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New scenes for beta
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Grant Sanderson
parent
d4790beb24
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2 changed files with 1096 additions and 126 deletions
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@ -1,4 +1,122 @@
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from manimlib.imports import *
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import scipy.stats
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CMARK_TEX = "\\text{\\ding{51}}"
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XMARK_TEX = "\\text{\\ding{55}}"
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class Histogram(Group):
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CONFIG = {
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"height": 5,
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"width": 10,
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"y_max": 1,
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"y_axis_numbers_to_show": range(20, 120, 20),
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"y_axis_label_height": 0.25,
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"y_tick_freq": 0.2,
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"x_label_freq": 1,
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"include_h_lines": True,
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"h_line_style": {
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"stroke_width": 1,
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"stroke_color": LIGHT_GREY,
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# "draw_stroke_behind_fill": True,
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},
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"bar_style": {
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"stroke_width": 1,
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"stroke_color": WHITE,
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"fill_opacity": 1,
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},
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"bar_colors": [BLUE, GREEN]
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}
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def __init__(self, data, **kwargs):
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super().__init__(**kwargs)
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self.data = data
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self.add_axes()
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if self.include_h_lines:
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self.add_h_lines()
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self.add_bars(data)
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self.add_x_axis_labels()
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self.add_y_axis_labels()
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def add_axes(self):
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n_bars = len(self.data)
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axes_config = {
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"x_min": 0,
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"x_max": n_bars,
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"x_axis_config": {
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"unit_size": self.width / n_bars,
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"include_tip": False,
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},
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"y_min": 0,
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"y_max": self.y_max,
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"y_axis_config": {
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"unit_size": self.height / self.y_max,
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"include_tip": False,
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"tick_frequency": self.y_tick_freq,
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},
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}
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axes = Axes(**axes_config)
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axes.center()
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self.axes = axes
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self.add(axes)
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def add_h_lines(self):
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axes = self.axes
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axes.h_lines = VGroup()
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for tick in axes.y_axis.tick_marks:
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line = Line(**self.h_line_style)
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line.match_width(axes.x_axis)
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line.move_to(tick.get_center(), LEFT)
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axes.h_lines.add(line)
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axes.add(axes.h_lines)
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def add_bars(self, data):
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self.bars = self.get_bars(data)
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self.add(self.bars)
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def add_x_axis_labels(self):
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axes = self.axes
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axes.x_labels = VGroup()
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for x, bar in list(enumerate(self.bars))[::self.x_label_freq]:
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label = Integer(x)
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label.set_height(0.25)
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label.next_to(bar, DOWN)
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axes.x_labels.add(label)
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axes.add(axes.x_labels)
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def add_y_axis_labels(self):
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axes = self.axes
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labels = VGroup()
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for value in self.y_axis_numbers_to_show:
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label = Integer(value, unit="\\%")
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fix_percent(label[-1][0])
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label.set_height(self.y_axis_label_height)
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label.next_to(axes.y_axis.n2p(0.01 * value), LEFT)
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labels.add(label)
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axes.y_labels = labels
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axes.y_axis.add(labels)
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# Bar manipulations
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def get_bars(self, data):
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portions = np.array(data).astype(float)
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total = portions.sum()
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if total == 0:
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portions[:] = 0
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else:
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portions /= total
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bars = VGroup()
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for x, prop in enumerate(portions):
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bar = Rectangle()
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bar.set_width(self.width / len(data))
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bar.set_height(self.height * prop / self.y_max, stretch=True)
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bar.move_to(self.axes.c2p(x, 0), DL)
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bars.add(bar)
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bars.set_submobject_colors_by_gradient(*self.bar_colors)
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bars.set_style(**self.bar_style)
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return bars
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# Images of randomness
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@ -16,8 +134,8 @@ def fix_percent(sym):
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sym.lock_triangulation()
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def get_random_process(choices, shuffle_time=2, total_time=4, change_rate=0.05,
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h_buff=0.05, v_buff=0.05):
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def get_random_process(choices, shuffle_time=2, total_time=3, change_rate=0.05,
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h_buff=0.1, v_buff=0.1):
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content = choices[0]
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container = Square()
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@ -31,10 +149,9 @@ def get_random_process(choices, shuffle_time=2, total_time=4, change_rate=0.05,
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def update(container, dt):
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container.time += dt
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time = container.time
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t = container.time
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change = all([
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(time % total_time) < shuffle_time,
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(time - container.last_change_time) > change_rate,
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(t % total_time) < shuffle_time,
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])
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if change:
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mob = container.submobjects[0]
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@ -43,7 +160,7 @@ def get_random_process(choices, shuffle_time=2, total_time=4, change_rate=0.05,
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new_mob.move_to(container, DL)
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new_mob.shift(2 * np.random.random() * h_buff * RIGHT)
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new_mob.shift(2 * np.random.random() * v_buff * UP)
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container.submobjects = [new_mob]
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container.set_submobjects([new_mob])
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container.last_change_time = time
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container.add_updater(update)
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@ -121,7 +238,9 @@ def get_random_card(height=1, **kwargs):
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return get_random_process(cards, **kwargs)
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def get_prob_positive_experience_label():
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def get_prob_positive_experience_label(include_equals=False,
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include_decimal=False,
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include_q_mark=False):
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label = TexMobject(
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"P", "(", "00000", ")",
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)
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@ -133,10 +252,27 @@ def get_prob_positive_experience_label():
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VGroup(label[1], label[3]).match_height(
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pe, stretch=True, about_edge=DOWN,
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)
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if include_equals:
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eq = TexMobject("=").next_to(label, RIGHT)
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label.add(eq)
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if include_decimal:
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decimal = DecimalNumber(0.95)
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decimal.next_to(label, RIGHT)
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decimal.set_color(YELLOW)
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label.decimal = decimal
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label.add(decimal)
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if include_q_mark:
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q_mark = TexMobject("?")
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q_mark.relative_mob = label[-1]
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q_mark.add_updater(
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lambda m: m.next_to(m.relative_mob, RIGHT, SMALL_BUFF)
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)
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label.add(q_mark)
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return label
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def get_beta_dist_axes(y_max=20, y_unit=2, **kwargs):
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def get_beta_dist_axes(y_max=20, y_unit=2, label_y=False, **kwargs):
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config = {
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"x_min": 0,
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"x_max": 1,
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@ -168,6 +304,140 @@ def get_beta_dist_axes(y_max=20, y_unit=2, **kwargs):
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number_config={"num_decimal_places": 1}
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)
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if label_y:
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result.y_axis.add_numbers(
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*range(y_unit, y_max, y_unit)
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)
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label = TextMobject("Probability density")
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label.scale(0.5)
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label.next_to(result.y_axis.get_top(), UR, SMALL_BUFF)
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label.next_to(result.y_axis, UP, SMALL_BUFF)
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label.align_to(result.y_axis.numbers, LEFT)
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result.add(label)
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result.to_corner(DR, LARGE_BUFF)
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return result
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def get_beta_graph(axes, n_plus, n_minus):
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dist = scipy.stats.beta(n_plus + 1, n_minus + 1)
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graph = axes.get_graph(dist.pdf)
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graph.add_line_to(axes.c2p(1, 0))
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graph.add_line_to(axes.c2p(0, 0))
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graph.set_stroke(BLUE, 2)
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graph.set_fill(BLUE_E, 1)
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graph.lock_triangulation()
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return graph
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def get_beta_label(n_plus, n_minus, point=ORIGIN):
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template = TextMobject("beta(", "00", ",", "00", ")")
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template.scale(1.5)
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a_label = Integer(n_plus + 1)
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a_label.set_color(GREEN)
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b_label = Integer(n_minus + 1)
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b_label.set_color(RED)
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for i, label in (1, a_label), (3, b_label):
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label.match_height(template[i])
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label.move_to(template[i], DOWN)
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template.replace_submobject(i, label)
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template.save_state()
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template.arrange(RIGHT, buff=0.15)
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for t1, t2 in zip(template, template.saved_state):
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t1.align_to(t2, DOWN)
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return template
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def get_plusses_and_minuses(n_rows=15, n_cols=20, p=0.95):
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result = VGroup()
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for x in range(n_rows * n_cols):
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if random.random() < p:
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mob = TexMobject(CMARK_TEX)
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mob.set_color(GREEN)
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mob.is_plus = True
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else:
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mob = TexMobject("\\cross")
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mob.set_color(RED)
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mob.is_plus = False
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mob.set_width(1)
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result.add(mob)
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result.arrange_in_grid(n_rows, n_cols)
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result.set_width(5.5)
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return result
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def get_checks_and_crosses(bools, width=12):
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result = VGroup()
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for positive in bools:
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if positive:
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mob = TexMobject(CMARK_TEX)
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mob.set_color(GREEN)
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else:
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mob = TexMobject(XMARK_TEX)
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mob.set_color(RED)
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mob.positive = positive
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mob.set_height(0.5)
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result.add(mob)
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result.arrange(RIGHT, buff=MED_SMALL_BUFF)
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result.set_width(width)
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return result
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def get_random_checks_and_crosses(n=50, s=0.95, width=12):
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return get_checks_and_crosses(
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bools=(np.random.random(n) < s),
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width=width
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)
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def get_random_lt100_row(s, n=10):
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values = np.random.randint(0, 100, n)
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nums = VGroup()
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syms = VGroup()
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for x, value in enumerate(values):
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num = Integer(value)
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num.move_to(x * RIGHT)
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num.positive = (num.get_value() < s * 100)
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if num.positive:
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num.set_color(GREEN)
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sym = TexMobject(CMARK_TEX)
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else:
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num.set_color(RED)
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sym = TexMobject(XMARK_TEX)
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sym.match_color(num)
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sym.match_height(num)
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sym.positive = num.positive
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sym.next_to(num, UP)
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nums.add(num)
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syms.add(sym)
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row = VGroup(nums, syms)
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row.nums = nums
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row.syms = syms
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row.n_positive = sum([m.positive for m in nums])
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row.set_width(10)
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row.center().to_edge(UP)
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return row
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def get_prob_review_label(n_positive, n_negative, s=0.95):
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label = TexMobject(
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"P(",
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f"{n_positive}\\,{CMARK_TEX}", ",\\,",
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f"{n_negative}\\,{XMARK_TEX}",
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"\\,|\\,",
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"s = {:.2f}".format(s),
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")",
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)
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label.set_color_by_tex_to_color_map({
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CMARK_TEX: GREEN,
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XMARK_TEX: RED,
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"0.95": YELLOW,
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})
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return label
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