//+------------------------------------------------------------------+
//|                                                   RegimeMath.mqh |
//|                                                     AnimateDread |
//|                                                                  |
//| THE ONE COPY OF THE REGIME ARITHMETIC. Efficiency ratio, variance |
//| ratio and the three-way label they agree on used to live inside   |
//| CWarriorSignal, reading the stdlib series - which meant nothing   |
//| that was not a signal module (the Mind's price modality, the bar  |
//| cache) could ask "what is the market doing" without a second copy |
//| of the formulas, and two copies eventually disagree.              |
//|                                                                   |
//| Every function takes a NEWEST-FIRST array: x[0] is the bar being  |
//| judged, x[k] is k bars before it - the same orientation as a      |
//| series shift, so CWarriorSignal fills it with Close(shift + k) and |
//| CBarCache::ClosesBack() fills it from its oldest-first storage.   |
//| A caller must supply period + 1 values.                           |
//+------------------------------------------------------------------+
#ifndef WARRIOR_REGIMEMATH_MQH
#define WARRIOR_REGIMEMATH_MQH

class CRegimeMath
  {
public:
   //--- Net distance over path walked. 1 = a straight line, 0 = thrash that ends where it began.
   //--- A flat window (zero path) is "no information" and reads as chop, not as a 0/0 perfect trend.
   static double     Efficiency(const double &x[], const int period)
     {
      if(ArraySize(x) < period + 1)
         return 0.0;
      const double net = MathAbs(x[0] - x[period]);
      double path = 0.0;
      for(int i = 0; i < period; i++)
         path += MathAbs(x[i] - x[i + 1]);
      return (path <= 0.0) ? 0.0 : net / path;
     }
   //--- Var(q-bar) / (q * Var(1-bar)). A random walk gives 1.0; above it moves compound (trend),
   //--- below it they cancel (mean reversion). The q-blocks do not overlap, so they are independent.
   static double     Variance(const double &x[], const int period, const int q)
     {
      if(period < q * 4 || q < 2 || ArraySize(x) < period + 1)
         return 1.0;                    // too few independent blocks to estimate anything
      double m1 = 0.0;
      for(int i = 0; i < period; i++)
         m1 += (x[i] - x[i + 1]);
      m1 /= period;
      double v1 = 0.0;
      for(int i = 0; i < period; i++)
        {
         const double d = (x[i] - x[i + 1]) - m1;
         v1 += d * d;
        }
      v1 /= (period - 1);
      if(v1 <= 0.0)
         return 1.0;
      const int blocks = period / q;
      double mq = 0.0;
      for(int b = 0; b < blocks; b++)
         mq += (x[b * q] - x[(b + 1) * q]);
      mq /= blocks;
      double vq = 0.0;
      for(int b = 0; b < blocks; b++)
        {
         const double d = (x[b * q] - x[(b + 1) * q]) - mq;
         vq += d * d;
        }
      vq /= (blocks - 1);
      return vq / (q * v1);
     }
   //--- 0 = consolidation, 1 = trending, 2 = mean reverting. THREE, NOT MORE: every extra regime
   //--- divides the journal again, and a cell under the sample floor is no estimate at all.
   static int        Code(const double er, const double vr)
     {
      if(er >= 0.35 && vr >= 1.0)
         return 1;                      // efficient AND compounding: a trend
      if(vr <= 0.85 && er <= 0.15)
         return 2;                      // cancelling and inefficient: mean reverting
      return 0;
     }
   //--- The window every caller uses for the label: ER(20) and VR(60, q 5) need 61 values.
   static const int  LabelBars(void) { return 61; }
  };
#endif // WARRIOR_REGIMEMATH_MQH