2026_mcm_b/p1/richards_curve_1984.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Richards S-Curve Fit for 1984-2025 Data

Fits and visualizes the Richards growth model to rocket launch data
starting from 1984.
"""

import pandas as pd
import numpy as np
from scipy.optimize import curve_fit
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')

plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans']
plt.rcParams['axes.unicode_minus'] = False


def richards(t, K, r, t0, v):
    """
    Richards curve (generalized logistic model)
    
    N(t) = K / (1 + exp(-r*(t - t0)))^(1/v)
    """
    exp_term = np.exp(-r * (t - t0))
    exp_term = np.clip(exp_term, 1e-10, 1e10)
    return K / np.power(1 + exp_term, 1/v)


def load_data(filepath="rocket_launch_counts.csv"):
    """Load rocket launch data"""
    df = pd.read_csv(filepath)
    df = df.rename(columns={"YDate": "year", "Total": "launches"})
    df["year"] = pd.to_numeric(df["year"], errors="coerce")
    df["launches"] = pd.to_numeric(df["launches"], errors="coerce")
    df = df.dropna(subset=["year", "launches"])
    df = df[(df["year"] >= 1957) & (df["year"] <= 2025)]
    df = df.astype({"year": int, "launches": int})
    df = df.sort_values("year").reset_index(drop=True)
    return df


def fit_richards(years, launches, base_year=1984):
    """Fit Richards model to data"""
    t = (years - base_year).astype(float)
    
    # Initial parameters and bounds (unconstrained K)
    p0 = [5000.0, 0.1, 40.0, 2.0]
    bounds = ([500, 0.005, 10, 0.2], [100000, 1.0, 150, 10.0])
    
    popt, pcov = curve_fit(richards, t, launches, p0=p0, bounds=bounds, maxfev=100000)
    perr = np.sqrt(np.diag(pcov))
    
    # Calculate R²
    y_pred = richards(t, *popt)
    ss_res = np.sum((launches - y_pred) ** 2)
    ss_tot = np.sum((launches - np.mean(launches)) ** 2)
    r_squared = 1 - (ss_res / ss_tot)
    
    return popt, perr, r_squared


def main():
    print("=" * 60)
    print("Richards S-Curve Fit (1984-2025)")
    print("=" * 60)
    
    # Load data
    df = load_data()
    
    # Filter 1984-2025
    start_year = 1984
    data = df[(df["year"] >= start_year) & (df["year"] <= 2025)].copy()
    years = data["year"].values
    launches = data["launches"].values
    
    print(f"Data range: {start_year} - 2025")
    print(f"Data points: {len(data)}")
    
    # Fit model
    popt, perr, r_squared = fit_richards(years, launches, base_year=start_year)
    K, r, t0, v = popt
    
    print(f"\nFitted Parameters:")
    print(f"  K (carrying capacity) = {K:.0f} launches/year")
    print(f"  r (growth rate)       = {r:.4f}")
    print(f"  t0 (inflection point) = {start_year + t0:.1f}")
    print(f"  v (shape parameter)   = {v:.3f}")
    print(f"  R²                    = {r_squared:.4f}")
    
    # Physical limit
    physical_max = 3650
    print(f"\nPhysical limit: {physical_max} (10 sites × 365 days)")
    print(f"K / Physical limit = {K/physical_max:.2f}x")
    
    # ========== Create Visualization ==========
    fig, ax = plt.subplots(figsize=(12, 7))
    
    # Historical data points
    ax.scatter(years, launches, color='#2C3E50', s=80, alpha=0.8, 
               label='Historical Data (1984-2025)', zorder=3, edgecolor='white', linewidth=0.5)
    
    # Generate smooth S-curve
    years_smooth = np.linspace(start_year, 2100, 500)
    t_smooth = years_smooth - start_year
    pred_smooth = richards(t_smooth, *popt)
    
    # S-curve prediction
    ax.plot(years_smooth, pred_smooth, color='#27AE60', lw=3, 
            label=f'Richards Model (K={K:.0f}, R²={r_squared:.3f})', zorder=2)
    
    # Confidence band (approximate using parameter errors)
    K_low = max(500, K - 2*perr[0])
    K_high = K + 2*perr[0]
    pred_low = richards(t_smooth, K_low, r, t0, v)
    pred_high = richards(t_smooth, K_high, r, t0, v)
    ax.fill_between(years_smooth, pred_low, pred_high, color='#27AE60', alpha=0.15, 
                    label='95% Confidence Band')
    
    # Physical limit line
    ax.axhline(physical_max, color='#E74C3C', ls='--', lw=2.5, 
               label=f'Physical Limit: {physical_max} (1/site/day)')
    
    # Mark inflection point
    inflection_year = start_year + t0
    inflection_value = K / (v + 1) ** (1/v)
    ax.scatter([inflection_year], [inflection_value], color='#F39C12', s=150, 
               marker='*', zorder=5, label=f'Inflection Point ({inflection_year:.0f})')
    
    # Mark key years
    ax.axvline(2025, color='gray', ls=':', lw=1.5, alpha=0.7)
    ax.axvline(2050, color='#3498DB', ls=':', lw=2, alpha=0.8)
    ax.text(2026, K*0.95, '2025\n(Now)', fontsize=10, color='gray')
    ax.text(2051, K*0.85, '2050\n(Target)', fontsize=10, color='#3498DB')
    
    # Prediction for 2050
    t_2050 = 2050 - start_year
    pred_2050 = richards(t_2050, *popt)
    ax.scatter([2050], [pred_2050], color='#3498DB', s=100, marker='D', zorder=4)
    ax.annotate(f'{pred_2050:.0f}', xy=(2050, pred_2050), xytext=(2055, pred_2050-300),
                fontsize=10, color='#3498DB', fontweight='bold')
    
    # Formatting
    ax.set_xlabel('Year', fontsize=12)
    ax.set_ylabel('Annual Launches', fontsize=12)
    ax.set_title('Richards S-Curve Model Fit (1984-2025 Data)\nRocket Launch Capacity Projection', 
                fontsize=14, fontweight='bold')
    ax.legend(loc='upper left', fontsize=10)
    ax.grid(True, alpha=0.3)
    ax.set_xlim(1982, 2100)
    ax.set_ylim(0, K * 1.15)
    
    # Add text box with model info
    textstr = f'''Model: N(t) = K / (1 + e^(-r(t-t₀)))^(1/v)
    
Data Window: {start_year}-2025 ({len(data)} points)
K = {K:.0f} launches/year
r = {r:.4f}
t₀ = {start_year + t0:.1f}
v = {v:.3f}
R² = {r_squared:.4f}

Note: Physical limit (3,650) shown as
dashed red line'''
    
    props = dict(boxstyle='round', facecolor='wheat', alpha=0.8)
    ax.text(0.98, 0.35, textstr, transform=ax.transAxes, fontsize=9,
            verticalalignment='top', horizontalalignment='right', bbox=props, family='monospace')
    
    plt.tight_layout()
    plt.savefig('richards_curve_1984.png', dpi=150, bbox_inches='tight')
    plt.close()
    
    print("\nPlot saved: richards_curve_1984.png")
    print("=" * 60)


if __name__ == "__main__":
    main()