PROBLEM SymbReg

CODE <<
  double[,] x;
  double[] y;
  int[] variables;
  int[] rows;

  double RSquared(IEnumerable<double> xs, IEnumerable<double> ys) {
    // calculate Pearson's correlation in one pass over xs and ys
    double sumx = 0.0;
    double sumy = 0.0;
    double sumxSq = 0.0;
    double sumySq = 0.0;
    double sumxy = 0.0;
    int n = 0;
    var xEnum = xs.GetEnumerator();
    var yEnum = ys.GetEnumerator();
    while(xEnum.MoveNext() & yEnum.MoveNext()) {
      sumx += xEnum.Current;
      sumy += yEnum.Current;
      sumxSq += xEnum.Current * xEnum.Current;
      sumySq += yEnum.Current * yEnum.Current;
      sumxy += xEnum.Current * yEnum.Current;
      n++;
    }
    System.Diagnostics.Debug.Assert(!(xEnum.MoveNext() | yEnum.MoveNext()));

    double num;
    double den;
    double r = 0.0;
    num = sumxy - ( ( sumx * sumy ) / n );
    den = Math.Sqrt( ( sumxSq - ( sumx * sumx ) / n ) *
                     ( sumySq - ( sumy * sumy ) / n ) );
    if(den > 0){
      r = num / den;
    }
    return r*r;
  } 
>>

INIT <<
  // generate 500 cases of poly-10 benchmark function
  int n = 500;
  variables = new int[] {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
  var rand = new System.Random();
  x = new double[n, 10];
  y = new double[n];
  for(int row = 0; row < n; row++) {
    for(int col = 0; col < 10; col++) {
      x[row, col] = rand.NextDouble() * 2.0 - 1.0;
    }
    y[row] = x[row, 0] * x[row, 1] +
             x[row, 2] * x[row, 3] +
             x[row, 4] * x[row, 5] +
             x[row, 0] * x[row, 6] + x[row, 8] +
             x[row, 2] * x[row, 5] + x[row, 9];
  }

  rows = System.Linq.Enumerable.Range(0, n).ToArray();
>>

NONTERMINALS
  Model<<int row, out double val>>.
  RPB<<int row, out double val>>.
  Addition<<int row, out double val>>.
  Subtraction<<int row, out double val>>.
  Multiplication<<int row, out double val>>.
  Division<<int row, out double val>>.

TERMINALS
  Const<<out double val>> 
    CONSTRAINTS
      val IN RANGE <<-10.0>> .. <<10.0>>
  .
  Var<<out int variable, out double weight>>  
    CONSTRAINTS
      variable IN SET <<variables>>
      weight IN RANGE <<-10.0>> .. <<10.0>>
  .

RULES
  Model<<int row, out double val>> =                       
    RPB<<row, out val>> .
    
  RPB<<int row, out double val>> =                         LOCAL << int variable; double w; >> 
    Addition<<row, out val>>
    | Subtraction<<row, out val>>
    | Division<<row, out val>>
    | Multiplication<<row, out val>>                       
    | Var<<out variable, out w>>                            SEM << val = w * x[row, variable]; >>
    | Const<<out val>>
  .

  Addition<<int row, out double val>> =                    LOCAL << double x1, x2; >>
    RPB<<row, out x1>> RPB<<row, out x2>>                  SEM << val = x1 + x2; >>
  .
  Subtraction<<int row, out double val>> =                 LOCAL << double x1, x2; >>
    RPB<<row, out x1>> RPB<<row, out x2>>                  SEM << val = x1 - x2; >>
  .
  Division<<int row, out double val>> =                    LOCAL << double x1, x2; >>
    RPB<<row, out x1>> RPB<<row, out x2>>                  SEM << val = x1 / x2; >>
  .
  Multiplication<<int row, out double val>> =              LOCAL << double x1, x2; >>
    RPB<<row, out x1>> RPB<<row, out x2>>                  SEM << val = x1 * x2; >>
  .

MAXIMIZE
  << 
    var predicted = rows.Select(r => {
      double result;
      Model(r, out result);                                /* we can call the root symbol directly */
      return result;
    });
    return RSquared(predicted, y);
  >>
END SymbReg.