Just starting Bayes video for eop

This commit is contained in:
Grant Sanderson
2017-06-05 21:35:09 -07:00
parent 1e8002bde3
commit 28c664ceb6
6 changed files with 729 additions and 19 deletions

0
eop/__init__.py Normal file
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369
eop/bayes.py Normal file
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@ -0,0 +1,369 @@
from helpers import *
from mobject.tex_mobject import TexMobject
from mobject import Mobject
from mobject.image_mobject import ImageMobject
from mobject.vectorized_mobject import *
from animation.animation import Animation
from animation.transform import *
from animation.simple_animations import *
from animation.playground import *
from topics.geometry import *
from topics.characters import *
from topics.functions import *
from topics.fractals import *
from topics.number_line import *
from topics.combinatorics import *
from topics.numerals import *
from topics.three_dimensions import *
from topics.objects import *
from topics.complex_numbers import *
from topics.common_scenes import *
from topics.probability import *
from scene import Scene
from scene.reconfigurable_scene import ReconfigurableScene
from scene.zoomed_scene import *
from camera import Camera
from mobject.svg_mobject import *
from mobject.tex_mobject import *
#revert_to_original_skipping_status
#########
class BayesOpeningQuote(OpeningQuote):
CONFIG = {
"quote" : [
"Inside every non-Bayesian there \\\\ is a Bayesian struggling to get out."
],
"author" : "Dennis V. Lindley",
}
class IntroducePokerHand(PiCreatureScene):
CONFIG = {
"community_cards_center" : 1.5*DOWN,
"community_card_values" : ["AS", "QH", "10H", "2C", "5H"],
"your_hand_values" : ["JS", "KC"],
}
def construct(self):
self.force_skipping()
self.add_cards()
# self.indicate_straight()
self.show_flush_potential()
self.compute_flush_probability()
self.show_flush_sample_space()
self.place_high_bet()
def add_cards(self):
you, her = self.you, self.her
community_cards = VGroup(*map(
PlayingCard, self.community_card_values
))
community_cards.arrange_submobjects(RIGHT)
community_cards.move_to(self.community_cards_center)
deck = VGroup(*[
PlayingCard(turned_over = True)
for x in range(5)
])
for i, card in enumerate(deck):
card.shift(i*(0.03*RIGHT + 0.015*DOWN))
deck.next_to(community_cards, LEFT)
you.hand = self.get_hand(you, self.your_hand_values)
her.hand = self.get_hand(her, None)
hand_cards = VGroup(*it.chain(*zip(you.hand, her.hand)))
self.add(deck)
for group in hand_cards, community_cards:
for card in group:
card.generate_target()
card.scale(0.01)
card.move_to(deck[-1], UP+RIGHT)
self.play(LaggedStart(MoveToTarget, group, lag_ratio = 0.8))
self.dither()
self.dither()
self.community_cards = community_cards
def indicate_straight(self):
you = self.you
community_cards = self.community_cards
you.hand.save_state()
you.hand.generate_target()
for card in you.hand.target:
card.scale_to_fit_height(community_cards.get_height())
selected_community_cards = VGroup(*filter(
lambda card : card.numerical_value >= 10,
community_cards
))
card_cmp = lambda c1, c2 : cmp(
c1.numerical_value, c2.numerical_value
)
selected_community_cards.submobjects.sort(card_cmp)
selected_community_cards.save_state()
for card in selected_community_cards:
card.generate_target()
straight_cards = VGroup(*it.chain(
you.hand.target,
[c.target for c in selected_community_cards]
))
straight_cards.submobjects.sort(card_cmp)
straight_cards.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
straight_cards.next_to(community_cards, UP, aligned_edge = LEFT)
self.play(LaggedStart(
MoveToTarget,
selected_community_cards,
run_time = 1.5
))
self.play(MoveToTarget(you.hand))
self.play(you.change, "hooray", straight_cards)
self.play(LaggedStart(
ApplyMethod,
straight_cards,
lambda m : (m.highlight, YELLOW),
rate_func = there_and_back,
run_time = 1.5,
lag_ratio = 0.5,
remover = True,
))
self.dither(2)
self.play(
selected_community_cards.restore,
you.hand.restore,
you.change_mode, "happy"
)
def show_flush_potential(self):
you, her = self.you, self.her
heart_cards = VGroup(*filter(
lambda c : c.suit == "hearts",
self.community_cards
))
heart_cards.save_state()
her.hand.save_state()
her.hand.generate_target()
her.hand.target.arrange_submobjects(RIGHT)
her.hand.target.next_to(heart_cards, UP)
her.hand.target.to_edge(UP)
heart_qs = VGroup()
hearts = VGroup()
q_marks = VGroup()
for target in her.hand.target:
heart = SuitSymbol("hearts")
q_mark = TexMobject("?")
heart_q = VGroup(heart, q_mark)
for mob in heart_q:
mob.scale_to_fit_height(0.5)
heart_q.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
heart_q.move_to(target)
heart_qs.add(heart, q_mark)
hearts.add(heart)
q_marks.add(q_mark)
self.play(heart_cards.shift, heart_cards.get_height()*UP)
self.play(you.change_mode, "hesitant")
self.play(MoveToTarget(her.hand))
self.play(LaggedStart(DrawBorderThenFill, heart_qs))
self.play(
her.change, "happy",
DrawBorderThenFill(her.glasses)
)
self.pi_creatures.remove(her)
new_suit_pairs = [
("clubs", "diamonds"),
("diamonds", "spades"),
("spades", "clubs"),
("hearts", "hearts"),
]
for new_suit_pair in new_suit_pairs:
new_symbols = VGroup(*map(SuitSymbol, new_suit_pair))
for new_symbol, heart in zip(new_symbols, hearts):
new_symbol.replace(heart, dim_to_match = 1)
self.play(Transform(
hearts, new_symbols,
submobject_mode = "lagged_start"
))
self.dither()
self.play(FadeOut(heart_qs))
self.play(
heart_cards.restore,
her.hand.restore,
you.change_mode, "pondering",
)
self.q_marks = q_marks
def compute_flush_probability(self):
you, her = self.you, self.her
equation = TexMobject(
"{ {10 \\choose 2}", "\\over", "{45 \\choose 2} }",
"=", "{1 \\over 22}", "\\approx", "4.5\\%"
)
equation.next_to(self.community_cards, UP, buff = LARGE_BUFF)
percentage = equation.get_part_by_tex("4.5")
ten = VGroup(*equation[0][1:3])
num_hearts = TextMobject("\\# Remaining hearts")
num_hearts.scale(0.75)
num_hearts.next_to(
ten, UP, aligned_edge = LEFT
)
num_hearts.to_edge(UP)
num_hearts.highlight(RED)
num_hearts_arrow = Arrow(
num_hearts.get_bottom(), ten.get_right(),
color = RED, buff = SMALL_BUFF
)
fourty_five = VGroup(*equation[2][1:3])
num_cards = TextMobject("\\# Remaining cards")
num_cards.scale(0.75)
num_cards.next_to(fourty_five, LEFT)
num_cards.to_edge(LEFT)
num_cards.highlight(BLUE)
num_cards_arrow = Arrow(
num_cards, fourty_five,
color = BLUE, buff = SMALL_BUFF
)
self.revert_to_original_skipping_status()
self.play(LaggedStart(FadeIn, equation))
self.dither(2)
self.play(
FadeIn(num_hearts),
ShowCreation(num_hearts_arrow),
ten.highlight, RED,
)
self.play(
FadeIn(num_cards),
ShowCreation(num_cards_arrow),
fourty_five.highlight, BLUE
)
self.dither(3)
equation.remove(percentage)
self.play(*map(FadeOut, [
equation,
num_hearts, num_hearts_arrow,
num_cards, num_cards_arrow,
]))
self.percentage = percentage
def show_flush_sample_space(self):
you, her = self.you, self.her
percentage = self.percentage
sample_space = SampleSpace()
sample_space.add_title()
sample_space.move_to(VGroup(you.hand, her.hand))
sample_space.to_edge(UP, buff = MED_SMALL_BUFF)
sample_space.shift(RIGHT)
p = 1./22
top_part, bottom_part = sample_space.divide_horizontally(
p, colors = [SuitSymbol.CONFIG["red"], BLUE_E]
)
self.revert_to_original_skipping_status()
self.play(FadeIn(sample_space))
self.dither()
self.add(top_part, bottom_part)
def place_high_bet(self):
pass
######
def create_pi_creatures(self):
shift_val = 3
you = PiCreature(color = BLUE_D)
her = PiCreature(color = BLUE_B).flip()
for pi in you, her:
pi.scale(0.5)
you.to_corner(UP+LEFT)
her.to_corner(UP+RIGHT)
you.make_eye_contact(her)
glasses = SVGMobject(file_name = "sunglasses")
glasses.set_stroke(WHITE, width = 0)
glasses.set_fill(GREY, 1)
glasses.scale_to_fit_width(
1.1*her.eyes.get_width()
)
glasses.move_to(her.eyes, UP)
her.glasses = glasses
self.you = you
self.her = her
return VGroup(you, her)
def get_hand(self, pi_creature, keys = None):
if keys is not None:
hand = VGroup(*map(PlayingCard, keys))
else:
hand = VGroup(*[
PlayingCard(turned_over = True)
for x in range(2)
])
hand.scale(0.7)
card1, card2 = hand
vect = np.sign(pi_creature.get_center()[0])*LEFT
card2.move_to(card1)
card2.shift(MED_SMALL_BUFF*RIGHT + SMALL_BUFF*DOWN)
hand.next_to(
pi_creature, vect,
buff = MED_LARGE_BUFF,
aligned_edge = UP
)
return hand
class HowDoesPokerWork(TeacherStudentsScene):
def construct(self):
self.student_says(
"Wait, how does \\\\ poker work again?",
target_mode = "confused",
run_time = 1
)
self.change_student_modes(*["confused"]*3)
self.dither(2)
class ShowCountingArgument(IntroducePokerHand):
def construct(self):
pass

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@ -186,8 +186,8 @@ def main():
try:
handle_scene(SceneClass(**scene_kwargs), **config)
play_finish_sound()
except RuntimeError:
play_finish_sound()
# except RuntimeError as e:
# play_finish_sound()
except:
print "\n\n"
traceback.print_exc()

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@ -20,6 +20,7 @@ class SVGMobject(VMobject):
"should_center" : True,
#Must be filled in in a subclass, or when called
"file_name" : None,
"propogate_style_to_family" : True,
}
def __init__(self, **kwargs):
digest_config(self, kwargs, locals())

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@ -1,7 +1,7 @@
from helpers import *
from mobject import Mobject
from mobject.vectorized_mobject import VGroup, VMobject
from mobject.vectorized_mobject import VGroup, VMobject, VectorizedPoint
from mobject.svg_mobject import SVGMobject
from mobject.tex_mobject import TextMobject, TexMobject
@ -26,13 +26,21 @@ class PlayingCard(VGroup):
CONFIG = {
"value" : None,
"suit" : None,
"height" : 1.5,
"key" : None, ##String like "8H" or "KS"
"height" : 2,
"height_to_width" : 3.5/2.5,
"card_height_to_symbol_height" : 7,
"card_width_to_corner_num_width" : 10,
"card_height_to_corner_num_height" : 10,
"color" : LIGHT_GREY,
"turned_over" : False,
"possible_suits" : ["hearts", "diamonds", "spades", "clubs"],
"possible_values" : map(str, range(2, 11)) + ["J", "Q", "K", "A"],
}
def __init__(self, key = None, **kwargs):
VGroup.__init__(self, key = key, **kwargs)
def generate_points(self):
self.add(Rectangle(
height = self.height,
@ -42,32 +50,58 @@ class PlayingCard(VGroup):
fill_color = self.color,
fill_opacity = 1,
))
value = self.get_value()
symbol = self.get_symbol()
design = self.get_design(value, symbol)
corner_numbers = self.get_corner_numbers(value, symbol)
self.add(design, corner_numbers)
if self.turned_over:
self.set_fill(DARK_GREY)
self.set_stroke(LIGHT_GREY)
contents = VectorizedPoint(self.get_center())
else:
value = self.get_value()
symbol = self.get_symbol()
design = self.get_design(value, symbol)
corner_numbers = self.get_corner_numbers(value, symbol)
contents = VGroup(design, corner_numbers)
self.design = design
self.corner_numbers = corner_numbers
self.add(contents)
def get_value(self):
value = self.value
possible_values = map(str, range(1, 11)) + ["J", "Q", "K"]
if value is None:
value = random.choice(possible_values)
value = str(value)
if value not in possible_values:
raise Exception("Invalid card value")
value = value.capitalize()
if self.key is not None:
value = self.key[:-1]
else:
value = random.choice(self.possible_values)
value = string.upper(str(value))
if value == "1":
value = "A"
if value not in self.possible_values:
raise Exception("Invalid card value")
face_card_to_value = {
"J" : 11,
"Q" : 12,
"K" : 13,
"A" : 14,
}
try:
self.numerical_value = int(value)
except:
self.numerical_value = face_card_to_value[value]
return value
def get_symbol(self):
suit = self.suit
possible_suits = ["hearts", "diamonds", "spades", "clubs"]
if suit is None:
suit = random.choice(possible_suits)
if suit not in possible_suits:
if self.key is not None:
suit = dict([
(string.upper(s[0]), s)
for s in self.possible_suits
])[string.upper(self.key[-1])]
else:
suit = random.choice(self.possible_suits)
if suit not in self.possible_suits:
raise Exception("Invalud suit value")
self.suit = suit
symbol_height = float(self.height) / self.card_height_to_symbol_height
symbol = SuitSymbol(suit, height = symbol_height)
return symbol
@ -225,7 +259,6 @@ class SuitSymbol(SVGMobject):
self.set_fill(color, 1)
self.scale_to_fit_height(self.height)
class Speedometer(VMobject):
CONFIG = {
"arc_angle" : 4*np.pi/3,

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topics/probability.py Normal file
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@ -0,0 +1,307 @@
from helpers import *
from mobject import Mobject
from mobject.vectorized_mobject import VGroup, VMobject, VectorizedPoint
from mobject.svg_mobject import SVGMobject
from mobject.tex_mobject import TextMobject, TexMobject
from topics.geometry import Circle, Line, Rectangle, Square, Arc, Polygon
class SampleSpace(VGroup):
CONFIG = {
"full_space_config" : {
"height" : 3,
"width" : 3,
"fill_color" : DARK_GREY,
"fill_opacity" : 0.8,
"stroke_width" : 0,
}
}
def __init__(self, **kwargs):
VGroup.__init__(self, **kwargs)
full_space = Rectangle(**self.full_space_config)
self.full_space = full_space
self.add(full_space)
def add_title(self, title = "Sample space", buff = MED_SMALL_BUFF):
title_mob = TextMobject(title)
if title_mob.get_width() > self.get_width():
title_mob.scale_to_fit_width(self.get_width())
title_mob.next_to(self.full_space, UP, buff = buff)
self.title = title_mob
self.add(title_mob)
def divide_along_dimension(self, p, dim, colors):
perp_dim = 1-dim
if dim == 0:
vects = [UP, DOWN]
else:
vects = [LEFT, RIGHT]
parts = VGroup()
for factor, vect, color in zip([p, 1-p], vects, colors):
part = self.full_space.copy()
part.set_fill(color, 1)
part.stretch(factor, perp_dim)
part.move_to(self.full_space, vect)
parts.add(part)
return parts
def divide_horizontally(self, p, colors = [GREEN_E, RED_E]):
result = self.divide_along_dimension(p, 0, colors)
self.top_part, self.bottom_part = result
return result
def divide_vertically(self, p, colors = [MAROON_B, YELLOW]):
result = self.divide_along_dimension(p, 1, colors)
self.left_part, self.right_part = result
return result
### Cards ###
class DeckOfCards(VGroup):
def __init__(self, **kwargs):
possible_values = map(str, range(1, 11)) + ["J", "Q", "K"]
possible_suits = ["hearts", "diamonds", "spades", "clubs"]
VGroup.__init__(self, *[
PlayingCard(value = value, suit = suit, **kwargs)
for value in possible_values
for suit in possible_suits
])
class PlayingCard(VGroup):
CONFIG = {
"value" : None,
"suit" : None,
"key" : None, ##String like "8H" or "KS"
"height" : 2,
"height_to_width" : 3.5/2.5,
"card_height_to_symbol_height" : 7,
"card_width_to_corner_num_width" : 10,
"card_height_to_corner_num_height" : 10,
"color" : LIGHT_GREY,
"turned_over" : False,
"possible_suits" : ["hearts", "diamonds", "spades", "clubs"],
"possible_values" : map(str, range(2, 11)) + ["J", "Q", "K", "A"],
}
def __init__(self, key = None, **kwargs):
VGroup.__init__(self, key = key, **kwargs)
def generate_points(self):
self.add(Rectangle(
height = self.height,
width = self.height/self.height_to_width,
stroke_color = WHITE,
stroke_width = 2,
fill_color = self.color,
fill_opacity = 1,
))
if self.turned_over:
self.set_fill(DARK_GREY)
self.set_stroke(LIGHT_GREY)
contents = VectorizedPoint(self.get_center())
else:
value = self.get_value()
symbol = self.get_symbol()
design = self.get_design(value, symbol)
corner_numbers = self.get_corner_numbers(value, symbol)
contents = VGroup(design, corner_numbers)
self.design = design
self.corner_numbers = corner_numbers
self.add(contents)
def get_value(self):
value = self.value
if value is None:
if self.key is not None:
value = self.key[:-1]
else:
value = random.choice(self.possible_values)
value = string.upper(str(value))
if value == "1":
value = "A"
if value not in self.possible_values:
raise Exception("Invalid card value")
face_card_to_value = {
"J" : 11,
"Q" : 12,
"K" : 13,
"A" : 14,
}
try:
self.numerical_value = int(value)
except:
self.numerical_value = face_card_to_value[value]
return value
def get_symbol(self):
suit = self.suit
if suit is None:
if self.key is not None:
suit = dict([
(string.upper(s[0]), s)
for s in self.possible_suits
])[string.upper(self.key[-1])]
else:
suit = random.choice(self.possible_suits)
if suit not in self.possible_suits:
raise Exception("Invalud suit value")
self.suit = suit
symbol_height = float(self.height) / self.card_height_to_symbol_height
symbol = SuitSymbol(suit, height = symbol_height)
return symbol
def get_design(self, value, symbol):
if value == "A":
return self.get_ace_design(symbol)
if value in map(str, range(2, 11)):
return self.get_number_design(value, symbol)
else:
return self.get_face_card_design(value, symbol)
def get_ace_design(self, symbol):
design = symbol.copy().scale(1.5)
design.move_to(self)
return design
def get_number_design(self, value, symbol):
num = int(value)
n_rows = {
2 : 2,
3 : 3,
4 : 2,
5 : 2,
6 : 3,
7 : 3,
8 : 3,
9 : 4,
10 : 4,
}[num]
n_cols = 1 if num in [2, 3] else 2
insertion_indices = {
5 : [0],
7 : [0],
8 : [0, 1],
9 : [1],
10 : [0, 2],
}.get(num, [])
top = self.get_top() + symbol.get_height()*DOWN
bottom = self.get_bottom() + symbol.get_height()*UP
column_points = [
interpolate(top, bottom, alpha)
for alpha in np.linspace(0, 1, n_rows)
]
design = VGroup(*[
symbol.copy().move_to(point)
for point in column_points
])
if n_cols == 2:
space = 0.2*self.get_width()
column_copy = design.copy().shift(space*RIGHT)
design.shift(space*LEFT)
design.add(*column_copy)
design.add(*[
symbol.copy().move_to(
center_of_mass(column_points[i:i+2])
)
for i in insertion_indices
])
for symbol in design:
if symbol.get_center()[1] < self.get_center()[1]:
symbol.rotate_in_place(np.pi)
return design
def get_face_card_design(self, value, symbol):
from topics.characters import PiCreature
sub_rect = Rectangle(
stroke_color = BLACK,
fill_opacity = 0,
height = 0.9*self.get_height(),
width = 0.6*self.get_width(),
)
sub_rect.move_to(self)
pi_color = average_color(symbol.get_color(), GREY)
pi_mode = {
"J" : "plain",
"Q" : "thinking",
"K" : "hooray"
}[value]
pi_creature = PiCreature(
mode = pi_mode,
color = pi_color,
)
pi_creature.scale_to_fit_width(0.8*sub_rect.get_width())
if value in ["Q", "K"]:
prefix = "king" if value == "K" else "queen"
crown = SVGMobject(file_name = prefix + "_crown")
crown.set_stroke(width = 0)
crown.set_fill(YELLOW, 1)
crown.stretch_to_fit_width(0.5*sub_rect.get_width())
crown.stretch_to_fit_height(0.17*sub_rect.get_height())
crown.move_to(pi_creature.eyes.get_center(), DOWN)
pi_creature.add_to_back(crown)
to_top_buff = 0
else:
to_top_buff = SMALL_BUFF*sub_rect.get_height()
pi_creature.next_to(sub_rect.get_top(), DOWN, to_top_buff)
# pi_creature.shift(0.05*sub_rect.get_width()*RIGHT)
pi_copy = pi_creature.copy()
pi_copy.rotate(np.pi, about_point = sub_rect.get_center())
return VGroup(sub_rect, pi_creature, pi_copy)
def get_corner_numbers(self, value, symbol):
value_mob = TextMobject(value)
width = self.get_width()/self.card_width_to_corner_num_width
height = self.get_height()/self.card_height_to_corner_num_height
value_mob.scale_to_fit_width(width)
value_mob.stretch_to_fit_height(height)
value_mob.next_to(
self.get_corner(UP+LEFT), DOWN+RIGHT,
buff = MED_LARGE_BUFF*width
)
value_mob.highlight(symbol.get_color())
corner_symbol = symbol.copy()
corner_symbol.scale_to_fit_width(width)
corner_symbol.next_to(
value_mob, DOWN,
buff = MED_SMALL_BUFF*width
)
corner_group = VGroup(value_mob, corner_symbol)
opposite_corner_group = corner_group.copy()
opposite_corner_group.rotate(
np.pi, about_point = self.get_center()
)
return VGroup(corner_group, opposite_corner_group)
class SuitSymbol(SVGMobject):
CONFIG = {
"height" : 0.5,
"fill_opacity" : 1,
"stroke_width" : 0,
"red" : "#D02028",
"black" : BLACK,
}
def __init__(self, suit_name, **kwargs):
digest_config(self, kwargs)
suits_to_colors = {
"hearts" : self.red,
"diamonds" : self.red,
"spades" : self.black,
"clubs" : self.black,
}
if suit_name not in suits_to_colors:
raise Exception("Invalid suit name")
SVGMobject.__init__(self, file_name = suit_name, **kwargs)
color = suits_to_colors[suit_name]
self.set_stroke(width = 0)
self.set_fill(color, 1)
self.scale_to_fit_height(self.height)