def ncr(n, r):
# Handle special cases
if (n < r) or (r < 0) or (n < 0):
return 0
if (n == r) or (r == 0):
return 1
# If the parent choices in the parent node is larger than the
# maximum sample count, we don't have to be that exact
vmax = 0x7FFFFFFF
lmax = 9.33
ptotal = vmax if parent is None else parent.total
if ptotal >= vmax:
# Check the lower bound nCr >= (n/r)^r
lmin_val = r * math.log(n / float(r))
if (lmin_val > lmax):
return vmax
# Use the lnncrr function to compute ncr (faster for large r)
if r < 100:
return entropy.ncr(n, r)
res = entropy.lnncrr(n, r)
if res > lmax:
return vmax
return int(round(math.exp(res)))
fig.savefig("out/sketch_info.pdf", format='pdf', bbox_inches='tight')
print("Plotting information per sample...")
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(1, 1, 1)
ax.plot(xs, info / xs, label="Information per sample", lw=0.75, color="k")
ax.plot(xs, n_false_positives_mean, '--', label="False positives per sample", lw=0.75, color="#3465a4")
ax.plot(xs, n_false_positives_min, ':', lw=0.25, color="#3465a4")
ax.plot(xs, n_false_positives_max, ':', lw=0.25, color="#3465a4")
ax.plot([0, n_samples], [n_bits - n_ones, n_bits - n_ones], '--', lw=0.5, color="#3465a4")
ax.annotate(s="\\textit{Maximum false positives}", xy=(n_samples * 0.975, n_bits - n_ones),
verticalalignment="bottom", horizontalalignment="right", fontsize=8.0)
mInfo = entropy.lnncrr(n_bits, n_ones) / math.log(2.0)
ax.plot([0, n_samples], [mInfo, mInfo], '-', lw=0.5, color="k")
ax.annotate(s="\\textit{Maximum information}", xy=(n_samples * 0.975, mInfo),
verticalalignment="bottom", horizontalalignment="right", fontsize=8.0)
ax.set_xlim(1, n_samples)
ax.set_xlabel("Sample count $N$")
ax.set_ylabel("Bits")
ax.legend(loc='lower center', bbox_to_anchor=(0.5, 1.05), ncol=2)
fig.savefig("out/sketch_info_per_sample.pdf", format='pdf', bbox_inches='tight')
print("Plotting errors...")
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(1, 1, 1)
ax.plot(xs, n_false_positives_mean, label="False positives", color="#3465a4")
