Optimize EMA indicator with Numba JIT compilation

- Implement Numba-accelerated EMA calculation function
- Replace vectorized implementation with loop-based Numba implementation
- Improve computational efficiency for Exponential Moving Average calculation
- Maintain consistent function interface and return types

Author: saleh-mir

jesse/indicators/ema.py

@@ -1,14 +1,35 @@
 from typing import Union
 
 import numpy as np
+from numba import njit
 
 from jesse.helpers import get_candle_source, slice_candles
 
 
+@njit
+def _ema(source: np.ndarray, period: int) -> np.ndarray:
+    """
+    Compute the Exponential Moving Average using a loop.
+    """
+    n = len(source)
+    result = np.full(n, np.nan)
+    if n < period:
+        return result
+    alpha = 2 / (period + 1)
+    # Initialize EMA with the simple average of the first "period" values
+    initial = np.mean(source[:period])
+    result[period - 1] = initial
+    prev = initial
+    for i in range(period, n):
+        current = alpha * source[i] + (1 - alpha) * prev
+        result[i] = current
+        prev = current
+    return result
+
 def ema(candles: np.ndarray, period: int = 5, source_type: str = "close", sequential: bool = False) -> Union[
     float, np.ndarray]:
     """
-    EMA - Exponential Moving Average
+    EMA - Exponential Moving Average using Numba for optimization
 
     :param candles: np.ndarray
     :param period: int - default: 5
@@ -23,27 +44,5 @@ def ema(candles: np.ndarray, period: int = 5, source_type: str = "close", sequen
         candles = slice_candles(candles, sequential)
         source = get_candle_source(candles, source_type=source_type)
 
-    if len(source) < period:
-        result = np.full_like(source, np.nan, dtype=float)
-    else:
-        alpha = 2 / (period + 1)
-        
-        # Compute EMA using vectorized operations
-        f = period - 1  # the index at which EMA calculation begins
-        initial = np.mean(source[:period])
-        L = len(source) - f  # number of points from the start of EMA calculation
-        if L > 1:
-            # X contains the source values after the initial period
-            X = source[f+1:]
-            # Create a lower-triangular matrix T of shape (L, L-1) where T[m, j] = (1-alpha)**(m-1-j) for j < m, else 0
-            m_idx, j_idx = np.indices((L, L-1))
-            T = np.where(j_idx < m_idx, (1 - alpha)**(m_idx - 1 - j_idx), 0)
-            dot_sums = T.dot(X)
-        else:
-            dot_sums = np.zeros(L)
-        m_vec = np.arange(L)
-        y = (1 - alpha)**m_vec * initial + alpha * dot_sums
-        result = np.full_like(source, np.nan, dtype=float)
-        result[f:] = y
-
+    result = _ema(source, period)
     return result if sequential else result[-1]