"""Poissonized displayed-library occupancy, Python 3.14 + NumPy/Matplotlib.

Run in mirrored _media; write a white PNG to the current directory.
The complete-coverage curve assumes independent Poisson counts, not a fixed
number of usable molecules. No experimental data are plotted.
"""
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

variants = 1000
mean_count = np.linspace(0.0, 14.0, 1001)
represented = -np.expm1(-mean_count)
complete = represented**variants
fig, ax = plt.subplots(figsize=(9.6, 4.2), dpi=100, facecolor='white')
ax.set_facecolor('white')
ax.plot(mean_count, represented, lw=2.5, color='#1261a0',
        label='Expected represented fraction')
ax.plot(mean_count, complete, lw=2.5, color='#d46216',
        label='Probability all 1000 variants are present')
ax.axvline(3.0, lw=1, color='#777777', linestyle='--')
ax.annotate('Mean coverage ≈95%\nComplete coverage ≈0',
            (3.0, -np.expm1(-3.0)), xytext=(4.1, 0.64),
            arrowprops={'arrowstyle': '->', 'color': '#555555'}, fontsize=10)
ax.set(xlim=(0, 14), ylim=(0, 1.04), xlabel='Mean usable molecules per variant, λ',
       ylabel='Expected fraction / probability',
       title='Library coverage: representing most variants is easier than representing all')
ax.grid(alpha=0.2)
ax.legend(loc='lower right', frameon=False)
fig.text(0.5, 0.02, 'Original model: 1000 equally represented variants; independent Poisson counts. No measured data.',
         ha='center', fontsize=9)
fig.tight_layout(rect=(0, 0.04, 1, 1))
fig.savefig('display-library-mean-versus-complete-coverage.png', dpi=100, facecolor='white')
plt.close(fig)