"""
Analyze the support structure of our best function and try to modify it.
"""
import numpy as np

f = np.load('/workspace/best_f_10000.npy')
N = len(f)
dx = 0.5 / N

print(f"N = {N}")
print(f"Nonzero entries (>1e-8): {np.sum(f > 1e-8)}")
print(f"Nonzero fraction: {np.mean(f > 1e-8):.4f}")

# Find connected nonzero runs
runs = []
in_run = False
run_start = 0
for i in range(N):
    if f[i] > 1e-8:
        if not in_run:
            run_start = i
            in_run = True
    else:
        if in_run:
            runs.append((run_start, i - 1, i - run_start))
            in_run = False
if in_run:
    runs.append((run_start, N - 1, N - run_start))

print(f"\nNumber of runs: {len(runs)}")
print(f"Run lengths: min={min(r[2] for r in runs)}, max={max(r[2] for r in runs)}, "
      f"mean={np.mean([r[2] for r in runs]):.1f}")

# Show gaps
gaps = []
for i in range(1, len(runs)):
    gap = runs[i][0] - runs[i-1][1] - 1
    gaps.append(gap)

if gaps:
    print(f"\nGaps: min={min(gaps)}, max={max(gaps)}, mean={np.mean(gaps):.1f}")

# Show the run/gap pattern as a binary string
pattern = ''.join(['1' if f[i] > 1e-8 else '0' for i in range(0, N, N//100)])
print(f"\nBinary pattern (100 chars, 1=nonzero): {pattern}")

# Autoconvolution analysis
M = 2 * N
fft_f = np.fft.rfft(f, n=M)
conv = np.fft.irfft(fft_f * fft_f, n=M) * dx
integral_sq = (np.sum(f) * dx) ** 2
c1_profile = conv / integral_sq

max_c1 = np.max(c1_profile)
argmax = np.argmax(c1_profile)

# Show the autoconvolution near the max
print(f"\nAutoconvolution max: {max_c1:.12f}")
print(f"Max position: {argmax} (of {len(c1_profile)})")
print(f"Points within 0.01% of max: {np.sum(c1_profile > max_c1 * 0.9999)}")
print(f"Points within 0.001% of max: {np.sum(c1_profile > max_c1 * 0.99999)}")

# Show the top 20 height values
print(f"\nTop 20 function values:")
top_idx = np.argsort(f)[::-1][:20]
for i, idx in enumerate(top_idx):
    print(f"  f[{idx}] = {f[idx]:.6f}")

# Show overall statistics
print(f"\nFunction stats (nonzero only):")
f_nz = f[f > 1e-8]
print(f"  Min: {f_nz.min():.6f}")
print(f"  Max: {f_nz.max():.6f}")
print(f"  Mean: {f_nz.mean():.6f}")
print(f"  Std: {f_nz.std():.6f}")
print(f"  Median: {np.median(f_nz):.6f}")

# Histogram of nonzero values
hist, edges = np.histogram(f_nz, bins=20)
print(f"\nHistogram of nonzero values:")
for i in range(len(hist)):
    bar = '#' * (hist[i] * 50 // max(hist))
    print(f"  [{edges[i]:.3f}, {edges[i+1]:.3f}]: {hist[i]:5d} {bar}")