p2: fig
This commit is contained in:
@@ -1,160 +1,160 @@
|
||||
#!/usr/bin/env python3
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Richards S-Curve Fit for 2010-2025 Data with K=4298
|
||||
|
||||
Fits Richards model to 2010-2025 launch data with carrying capacity
|
||||
constrained to K=4298 (close to physical limit of 3650).
|
||||
"""
|
||||
|
||||
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)"""
|
||||
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 richards_fixed_K(t, r, t0, v):
|
||||
"""Richards curve with fixed K=4298"""
|
||||
K = 4298
|
||||
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 main():
|
||||
print("=" * 60)
|
||||
print("Richards S-Curve Fit (2010-2025 Data, K=4298)")
|
||||
print("=" * 60)
|
||||
|
||||
# Load data
|
||||
df = load_data()
|
||||
|
||||
# Filter 2010-2025
|
||||
start_year = 2010
|
||||
end_year = 2025
|
||||
data = df[(df["year"] >= start_year) & (df["year"] <= end_year)].copy()
|
||||
years = data["year"].values
|
||||
launches = data["launches"].values
|
||||
|
||||
print(f"Data range: {start_year} - {end_year}")
|
||||
print(f"Data points: {len(data)}")
|
||||
print(f"\nHistorical data:")
|
||||
for y, l in zip(years, launches):
|
||||
print(f" {y}: {l} launches")
|
||||
|
||||
# Fit with fixed K=4298
|
||||
K_fixed = 4298
|
||||
t = (years - start_year).astype(float)
|
||||
|
||||
p0 = [0.2, 20.0, 2.0] # r, t0, v
|
||||
bounds = ([0.01, 5, 0.5], [1.0, 100, 10.0])
|
||||
|
||||
try:
|
||||
popt, pcov = curve_fit(richards_fixed_K, t, launches, p0=p0, bounds=bounds, maxfev=100000)
|
||||
r, t0, v = popt
|
||||
|
||||
# Calculate R²
|
||||
y_pred = richards_fixed_K(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)
|
||||
|
||||
print(f"\nFitted Parameters (K fixed at {K_fixed}):")
|
||||
print(f" K (carrying capacity) = {K_fixed} launches/year (FIXED)")
|
||||
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}")
|
||||
|
||||
except Exception as e:
|
||||
print(f"Fitting error: {e}")
|
||||
return
|
||||
|
||||
# Physical limit
|
||||
physical_max = 3650
|
||||
print(f"\nPhysical limit: {physical_max} (10 sites × 365 days)")
|
||||
print(f"K / Physical limit = {K_fixed/physical_max:.2f}x")
|
||||
|
||||
# ========== Create Visualization ==========
|
||||
# 缩小图片尺寸（比例不变），使字体相对更大
|
||||
fig, ax = plt.subplots(figsize=(8, 4.67))
|
||||
|
||||
# 中低饱和度配色
|
||||
color_data = '#5D6D7E' # 灰蓝色 - 数据点
|
||||
color_curve = '#52796F' # 暗绿色 - S曲线
|
||||
color_target = '#7B9EA8' # 灰蓝绿色 - 2050标记
|
||||
|
||||
# Historical data points
|
||||
ax.scatter(years, launches, color=color_data, s=80, alpha=0.85,
|
||||
label='Historical Data (2010-2025)', zorder=4, edgecolor='white', linewidth=1)
|
||||
|
||||
# Generate smooth S-curve
|
||||
years_smooth = np.linspace(start_year, 2055, 500)
|
||||
t_smooth = years_smooth - start_year
|
||||
pred_smooth = richards(t_smooth, K_fixed, r, t0, v)
|
||||
|
||||
# S-curve prediction
|
||||
ax.plot(years_smooth, pred_smooth, color=color_curve, lw=2.5,
|
||||
label=f'Richards Model (K={K_fixed}, R²={r_squared:.3f})', zorder=2)
|
||||
|
||||
# K=4298 saturation line
|
||||
ax.axhline(K_fixed, color=color_curve, ls=':', lw=1.5, alpha=0.6,
|
||||
label=f'K = {K_fixed}')
|
||||
|
||||
# Mark 2050 line only
|
||||
ax.axvline(2050, color=color_target, ls=':', lw=1.5, alpha=0.7)
|
||||
ax.text(2050.5, K_fixed*0.83, '2050\n(Target)', fontsize=9, color=color_target)
|
||||
|
||||
# Only show 2050 prediction point
|
||||
t_2050 = 2050 - start_year
|
||||
pred_2050 = richards(t_2050, K_fixed, r, t0, v)
|
||||
ax.scatter([2050], [pred_2050], color=color_target, s=60, marker='D', zorder=4)
|
||||
ax.annotate(f'{pred_2050:.0f}', xy=(2050, pred_2050),
|
||||
xytext=(2050.5, pred_2050+180),
|
||||
fontsize=9, color=color_target, fontweight='bold')
|
||||
|
||||
# Formatting
|
||||
ax.set_xlabel('Year', fontsize=11)
|
||||
ax.set_ylabel('Annual Launches', fontsize=11)
|
||||
ax.legend(loc='upper left', fontsize=9)
|
||||
ax.grid(True, alpha=0.25)
|
||||
ax.set_xlim(2010, 2055)
|
||||
ax.set_ylim(0, K_fixed * 1.15)
|
||||
|
||||
plt.tight_layout()
|
||||
plt.savefig('richards_curve_2010_K4298.png', dpi=150, bbox_inches='tight')
|
||||
plt.close()
|
||||
|
||||
print("\nPlot saved: richards_curve_2010_K4298.png")
|
||||
print("=" * 60)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
#!/usr/bin/env python3
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Richards S-Curve Fit for 2010-2025 Data with K=4298
|
||||
|
||||
Fits Richards model to 2010-2025 launch data with carrying capacity
|
||||
constrained to K=4298 (close to physical limit of 3650).
|
||||
"""
|
||||
|
||||
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)"""
|
||||
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 richards_fixed_K(t, r, t0, v):
|
||||
"""Richards curve with fixed K=4298"""
|
||||
K = 4298
|
||||
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 main():
|
||||
print("=" * 60)
|
||||
print("Richards S-Curve Fit (2010-2025 Data, K=4298)")
|
||||
print("=" * 60)
|
||||
|
||||
# Load data
|
||||
df = load_data()
|
||||
|
||||
# Filter 2010-2025
|
||||
start_year = 2010
|
||||
end_year = 2025
|
||||
data = df[(df["year"] >= start_year) & (df["year"] <= end_year)].copy()
|
||||
years = data["year"].values
|
||||
launches = data["launches"].values
|
||||
|
||||
print(f"Data range: {start_year} - {end_year}")
|
||||
print(f"Data points: {len(data)}")
|
||||
print(f"\nHistorical data:")
|
||||
for y, l in zip(years, launches):
|
||||
print(f" {y}: {l} launches")
|
||||
|
||||
# Fit with fixed K=4298
|
||||
K_fixed = 4298
|
||||
t = (years - start_year).astype(float)
|
||||
|
||||
p0 = [0.2, 20.0, 2.0] # r, t0, v
|
||||
bounds = ([0.01, 5, 0.5], [1.0, 100, 10.0])
|
||||
|
||||
try:
|
||||
popt, pcov = curve_fit(richards_fixed_K, t, launches, p0=p0, bounds=bounds, maxfev=100000)
|
||||
r, t0, v = popt
|
||||
|
||||
# Calculate R²
|
||||
y_pred = richards_fixed_K(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)
|
||||
|
||||
print(f"\nFitted Parameters (K fixed at {K_fixed}):")
|
||||
print(f" K (carrying capacity) = {K_fixed} launches/year (FIXED)")
|
||||
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}")
|
||||
|
||||
except Exception as e:
|
||||
print(f"Fitting error: {e}")
|
||||
return
|
||||
|
||||
# Physical limit
|
||||
physical_max = 3650
|
||||
print(f"\nPhysical limit: {physical_max} (10 sites × 365 days)")
|
||||
print(f"K / Physical limit = {K_fixed/physical_max:.2f}x")
|
||||
|
||||
# ========== Create Visualization ==========
|
||||
# 缩小图片尺寸（比例不变），使字体相对更大
|
||||
fig, ax = plt.subplots(figsize=(8, 4.67))
|
||||
|
||||
# 中低饱和度配色
|
||||
color_data = '#5D6D7E' # 灰蓝色 - 数据点
|
||||
color_curve = '#52796F' # 暗绿色 - S曲线
|
||||
color_target = '#7B9EA8' # 灰蓝绿色 - 2050标记
|
||||
|
||||
# Historical data points
|
||||
ax.scatter(years, launches, color=color_data, s=80, alpha=0.85,
|
||||
label='Historical Data (2010-2025)', zorder=4, edgecolor='white', linewidth=1)
|
||||
|
||||
# Generate smooth S-curve
|
||||
years_smooth = np.linspace(start_year, 2055, 500)
|
||||
t_smooth = years_smooth - start_year
|
||||
pred_smooth = richards(t_smooth, K_fixed, r, t0, v)
|
||||
|
||||
# S-curve prediction
|
||||
ax.plot(years_smooth, pred_smooth, color=color_curve, lw=2.5,
|
||||
label=f'Richards Model (K={K_fixed}, R²={r_squared:.3f})', zorder=2)
|
||||
|
||||
# K=4298 saturation line
|
||||
ax.axhline(K_fixed, color=color_curve, ls=':', lw=1.5, alpha=0.6,
|
||||
label=f'K = {K_fixed}')
|
||||
|
||||
# Mark 2050 line only
|
||||
ax.axvline(2050, color=color_target, ls=':', lw=1.5, alpha=0.7)
|
||||
ax.text(2050.5, K_fixed*0.83, '2050\n(Target)', fontsize=9, color=color_target)
|
||||
|
||||
# Only show 2050 prediction point
|
||||
t_2050 = 2050 - start_year
|
||||
pred_2050 = richards(t_2050, K_fixed, r, t0, v)
|
||||
ax.scatter([2050], [pred_2050], color=color_target, s=60, marker='D', zorder=4)
|
||||
ax.annotate(f'{pred_2050:.0f}', xy=(2050, pred_2050),
|
||||
xytext=(2050.5, pred_2050+180),
|
||||
fontsize=9, color=color_target, fontweight='bold')
|
||||
|
||||
# Formatting
|
||||
ax.set_xlabel('Year', fontsize=11)
|
||||
ax.set_ylabel('Annual Launches', fontsize=11)
|
||||
ax.legend(loc='upper left', fontsize=9)
|
||||
ax.grid(True, alpha=0.25)
|
||||
ax.set_xlim(2010, 2055)
|
||||
ax.set_ylim(0, K_fixed * 1.15)
|
||||
|
||||
plt.tight_layout()
|
||||
plt.savefig('richards_curve_2010_K4298.png', dpi=150, bbox_inches='tight')
|
||||
plt.close()
|
||||
|
||||
print("\nPlot saved: richards_curve_2010_K4298.png")
|
||||
print("=" * 60)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user