//
// ペアトレで使用する数学系の関数まとめファイル
//

//+------------------------------------------------------------------+
//|  線形回帰 学習
//+------------------------------------------------------------------+
vector LinearRegression(const vector &x, const vector &y)
{
  vector results = vector::Zeros(2);

//--- サイズが違うときは0を返す
  int size = (int)x.Size();
  if(size != y.Size()) {
    return results;
  }

  double x_mean = x.Mean();
  double y_mean = y.Mean();
  double numerator = 0.0, denominator = 0.0;

//--- 最小二乗法
  for (int i = 0; i < size; i++) {
    numerator += (x[i] - x_mean) * (y[i] - y_mean);
    denominator += (x[i] - x_mean) * (x[i] - x_mean);
  }
  results[0] = numerator / denominator;
  results[1] = y_mean - results[0] * x_mean;

  return results;
}
//+------------------------------------------------------------------+
//| 線形回帰 予測
//+------------------------------------------------------------------+
double LinearRegressionPredict(double x, const vector &results)
{
  return x * results[0] + results[1];
}
//+------------------------------------------------------------------+
//| 線形回帰 残差
//+------------------------------------------------------------------+
double LinearRegressionResidual(double x, double y, const vector &results)
{
  return y - (x * results[0] + results[1]);
}