 'D' or 'd', exponent marker,
//       7 exponent sign,
//       8 exponent integer part,
//       9 exponent decimal point,
//      10 exponent fraction part,
//      11 blanks,
//      12 final comma or semicolon.
//
//    with most quantities optional.
//
//  Example:
//
//    S                 R
//
//    '1'               1.0
//    '     1   '       1.0
//    '1A'              1.0
//    '12,34,56'        12.0
//    '  34 7'          34.0
//    '-1E2ABCD'        -100.0
//    '-1X2ABCD'        -1.0
//    ' 2E-1'           0.2
//    '23.45'           23.45
//    '-4.2E+2'         -420.0
//    '17d2'            1700.0
//    '-14e-2'         -0.14
//    'e2'              100.0
//    '-12.73e-9.23'   -12.73 * 10.0**(-9.23)
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, the string containing the
//    data to be read.  Reading will begin at position 1 and
//    terminate at the end of the string, or when no more
//    characters can be read to form a legal real.  Blanks,
//    commas, or other nonnumeric data will, in particular,
//    cause the conversion to halt.
//
//    Output, int *LCHAR, the number of characters read from
//    the string to form the number, including any terminating
//    characters such as a trailing comma or blanks.
//
//    Output, bool *ERROR, is true if an error occurred.
//
//    Output, double S_TO_R8, the real value that was read from the string.
//
{
  char c;
  int ihave;
  int isgn;
  int iterm;
  int jbot;
  int jsgn;
  int jtop;
  int nchar;
  int ndig;
  double r;
  double rbot;
  double rexp;
  double rtop;
  char TAB = 9;

  nchar = s_len_trim ( s );
  *error = false;
  r = 0.0;
  *lchar = -1;
  isgn = 1;
  rtop = 0.0;
  rbot = 1.0;
  jsgn = 1;
  jtop = 0;
  jbot = 1;
  ihave = 1;
  iterm = 0;

  for ( ; ; )
  {
    c = s[*lchar+1];
    *lchar = *lchar + 1;
//
//  Blank or TAB character.
//
    if ( c == ' ' || c == TAB )
    {
      if ( ihave == 2 )
      {
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        iterm = 1;
      }
      else if ( 1 < ihave )
      {
        ihave = 11;
      }
    }
//
//  Comma.
//
    else if ( c == ',' || c == ';' )
    {
      if ( ihave != 1 )
      {
        iterm = 1;
        ihave = 12;
        *lchar = *lchar + 1;
      }
    }
//
//  Minus sign.
//
    else if ( c == '-' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
        isgn = -1;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
        jsgn = -1;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Plus sign.
//
    else if ( c == '+' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Decimal point.
//
    else if ( c == '.' )
    {
      if ( ihave < 4 )
      {
        ihave = 4;
      }
      else if ( 6 <= ihave && ihave <= 8 )
      {
        ihave = 9;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Exponent marker.
//
    else if ( ch_eqi ( c, 'E' ) || ch_eqi ( c, 'D' ) )
    {
      if ( ihave < 6 )
      {
        ihave = 6;
      }
      else
      {
        iterm = 1;
      }
    }
//
//  Digit.
//
    else if ( ihave < 11 && '0' <= c && c <= '9' )
    {
      if ( ihave <= 2 )
      {
        ihave = 3;
      }
      else if ( ihave == 4 )
      {
        ihave = 5;
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        ihave = 8;
      }
      else if ( ihave == 9 )
      {
        ihave = 10;
      }

      ndig = ch_to_digit ( c );

      if ( ihave == 3 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
      }
      else if ( ihave == 5 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
        rbot = 10.0 * rbot;
      }
      else if ( ihave == 8 )
      {
        jtop = 10 * jtop + ndig;
      }
      else if ( ihave == 10 )
      {
        jtop = 10 * jtop + ndig;
        jbot = 10 * jbot;
      }

    }
//
//  Anything else is regarded as a terminator.
//
    else
    {
      iterm = 1;
    }
//
//  If we haven't seen a terminator, and we haven't examined the
//  entire string, go get the next character.
//
    if ( iterm == 1 || nchar <= *lchar + 1 )
    {
      break;
    }

  }
//
//  If we haven't seen a terminator, and we have examined the
//  entire string, then we're done, and LCHAR is equal to NCHAR.
//
  if ( iterm != 1 && (*lchar) + 1 == nchar )
  {
    *lchar = nchar;
  }
//
//  Number seems to have terminated.  Have we got a legal number?
//  Not if we terminated in states 1, 2, 6 or 7!
//
  if ( ihave == 1 || ihave == 2 || ihave == 6 || ihave == 7 )
  {
    *error = true;
    return r;
  }
//
//  Number seems OK.  Form it.
//
  if ( jtop == 0 )
  {
    rexp = 1.0;
  }
  else
  {
    if ( jbot == 1 )
    {
      rexp = pow ( 10.0, jsgn * jtop );
    }
    else
    {
      rexp = jsgn * jtop;
      rexp = rexp / jbot;
      rexp = pow ( 10.0, rexp );
    }

  }

  r = isgn * rexp * rtop / rbot;

  return r;
}
//****************************************************************************80

bool s_to_r8vec ( string s, int n, double rvec[] )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8VEC reads an R8VEC from a string.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, the string to be read.
//
//    Input, int N, the number of values expected.
//
//    Output, double RVEC[N], the values read from the string.
//
//    Output, bool S_TO_R8VEC, is true if an error occurred.
//
{
  int begin;
  bool error;
  int i;
  int lchar;
  int length;

  begin = 0;
  length = s.length ( );
  error = 0;

  for ( i = 0; i < n; i++ )
  {
    rvec[i] = s_to_r8 ( s.substr(begin,length), &lchar, &error );

    if ( error )
    {
      return error;
    }
    begin = begin + lchar;
    length = length - lchar;
  }

  return error;
}
//****************************************************************************80

int s_word_count ( string s )

//****************************************************************************80
//
//  Purpose:
//
//    S_WORD_COUNT counts the number of "words" in a string.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, the string to be examined.
//
//    Output, int S_WORD_COUNT, the number of "words" in the string.
//    Words are presumed to be separated by one or more blanks.
//
{
  bool blank;
  int char_count;
  int i;
  int word_count;

  word_count = 0;
  blank = true;

  char_count = s.length ( );

  for ( i = 0; i < char_count; i++ )
  {
    if ( isspace ( s[i] ) )
    {
      blank = true;
    }
    else if ( blank )
    {
      word_count = word_count + 1;
      blank = false;
    }
  }

  return word_count;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  size_t len;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  len = std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}