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344from manim_imports_ext import *
from _2023.clt.main import *
# Dice Simulations
class DiceSimulation(InteractiveScene):
n_dice = 10
n_samples = 3000
distribution = [1 / 6] * 6
die_distribution_config = dict(
axes_config=dict(width=3.5, height=1.5),
y_range=(0, 0.5, 0.25),
)
brick_height = 0.2
initial_brick_color = YELLOW
full_dist_color = GREEN_D
spread = 22
dice_width = 5
def setup(self):
super().setup()
self.add_die_distribution()
self.add_sum_axes()
self.add_sample_label()
self.buckets = dict()
self.all_bricks = VGroup()
def construct(self):
# Slow samples
for _ in range(3):
self.run_one_sum()
# Speedier samples
for _ in range(10):
self.run_one_sum(run_time=0.5, transition_time=0.5)
# First few instant samples
for _ in range(200):
self.run_one_sum(transition_time=1 / 30, still_frame=True)
# Thousands of samples
self.scale_brick_height(0.1)
for _ in range(self.n_samples - int(self.sample_label.count.get_value())):
self.run_one_sum(transition_time=1 / 30, still_frame=True)
self.play(self.all_bricks.animate.set_fill(color=self.full_dist_color))
def add_die_distribution(self, animate=False):
die_dist = get_die_distribution_chart(
self.distribution,
**self.die_distribution_config,
)
die_dist.to_corner(UL)
die_dist.shift(0.25 * DOWN)
axes, bars, dice = die_dist
if animate:
self.play(
Write(axes),
LaggedStartMap(GrowFromEdge, bars, edge=DOWN),
Write(dice),
)
self.add(die_dist)
self.die_dist = die_dist
def add_sum_axes(self):
# (Value, probability) pairs
vps = list(zip(it.count(1), self.distribution))
mu = sum(v * p for v, p in vps)
var = sum(p * (v - mu)**2 for v, p in vps)
n = self.n_dice
x_mid = int(n * mu)
spread = self.spread or int(2.5 * math.sqrt(var * n))
x_range = (x_mid - spread, x_mid + spread, 1)
axes = Axes(
x_range,
(0, int(math.sqrt(self.n_samples))),
width=FRAME_WIDTH - 1,
height=4,
)
# dots = Tex(R"\dots", font_size=24)
# dots.next_to(axes.x_axis, LEFT, SMALL_BUFF)
# axes.y_axis.set_x(dots.get_left()[0] - SMALL_BUFF)
# axes.add(dots)
x_axis = axes.x_axis
x_axis.add_numbers(font_size=16)
x_axis.numbers.remove(x_axis.numbers[-1])
x_axis.numbers.shift(
0.5 * x_axis.get_unit_size() * RIGHT + \
0.1 * UP
)
# axes.center()
# axes.to_edge(DOWN)
x_axis.center()
x_axis.to_edge(DOWN)
self.add(x_axis)
self.sum_axes = axes
self.sum_axis = x_axis
def add_sample_label(self):
label = TexText(R"\# Sums = 0", font_size=36)
label.set_fill(GREY_B)
label.to_edge(LEFT)
label.count = label.make_number_changeable("0")
label.count.edge_to_fix = LEFT
self.add(label)
self.sample_label = label
def run_one_sum(self, run_time=3.0, transition_time=1.0, still_frame=False):
# Setup sample
values = list(range(1, 7))
bars = self.die_dist.bars
samples = np.random.choice(values, size=self.n_dice, p=self.distribution)
dice = VGroup(*(DieFace(sample) for sample in samples))
dice.arrange_in_grid(n_cols=5)
dice.set_width(self.dice_width)
dice.to_corner(UR)
bar_highlights = VGroup(*(
bars[sample - 1].copy()
for sample in samples
))
bar_highlights.set_fill(YELLOW, 1)
face_counts = [0] * len(self.distribution)
for sample in samples:
face_counts[sample - 1] += 1
# Tips
tips = get_sample_markers(bars, samples)
def get_sum():
return sum(d.value for d in dice)
# Sum label
sum_label = TexText(f"Sum = 0")
sum_label.count = sum_label.make_number_changeable(0)
sum_label.next_to(dice, DOWN, buff=MED_LARGE_BUFF)
sum_label.count.set_value(get_sum())
# Mark the sample
brick = self.get_brick()
s = get_sum()
if s not in self.buckets:
self.buckets[s] = VGroup(VectorizedPoint(
self.sum_axis.n2p(s + 0.5)
))
bucket = self.buckets[s]
brick.next_to(bucket, UP, buff=0)
count_copy = sum_label.count.copy()
count_copy.target = bucket[0]
for number in self.sum_axis.numbers:
if number.get_value() == sum_label.count.get_value():
sum_label.count.target = number
break
# Animate!
if still_frame:
self.all_bricks.set_fill(color=self.full_dist_color)
self.sample_label.count.increment_value()
self.add(dice, brick, sum_label, tips)
self.wait(transition_time)
self.remove(dice, sum_label, tips)
else:
self.play(
ShowIncreasingSubsets(dice, int_func=np.ceil),
ShowIncreasingSubsets(tips, int_func=np.ceil),
ShowSubmobjectsOneByOne(bar_highlights, remover=True),
UpdateFromFunc(sum_label, lambda m: m.count.set_value(get_sum())),
self.all_bricks.animate.set_fill(color=self.full_dist_color),
run_time=run_time,
)
self.wait(transition_time)
self.play(
FadeInFromPoint(brick, count_copy.get_center()),
MoveToTarget(count_copy),
FadeOut(sum_label, lag_ratio=0.1),
FadeOut(dice, lag_ratio=0.1),
FadeOut(tips, lag_ratio=0.1),
run_time=transition_time
)
self.sample_label.count.increment_value()
self.wait(transition_time)
self.buckets[s].add(brick)
self.all_bricks.add(brick)
self.add(self.all_bricks)
def scale_brick_height(self, scale_factor):
self.brick_height *= scale_factor
bricks = self.all_bricks
bricks.target = bricks.generate_target()
bricks.target.stretch(scale_factor, 1, about_edge=DOWN)
bricks.target.set_stroke(width=scale_factor * bricks[0].get_stroke_width())
self.play(MoveToTarget(bricks), run_time=3)
self.wait()
def get_brick(self):
return Rectangle(
stroke_width=self.brick_height * 5,
stroke_color=BLACK,
fill_color=self.initial_brick_color,
fill_opacity=1,
height=self.brick_height,
width=0.8 * self.sum_axis.get_unit_size()
)
class DiceSimulationAlt1(DiceSimulation):
random_seed = 1
class DiceSimulationAlt2(DiceSimulation):
random_seed = 2
class DiceSimulationAlt3(DiceSimulation):
random_seed = 3
class DiceSimulationAlt4(DiceSimulation):
random_seed = 4
class DiceSimulationAlt5(DiceSimulation):
random_seed = 5
class LargerDiceSimulation(DiceSimulation):
n_samples = 3000
brick_height = 0.02
random_seed = 1
def construct(self):
# Larger sample
for _ in range(self.n_samples):
self.run_one_sum(transition_time=1 / 30, still_frame=True)
class SimulationWithUShapedDistribution(DiceSimulation):
random_seed = 1
distribution = U_SHAPED_DISTRIBUTION
brick_height = 0.2
n_samples = 3000
def construct(self):
# Transition
tmp_dist = self.distribution
tmp_die_dist = self.die_dist
self.remove(tmp_die_dist)
self.distribution = self.__class__.__base__.distribution
self.add_die_distribution()
self.play(Transform(self.die_dist, tmp_die_dist, run_time=3))
self.distribution = tmp_dist
# First few samples
for _ in range(2):
self.run_one_sum()
for _ in range(6):
self.run_one_sum(run_time=0.5, transition_time=0.5)
for _ in range(300):
self.run_one_sum(transition_time=1 / 30, still_frame=True)
# Thousands of samples
self.scale_brick_height(0.1)
for _ in range(self.n_samples - int(self.sample_label.count.get_value())):
self.run_one_sum(transition_time=1 / 30, still_frame=True)
self.play(self.all_bricks.animate.set_fill(color=self.full_dist_color))
class LargerUSimulation(SimulationWithUShapedDistribution):
n_samples = 10000
brick_height = 0.01
def construct(self):
# Thousands of samples
for _ in range(self.n_samples):
self.run_one_sum(transition_time=1 / 30, still_frame=True)
def get_brick(self):
return super().get_brick().set_stroke(width=0)
class SteeperUDistributionSimulation(SimulationWithUShapedDistribution):
distribution = STEEP_U_SHAPED_DISTRIBUTION
class SimulationWithSteepUShapedDistribution(LargerUSimulation):
distribution = [0.4, 0.075, 0.025, 0.025, 0.075, 0.4]
n_samples = 3000
brick_height = 0.02
class SimulationWithExpDistribution(SimulationWithUShapedDistribution):
random_seed = 1
distribution = EXP_DISTRIBUTION
class SimulationWithExpDistribution2(SimulationWithExpDistribution):
random_seed = 2
class SimulationWithExpDistribution2Dice(SimulationWithExpDistribution):
n_dice = 2
brick_height = 0.13
dice_width = 2
def get_brick(self):
return super().get_brick().set_stroke(width=0)
class SimulationWithRandomDistribution(SimulationWithUShapedDistribution):
random_seed = 1
n_dice = 15
distribution = [0.05, 0.17, 0.28, 0.05, 0.18, 0.27]
class SimulationWithExpDistribution5Dice(SimulationWithExpDistribution):
n_dice = 5
brick_height = 0.15
class SimulationWithExpDistribution15Dice(SimulationWithExpDistribution):
n_dice = 15