File size: 2,513 Bytes
2facf1f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | import numpy as np
from scipy.optimize import minimize, differential_evolution
def compute_c1(f_values, n_points):
dx = 0.5 / n_points
f_nn = np.maximum(f_values, 0.0)
autoconv = np.convolve(f_nn, f_nn, mode='full') * dx
integral_sq = (np.sum(f_nn) * dx) ** 2
if integral_sq < 1e-12:
return 1e10
return np.max(autoconv) / integral_sq
def heights_to_function(heights, n_eval):
"""Convert step heights to fine-grained function values"""
n_steps = len(heights)
f = np.zeros(n_eval)
step_width = n_eval / n_steps
for i in range(n_steps):
start = int(i * step_width)
end = int((i + 1) * step_width)
end = min(end, n_eval)
f[start:end] = max(heights[i], 0.0)
return f
def optimize_step_function(n_steps, n_eval, seed=42):
dx = 0.5 / n_eval
def objective(heights):
f = heights_to_function(np.maximum(heights, 0.0), n_eval)
return compute_c1(f, n_eval)
# Differential evolution
bounds = [(0.01, 5.0)] * n_steps
result = differential_evolution(
objective, bounds, seed=seed,
maxiter=2000, tol=1e-12, polish=True,
popsize=40, mutation=(0.5, 1.5), recombination=0.9,
workers=1,
)
heights = np.maximum(result.x, 0.0)
f = heights_to_function(heights, n_eval)
c1 = compute_c1(f, n_eval)
# Polish with Nelder-Mead
result2 = minimize(objective, heights, method='Nelder-Mead',
options={'maxiter': 50000, 'xatol': 1e-12, 'fatol': 1e-12})
heights2 = np.maximum(result2.x, 0.0)
f2 = heights_to_function(heights2, n_eval)
c1_2 = compute_c1(f2, n_eval)
if c1_2 < c1:
return f2, c1_2, heights2
return f, c1, heights
def run():
best_c1 = float('inf')
best_f = None
best_n = None
n_eval = 4000
configs = [
(10, 42), (15, 42), (20, 42), (25, 42), (30, 42),
(40, 42), (50, 42), (60, 42),
(20, 0), (30, 0), (40, 0), (50, 0),
(20, 7), (30, 7), (40, 7),
]
for n_steps, seed in configs:
print(f"n_steps={n_steps}, seed={seed}...", end=" ", flush=True)
f, c1, heights = optimize_step_function(n_steps, n_eval, seed)
print(f"C1={c1:.10f}")
if c1 < best_c1:
best_c1 = c1
best_f = f
best_n = n_eval
print(f" *** NEW BEST: C1={c1:.10f}, heights={np.round(heights, 4)}")
print(f"\nFinal best C1: {best_c1:.10f}")
return best_f, best_c1, best_c1, best_n
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