Intégration fonctions polynomiales
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Jérôme Delacotte
@@ -506,6 +506,7 @@ class Zeus_8_3_2_B_4_2(IStrategy):
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################### INFORMATIVE 1h
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informative = self.dp.get_pair_dataframe(pair=metadata['pair'], timeframe="1h")
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informative = self.calculateTendency(informative, 3)
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informative = self.apply_regression_derivatives(informative, column='mid', window=50, degree=3)
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informative['volatility'] = talib.STDDEV(informative['close'], timeperiod=14) / informative['close']
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informative['atr'] = (talib.ATR(informative['high'], informative['low'], informative['close'], timeperiod=14)) / informative['close']
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informative['rsi'] = talib.RSI(informative['close'], length=7)
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@@ -514,12 +515,14 @@ class Zeus_8_3_2_B_4_2(IStrategy):
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informative['sma5'] = talib.SMA(informative, timeperiod=5)
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informative['sma5_pct'] = 100 * (informative['sma5'] - informative['sma5'].shift(1)) / informative['sma5']
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dataframe = merge_informative_pair(dataframe, informative, self.timeframe, "1h", ffill=True)
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################### INFORMATIVE 1d
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informative = self.dp.get_pair_dataframe(pair=metadata['pair'], timeframe="1d")
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informative = self.calculateTendency(informative, 3)
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informative = self.apply_regression_derivatives(informative, column='mid', window=50, degree=3)
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informative['rsi'] = talib.RSI(informative['close'], length=7)
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informative['rsi_diff'] = informative['rsi'].diff()
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informative['rsi_diff_2'] = informative['rsi_diff'].diff()
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@@ -546,6 +549,8 @@ class Zeus_8_3_2_B_4_2(IStrategy):
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informative['mid_min_max'] = min_14_days + (max_14_days - min_14_days) / 2
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informative['middle'] = informative['lowest_4'] + (informative['highest_4'] - informative['lowest_4']) / 2
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informative['mid_min_max_0.98'] = informative['mid_min_max'] * 0.98
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dataframe = merge_informative_pair(dataframe, informative, self.timeframe, "1d", ffill=True)
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dataframe['count_buys'] = 0
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@@ -1391,3 +1396,38 @@ class Zeus_8_3_2_B_4_2(IStrategy):
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down_pct_values[i] = 100 * (dataframe['close'].iloc[i] - dataframe['close'].iloc[i - shift_value]) / \
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dataframe['close'].iloc[i - shift_value]
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return down_pct_values
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def apply_regression_derivatives(self, dataframe: DataFrame, column: str = 'close', window: int = 50, degree: int = 3):
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df = dataframe.copy()
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deriv1 = []
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deriv2 = []
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for i in range(len(df)):
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if i < window:
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deriv1.append(np.nan)
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deriv2.append(np.nan)
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continue
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y = df[column].iloc[i - window:i].values
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x = np.arange(window)
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# Régression polynomiale
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coeffs = np.polyfit(x, y, degree)
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poly = np.poly1d(coeffs)
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# Dérivées
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d1 = np.polyder(poly, 1) # première dérivée
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d2 = np.polyder(poly, 2) # seconde dérivée
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# On calcule les valeurs de la dérivée à la dernière bougie
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val_d1 = d1(window - 1)
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val_d2 = d2(window - 1)
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deriv1.append(val_d1)
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deriv2.append(val_d2)
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df['regression_deriv1'] = deriv1
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df['regression_deriv2'] = deriv2
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return df
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109
tools/polynomiale.py
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109
tools/polynomiale.py
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@@ -0,0 +1,109 @@
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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def polynomial_features(series, degree=3, verbose=True):
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x = np.arange(len(series))
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y = series.values
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# Fit du polynôme
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coeffs = np.polyfit(x, y, degree)
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poly = np.poly1d(coeffs)
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if verbose:
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print("⚙️ Coefficients (du plus haut degré au plus bas) :")
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for i, coef in enumerate(coeffs):
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deg = degree - i
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print(f" a{deg} = {coef:.6f}")
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print(f"\n📈 Fonction polynomiale :\n f(x) = {poly}")
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# ✅ Première dérivée(variation ou pente)
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# Positive: la courbe est croissante → tendance haussière.
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# Négative: la courbe est décroissante → tendance baissière.
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# Proche de 0: la courbe est plate → marché stable ou en transition.
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#
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# Applications:
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# Détecter les points d’inflexion(changement de tendance) quand elle s’annule.\
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# Analyser la vitesse d’un mouvement(plus elle est forte, plus le mouvement est impulsif).
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#
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# ✅ Seconde dérivée(accélération ou concavité)
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# Positive: la pente augmente → accélération de la hausse ou ralentissement de la baisse.
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# Négative: la pente diminue → accélération de la baisse ou ralentissement de la hausse.
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# Changement de signe: indique souvent un changement de courbure, utile pour prévoir des retournements.
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#
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# Exemples:
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# 🟢 Dérivée 1 > 0 et dérivée 2 > 0: tendance haussière qui s’accélère.
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# 🟡 Dérivée 1 > 0 et dérivée 2 < 0: tendance haussière qui ralentit → essoufflement potentiel.
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# 🔴 Dérivée 1 < 0 et dérivée 2 < 0: tendance baissière qui s’accélère.
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# 🟠 Dérivée 1 < 0 et dérivée 2 > 0: tendance baissière qui ralentit → possible bottom.
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#
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# Filtrer les signaux: ne prendre un signal haussier que si dérivée1 > 0 et dérivée2 > 0.
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# Détecter les zones de retournement: quand dérivée1 ≈ 0 et que dérivée2 change de signe.
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# Dérivées
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deriv1 = 10 * poly.deriv()
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deriv2 = 100 * deriv1.deriv()
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trend = poly(x)
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slope = deriv1(x)
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accel = deriv2(x)
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return trend, slope, accel, poly
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def polynomial_tail(series, degree=3, window=50, verbose=True):
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if len(series) < window:
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raise ValueError("Not enough data points for the specified window")
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# On garde les N dernières valeurs
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tail = series[-window:]
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x = np.arange(window)
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y = tail.values
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# Fit du polynôme
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coeffs = np.polyfit(x, y, degree)
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poly = np.poly1d(coeffs)
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if verbose:
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print(f"Régression sur les {window} derniers points :")
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print(poly)
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# Évaluation sur la même fenêtre
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trend = poly(x)
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slope = poly.deriv()(x)
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accel = poly.deriv().deriv()(x)
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return trend, slope, accel, poly
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# Exemple avec une série synthétique
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np.random.seed(0)
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x = np.linspace(0, 20, 250)
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y = 0.05 * x**3 - x**2 + 2 * x + 5 + np.random.normal(0, 15, size=len(x))
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series = pd.Series(y)
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trend, slope, accel, poly = polynomial_features(series, degree=3)
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# 🔍 Visualisation
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plt.figure(figsize=(10, 6))
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plt.plot(series, label="Original", alpha=0.5)
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plt.plot(trend, label="Trend (Poly)", linewidth=2)
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plt.plot(slope, label="1st Derivative", linestyle='--')
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plt.plot(accel, label="2nd Derivative", linestyle=':')
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plt.legend()
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plt.title("Régression polynomiale + dérivées")
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plt.grid(True)
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plt.show()
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# trend, slope, accel, poly = polynomial_tail(series, degree=3, window=50)
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#
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# # Visualisation de la portion utile
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# plt.figure(figsize=(10, 5))
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# plt.plot(series[-50:].values, label="Original (Last 50)")
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# plt.plot(trend, label="Trend (Poly)", linewidth=2)
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# plt.plot(slope, label="1st Derivative", linestyle='--')
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# plt.plot(accel, label="2nd Derivative", linestyle=':')
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# plt.title("Régression polynomiale sur les 50 dernières valeurs")
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# plt.legend()
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# plt.grid(True)
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# plt.show()
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42
tools/polynomiale2.py
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42
tools/polynomiale2.py
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@@ -0,0 +1,42 @@
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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def rolling_polyfit_curves(series, degree=3, window=50, step=10):
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curves = [] # Liste des courbes
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positions = [] # Index de départ pour chaque courbe
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for i in range(window, len(series), step):
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y = series[i - window:i].values
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x = np.arange(window)
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coeffs = np.polyfit(x, y, degree)
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poly = np.poly1d(coeffs)
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curve = poly(x)
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curves.append(curve)
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positions.append(i)
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return curves, positions
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# Exemple d'utilisation
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# Exemple avec une série synthétique
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np.random.seed(0)
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x = np.linspace(0, 20, 250)
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y = 0.05 * x**3 - x**2 + 2 * x + 5 + np.random.normal(0, 15, size=len(x))
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series = pd.Series(y)
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# series = pd.Series(np.sin(np.linspace(0, 10*np.pi, 300)) + np.random.normal(0, 0.2, 300))
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curves, positions = rolling_polyfit_curves(series, degree=3, window=50, step=10)
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# Visualisation
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plt.figure(figsize=(12, 6))
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plt.plot(series.values, label="Original")
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for curve, pos in zip(curves, positions):
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x_global = np.arange(pos - 50, pos)
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plt.plot(x_global, curve, alpha=0.6)
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plt.title("Régressions polynomiales glissantes (chaque 10 bougies sur 50 précédentes)")
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plt.legend()
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plt.grid(True)
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plt.show()
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