[WIP] Add robust implementation for computing Ψ_CY with validations

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Original prompt

IMPLEMENTACIÓN MEJORADA (con validaciones):
python
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
import warnings
warnings.filterwarnings('ignore')

def compute_psi_cy_robust(h11, h21):
"""
Calcula Ψ_CY de forma robusta manejando casos especiales.

Ψ_CY = (h11·log(h11) + h21·log(h21))/(h11 + h21) - 1

Args:
    h11, h21: arrays o valores de números de Hodge

Returns:
    array de Ψ_CY valores
"""
h11 = np.asarray(h11, dtype=float)
h21 = np.asarray(h21, dtype=float)

# Manejo de ceros (raro pero posible)
eps = 1e-10
h11_safe = np.where(h11 == 0, eps, h11)
h21_safe = np.where(h21 == 0, eps, h21)

# Calcular Ψ_CY
numerator = h11 * np.log(h11_safe) + h21 * np.log(h21_safe)
denominator = h11 + h21
psi = numerator / denominator - 1

# Verificar consistencia
valid_mask = (denominator > 0) & np.isfinite(psi)
return psi, valid_mask

def comprehensive_psi_analysis(df):
"""
Análisis completo de distribución de Ψ_CY
"""
# Calcular Ψ_CY
psi_values, valid_mask = compute_psi_cy_robust(df['h11'], df['h21'])
df_valid = df[valid_mask].copy()
df_valid['Psi_CY'] = psi_values[valid_mask]
df_valid['N'] = df_valid['h11'] + df_valid['h21']

# Estadísticas básicas
stats_dict = {
    'n_total': len(df),
    'n_valid': len(df_valid),
    'psi_mean': np.mean(df_valid['Psi_CY']),
    'psi_median': np.median(df_valid['Psi_CY']),
    'psi_std': np.std(df_valid['Psi_CY']),
    'psi_min': np.min(df_valid['Psi_CY']),
    'psi_max': np.max(df_valid['Psi_CY']),
    'psi_skewness': stats.skew(df_valid['Psi_CY']),
    'psi_kurtosis': stats.kurtosis(df_valid['Psi_CY'])
}

# Buscar clustering alrededor de 2.5773
tolerance = 0.05  # ±5%
near_257_mask = (df_valid['Psi_CY'] > 2.5773 - tolerance) & (df_valid['Psi_CY'] < 2.5773 + tolerance)
stats_dict['near_257_count'] = near_257_mask.sum()
stats_dict['near_257_percentage'] = near_257_mask.sum() / len(df_valid) * 100

# CY con Ψ_CY más cercano a 2.5773
if len(df_valid) > 0:
    closest_idx = np.argmin(np.abs(df_valid['Psi_CY'] - 2.5773))
    closest_row = df_valid.iloc[closest_idx]
    stats_dict['closest_to_257'] = {
        'h11': int(closest_row['h11']),
        'h21': int(closest_row['h21']),
        'N': int(closest_row['N']),
        'Psi_CY': float(closest_row['Psi_CY']),
        'difference': float(abs(closest_row['Psi_CY'] - 2.5773))
    }

return df_valid, stats_dict

def plot_psi_distribution(df_valid, stats_dict):
"""
Visualización completa de distribución Ψ_CY
"""
fig, axes = plt.subplots(2, 3, figsize=(15, 10))

# 1. Histograma de Ψ_CY
axes[0, 0].hist(df_valid['Psi_CY'], bins=50, density=True, alpha=0.7, color='steelblue', edgecolor='black')
axes[0, 0].axvline(2.5773, color='red', linestyle='--', label='2.5773', linewidth=2)
axes[0, 0].axvline(stats_dict['psi_mean'], color='green', linestyle='-', label=f"Media: {stats_dict['psi_mean']:.3f}")
axes[0, 0].set_xlabel('Ψ_CY')
axes[0, 0].set_ylabel('Densidad')
axes[0, 0].set_title('Distribución de Ψ_CY')
axes[0, 0].legend()
axes[0, 0].grid(True, alpha=0.3)

# 2. Ψ_CY vs N
axes[0, 1].scatter(df_valid['N'], df_valid['Psi_CY'], alpha=0.5, s=10)
axes[0, 1].set_xlabel('N = h¹¹ + h²¹')
axes[0, 1].set_ylabel('Ψ_CY')
axes[0, 1].set_title('Ψ_CY vs Número total de moduli')
axes[0, 1].set_xscale('log')
axes[0, 1].grid(True, alpha=0.3)

# 3. Ψ_CY vs ratio h11/h21
df_valid['ratio'] = df_valid['h11'] / df_valid['h21']
axes[0, 2].scatter(df_valid['ratio'], df_valid['Psi_CY'], alpha=0.5, s=10)
axes[0, 2].axvline(((1+np.sqrt(5))/2)**2, color='orange', linestyle='--', label='φ²')
axes[0, 2].set_xlabel('h¹¹ / h²¹')
axes[0, 2].set_ylabel('Ψ_CY')
axes[0, 2].set_title('Ψ_CY vs Ratio h¹¹/h²¹')
axes[0, 2].set_xscale('log')
axes[0, 2].legend()
axes[0, 2].grid(True, alpha=0.3)

# 4. Boxplot por cuartiles de N
n_quartiles = pd.qcut(df_valid['N'], q=4, duplicates='drop')
box_data = []
labels = []
for quartile in sorted(n_quartiles.unique()):
    mask = (n_quartiles == quartile)
    box_data.append(df_valid.loc[mask, 'Psi_CY'].values)
    labels.append(str(quartile))

axes[1, 0].boxplot(box_data, labels=labels)
axes[1, 0].axhline(2.5773, color='red', linestyle='--', alpha=0.5)
axes[1, 0].set_xticklabels(labels, rotation=45, ha='right')
axes[1, 0].set_ylabel('Ψ_CY')
axes[1, 0].set_title('Ψ_CY por cuartiles de N')
axes[1, 0].grid(True, alpha=0.3)

# 5. Q-Q plot (normalidad)
stats.probplot(df_valid['Psi_CY'], dist="norm", plot=axes[1, 1])
axes[1, 1].set_title('Q-Q Plot: Ψ_CY vs Distribución Normal')
axes[1, 1].grid(True, alpha=0.3)

# 6. ...

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Project	Deployment	Actions	Updated (UTC)
p-np	Ready	Preview, Comment	Feb 5, 2026 8:24pm

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