def make_ccdf_plot(die, offset=0, sd=None):
if sd is None:
gaussian = Die.gaussian(die)
else:
gaussian = Die.gaussian(die.mean(), sd)
print('KS: %0.2f%%' % (die.ks_stat(gaussian) * 100.0))
print('Above end: %0.2f%%' % ((gaussian > die.max_outcome()) * 100.0))
gaussian_clipped = gaussian.clip(die)
for outcome, die_chance, gaussian_chance in zip(die.outcomes(), die.ccdf(),
gaussian_clipped.ccdf()):
print(
'%d: %0.2f%%, %0.2f%%, %0.3f, %0.3f, %+0.2f%%' %
(outcome, 100.0 * die_chance, 100.0 * gaussian_chance, die_chance /
gaussian_chance, gaussian_chance / die_chance, 100.0 *
(gaussian_chance - die_chance)))
fig = plt.figure(figsize=figsize)
ax = plt.subplot(111)
ax.grid()
ax.plot(die.outcomes() + offset, die.ccdf() * 100.0, marker='.')
ax.plot(gaussian.outcomes() + offset, gaussian.ccdf() * 100.0, marker='.')
ax.set_ylim(bottom=0, top=100)
ax.set_ylabel('Chance (%) of rolling at least')
return ax
def make_pmf_plot(die, offset=0, sd=None):
if sd is None:
gaussian = Die.gaussian(die)
else:
gaussian = Die.gaussian(die.mean(), sd)
print('Var:', die.variance())
print('MAD median:', die.mad_median())
fig = plt.figure(figsize=figsize)
ax = plt.subplot(111)
ax.grid()
print('Gaussian mode:', gaussian.mode())
ax.plot(die.outcomes() + offset, die.pmf() * 100.0, marker='.')
ax.plot(gaussian.outcomes() + offset, gaussian.pmf() * 100.0, marker='.')
ax.set_ylim(bottom=0)
ax.set_ylabel('Chance (%) of rolling exactly')
return ax
def make_mos_plot(die, offset=0, sd=None):
if sd is None:
gaussian = Die.gaussian(die)
else:
gaussian = Die.gaussian(die.mean(), sd)
fig = plt.figure(figsize=figsize)
ax = plt.subplot(111)
ax.grid()
x = numpy.arange(min(0, die.min_outcome()), die.max_outcome() + 1)
y_die = [die.margin_of_success(t).mean() for t in x]
y_gaussian = [gaussian.margin_of_success(t).mean() for t in x]
ax.plot(x + offset, y_die, marker='.')
ax.plot(x + offset, y_gaussian, marker='.')
ax.set_xlim(left=x[0], right=x[-1])
ax.set_ylim(bottom=0)
ax.set_ylabel('Mean margin of success')
return ax
def objective(sd):
gaussian = Die.gaussian(10.5, sd)
return Die.d20.ks_stat(gaussian)
ax.legend(['d20', 'd20 + d6 - 3.5', 'd20 + d12 - 6.5', 'd20 + d20 - 10.5'])
plt.savefig('output/add_small_die_ccdf.png', dpi=dpi, bbox_inches="tight")
# Coin flips.
for coin_count in range(1, 11):
fig = plt.figure(figsize=figsize)
ax = plt.subplot(111)
ax.grid()
x = numpy.linspace(-3, 3, 1001)
y = numpy.exp(-0.5 * numpy.square(x)) / numpy.sqrt(2 * numpy.pi)
ax.plot(x, y, linestyle=':')
coins = Die.d(coin_count, 2)
gaussian = Die.gaussian(coins)
ks = coins.ks_stat(gaussian) * 100.0
print('KS %d: %0.2f%%' % (coin_count, ks))
ax.plot((coins.outcomes() - coins.mean()) / coins.standard_deviation(),
coins.pmf() * coins.standard_deviation(),
marker='.')
ax.set_xlim(-3, 3)
ax.set_xlabel('Deviation from mean in SDs')
ax.set_ylabel('Normalized probability')
ax.set_ylim(0, 0.4)
ax.set_title('%d coin(s): KS = %0.2f%%' % (coin_count, ks))
plt.savefig('output/frames/frame_%03d.png' % (coin_count - 1),
dpi=dpi,
bbox_inches="tight")