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Merge pull request #212 from 3b1b/eop

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Eop
This commit is contained in:
Grant Sanderson
2018-04-16 14:20:59 -07:00
committed by GitHub
parent 9a69aa4c95 51f002b3ba
commit 264da9b0ed
3 changed files with 382 additions and 129 deletions
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335
active_projects/eop/chapter1.py
View File

@@ -1,7 +1,6 @@
from big_ol_pile_of_manim_imports import *
from old_projects.eoc.chapter8 import *
from active_projects.eop.histograms import *
from svgpathtools import *
import scipy.special
@@ -75,7 +74,7 @@ class CoinFlippingPiCreature(PiCreature):
def __init__(self, **kwargs):
coin = PiCreatureCoin() # Line(ORIGIN, 0.4 * RIGHT, stroke_width = 15, color = YELLOW)
coin = PiCreatureCoin()
PiCreature.__init__(self,**kwargs)
self.coin = coin
self.add(coin)
@@ -107,12 +106,15 @@ class FlipCoin(AnimationGroup):
rate_func = self.rate_func,
**kwargs
)
coin_motion = FlipUpAndDown(
pi_creature.coin,
vector = UP,
nb_turns = 5,
rate_func = self.rate_func,
**kwargs
coin_motion = Succession(
EmptyAnimation(run_time = 1.0),
FlipUpAndDown(
pi_creature.coin,
vector = UP,
nb_turns = 5,
rate_func = self.rate_func,
**kwargs
)
)
AnimationGroup.__init__(self,pi_creature_motion, coin_motion)
@@ -270,19 +272,33 @@ class TailsStack(CoinStack):
}
class TallyStack(VGroup):
CONFIG = {
"coin_thickness": COIN_THICKNESS
}
def __init__(self,h,t,**kwargs):
def __init__(self,h,t,anchor = ORIGIN, **kwargs):
self.nb_heads = h
self.nb_tails = t
self.anchor = anchor
VGroup.__init__(self,**kwargs)
def generate_points(self):
stack1 = HeadsStack(size = self.nb_heads, coin_thickness = self.coin_thickness)
stack2 = TailsStack(size = self.nb_tails, coin_thickness = self.coin_thickness)
stack2.next_to(stack1, RIGHT, buff = SMALL_BUFF)
stack2.align_to(stack1, DOWN)
stack1.next_to(self.anchor, LEFT, buff = SMALL_BUFF)
stack2.next_to(self.anchor, RIGHT, buff = SMALL_BUFF)
stack1.align_to(self.anchor, DOWN)
stack2.align_to(self.anchor, DOWN)
self.heads_stack = stack1
self.tails_stack = stack2
self.add(stack1, stack2)
def move_anchor_to(self, new_anchor):
for submob in self.submobjects:
submob.shift(new_anchor - self.anchor)
self.anchor = new_anchor
return self
class CoinFlipTree(VGroup):
CONFIG = {
"total_width": 12,
@@ -362,36 +378,6 @@ class CoinFlipTree(VGroup):
class TestScene(Scene):
def construct(self):
#seq = CoinSequence(["H", "T", "T", "H"]).move_to(2 * LEFT)
#self.add(seq)
#stack = TallyStack(4,7, coin_thickness = COIN_THICKNESS)
#self.add(stack)
tree = CoinFlipTree(nb_levels = 7, sort_until_level = 0)
tree.move_to(ORIGIN)
self.add(tree)
for i in range(1, 8):
new_tree = CoinFlipTree(nb_levels = 7, sort_until_level = i)
new_tree.move_to(ORIGIN)
self.play(Transform(tree, new_tree))
self.wait()
self.wait()
class CoinFlipBranchToAreaScene(Scene):
def construct(self):
pass
class Chapter1OpeningQuote(OpeningQuote):
CONFIG = {
@@ -425,6 +411,7 @@ class Introduction(TeacherStudentsScene):
def construct(self):
self.show_series()
self.show_area_model1()
def show_series(self):
series = VideoSeries()
@@ -475,28 +462,28 @@ class Introduction(TeacherStudentsScene):
Animation(self.teacher.bubble.content),
])
essence_words = words.get_part_by_tex("Essence").copy()
self.play(
FadeOut(self.teacher.bubble),
FadeOut(self.teacher.bubble.content),
essence_words.next_to, series, DOWN,
*[
ApplyMethod(pi.change_mode, "pondering")
for pi in self.get_pi_creatures()
]
)
self.wait(3)
self.wait()
self.series = series
self.essence_words = essence_words
class IllustrateAreaModel1(Scene):
def construct(self):
# # # # # # # # # # # # # # # # # #
# show examples of the area model #
# # # # # # # # # # # # # # # # # #
def show_area_model1(self):
# show independent events
sample_space_width = sample_space_height = 3.0
sample_space_width = sample_space_height = 2.5
p_of_A = 0.7
p_of_not_A = 1 - p_of_A
p_of_B = 0.8
@@ -509,7 +496,8 @@ class IllustrateAreaModel1(Scene):
stroke_width = 0,
fill_color = BLUE,
fill_opacity = 1.0
)
).move_to(2 * RIGHT + 1.5 * UP)
rect_not_A = Rectangle(
width = p_of_not_A * sample_space_width,
height = 1 * sample_space_height,
@@ -523,18 +511,13 @@ class IllustrateAreaModel1(Scene):
brace_not_A = Brace(rect_not_A, DOWN)
label_not_A = TexMobject("P(\\text{not }A)").next_to(brace_not_A, DOWN).scale(0.7)
self.play(
LaggedStart(FadeIn, VGroup(rect_A, rect_not_A), lag_factor = 0.5)
)
self.play(
ShowCreation(brace_A),
Write(label_A),
)
# self.play(
# ShowCreation(brace_not_A),
# Write(label_not_A),
# LaggedStart(FadeIn, VGroup(rect_A, rect_not_A), lag_factor = 0.5)
# )
# self.play(
# ShowCreation(brace_A),
# Write(label_A),
# )
@@ -560,16 +543,12 @@ class IllustrateAreaModel1(Scene):
brace_not_B = Brace(rect_not_B, LEFT)
label_not_B = TexMobject("P(\\text{not }B)").next_to(brace_not_B, LEFT).scale(0.7)
self.play(
LaggedStart(FadeIn, VGroup(rect_B, rect_not_B), lag_factor = 0.5)
)
self.play(
ShowCreation(brace_B),
Write(label_B),
)
# self.play(
# ShowCreation(brace_not_B),
# Write(label_not_B),
# LaggedStart(FadeIn, VGroup(rect_B, rect_not_B), lag_factor = 0.5)
# )
# self.play(
# ShowCreation(brace_B),
# Write(label_B),
# )
rect_A_and_B = Rectangle(
@@ -581,11 +560,9 @@ class IllustrateAreaModel1(Scene):
label_A_and_B = TexMobject("P(A\\text{ and }B)").scale(0.7)
label_A_and_B.move_to(rect_A_and_B)
self.play(
ShowCreation(rect_A_and_B)
)
self.play(FadeIn(label_A_and_B))
self.add_foreground_mobject(label_A_and_B)
# self.play(
# ShowCreation(rect_A_and_B)
# )
indep_formula = TexMobject("P(A\\text{ and }B)", "=", "P(A)", "\cdot", "P(B)")
indep_formula = indep_formula.scale(0.7).next_to(rect_not_B, UP, buff = MED_LARGE_BUFF)
@@ -593,16 +570,19 @@ class IllustrateAreaModel1(Scene):
label_A_and_B_copy = label_A_and_B.copy()
label_A_copy = label_A.copy()
label_B_copy = label_B.copy()
self.add(label_A_and_B_copy, label_A_copy, label_B_copy)
# self.add(label_A_and_B_copy, label_A_copy, label_B_copy)
self.play(Transform(label_A_and_B_copy, indep_formula[0]))
self.play(FadeIn(indep_formula[1]))
self.play(Transform(label_A_copy, indep_formula[2]))
self.play(FadeIn(indep_formula[3]))
self.play(Transform(label_B_copy, indep_formula[4]))
# self.play(Transform(label_A_and_B_copy, indep_formula[0]))
# self.play(FadeIn(indep_formula[1]))
# self.play(Transform(label_A_copy, indep_formula[2]))
# self.play(FadeIn(indep_formula[3]))
# self.play(Transform(label_B_copy, indep_formula[4]))
self.wait()
#self.wait()
label_A_and_B_copy = indep_formula[0]
label_A_copy = indep_formula[2]
label_B_copy = indep_formula[4]
# show conditional prob
@@ -631,11 +611,22 @@ class IllustrateAreaModel1(Scene):
fill_opacity = 0.5
).next_to(rect_not_A_and_B, UP, buff = 0)
self.remove(rect_B, rect_not_B)
self.add(rect_A_and_not_B, rect_not_A_and_B, rect_not_A_and_not_B)
indep_formula.next_to(rect_not_A, LEFT, buff = 4)
indep_formula.shift(UP)
self.play(Write(indep_formula))
self.play(
FadeIn(VGroup(
rect_A, rect_not_A, brace_A, label_A, brace_B, label_B,
rect_A_and_not_B, rect_not_A_and_B, rect_not_A_and_not_B,
rect_A_and_B,
label_A_and_B,
))
)
self.wait()
p_of_B_knowing_A = 0.6
@@ -668,7 +659,7 @@ class IllustrateAreaModel1(Scene):
)
label_B_knowing_A = label_B
self.play(FadeOut(label_B_copy))
#self.play(FadeOut(label_B_copy))
self.remove(indep_formula.get_part_by_tex("P(B)"))
label_B_knowing_A_copy = label_B_knowing_A.copy()
self.add(label_B_knowing_A_copy)
@@ -684,6 +675,7 @@ class IllustrateAreaModel1(Scene):
self.wait()
self.play(
# in some places get_part_by_tex does not find the correct part
# so I picked out fitting indices
@@ -691,7 +683,17 @@ class IllustrateAreaModel1(Scene):
label_A_copy.move_to, rearranged_formula[-1][10],
label_A_and_B_copy.move_to, rearranged_formula[-1][3],
indep_formula.get_part_by_tex("=").move_to, rearranged_formula.get_part_by_tex("="),
Transform(indep_formula.get_part_by_tex("\cdot"), rearranged_formula[-1][8]),
Transform(indep_formula.get_part_by_tex("\cdot"), rearranged_formula[2][6]),
)
self.play(
FadeOut(VGroup(
indep_formula, rect_A, rect_B, rect_not_A, rect_not_B,
rect_A_and_B, rect_A_and_not_B, rect_not_A_and_B, rect_not_A_and_not_B,
brace_A, brace_B, label_A, label_B_knowing_A, label_A_and_B,
label_B_knowing_A_copy
))
)
@@ -776,8 +778,8 @@ class IllustrateAreaModel1(Scene):
class IllustrateAreaModel2(GraphScene):
CONFIG = {
"x_min" : -5,
"x_max" : 5,
"x_min" : -3.5,
"x_max" : 3.5,
"y_min" : -0,
"y_max" : 0.6,
"graph_origin": 3*DOWN,
@@ -785,7 +787,10 @@ class IllustrateAreaModel2(GraphScene):
"y_axis_label" : "",
"x_axis_label" : "",
"variable_point_label" : "x",
"y_axis_height" : 4
"y_axis_height" : 4,
"graph_origin": 2.5 * DOWN + 3 * LEFT,
"x_axis_width": 5,
"y_axis_height": 3
}
def construct(self):
@@ -793,7 +798,7 @@ class IllustrateAreaModel2(GraphScene):
x_max_1 = 0
x_min_1 = -x_max_1
x_max_2 = 5
x_max_2 = 3.5
x_min_2 = -x_max_2
@@ -802,10 +807,10 @@ class IllustrateAreaModel2(GraphScene):
self.add(graph)
cdf_formula = TexMobject("P(|X-\mu| < x) = \int_{-x}^x {\exp(-{1\over 2}({t\over \sigma})^2) \over \sigma\sqrt{2\pi}} dt")
cdf_formula.set_color_by_tex("x", YELLOW)
cdf_formula.next_to(graph, LEFT, buff = 1)
cdf_formula.next_to(graph, RIGHT, buff = -1)
self.add(cdf_formula)
@@ -1121,26 +1126,140 @@ class RowOfDice(VGroup):
class ShowUncertainty(PiCreatureScene):
class ShowUncertainty1(PiCreatureScene):
def throw_a_die(self):
eye = np.random.randint(1,7)
face = self.row_of_dice.submobjects[eye - 1]
self.tallies[eye - 1] += 1
new_hist = self.hist_from_tallies()
self.play(
ApplyMethod(face.submobjects[0].set_fill, {"opacity": 1},
rate_func = there_and_back,
run_time = 0.3,
),
)
self.play(
Transform(self.dice_histogram, new_hist,
run_time = 0.5)
)
def hist_from_tallies(self):
x_scale = self.row_of_dice.get_width() / np.size(self.tallies)
hist = Histogram(np.ones(6), self.tallies,
mode = "widths",
x_labels = "none",
y_scale = 0.5,
x_scale = x_scale
)
hist.next_to(self.row_of_dice, UP)
return hist
def construct(self):
row_of_dice = RowOfDice().scale(0.5).move_to(ORIGIN)
self.add(row_of_dice)
rounded_rect = RoundedRectangle(
width = 3,
height = 2,
corner_radius = 0.1
).shift(3*LEFT)
self.add(rounded_rect)
self.row_of_dice = RowOfDice().scale(0.5).move_to(3 * DOWN)
self.add(self.row_of_dice)
self.tallies = np.zeros(6)
self.dice_histogram = self.hist_from_tallies()
self.add(self.dice_histogram)
for i in range(30):
self.throw_a_die()
self.wait()
class ShowUncertainty2(PiCreatureScene):
def throw_darts(self, n, run_time = 1):
points = np.random.normal(
loc = self.dartboard.get_center(),
scale = 0.6 * np.ones(3),
size = (n,3)
)
points[:,2] = 0
dots = VGroup()
for point in points:
dot = Dot(point, radius = 0.04, fill_opacity = 0.7)
dots.add(dot)
self.add(dot)
self.play(
LaggedStart(FadeIn, dots, lag_ratio = 0.01, run_time = run_time)
)
def construct(self):
self.dartboard = ImageMobject("dartboard").scale(2)
dartboard_circle = Circle(
radius = self.dartboard.get_width() / 2,
fill_color = BLACK,
fill_opacity = 0.5,
stroke_color = WHITE,
stroke_width = 5
)
self.dartboard.add(dartboard_circle)
self.add(self.dartboard)
self.throw_darts(5,5)
self.throw_darts(20,5)
self.throw_darts(100,5)
self.throw_darts(1000,5)
class ShowUncertainty3(Scene):
def construct(self):
randy = CoinFlippingPiCreature(color = MAROON_E)
randy.scale(0.5).to_edge(LEFT + DOWN)
heads = tails = 0
tally = TallyStack(heads, tails, anchor = ORIGIN)
nb_flips = 10
flips = np.random.randint(2, size = nb_flips)
for i in range(nb_flips):
self.play(FlipCoin(randy))
self.wait(0.5)
flip = flips[i]
if flip == 0:
heads += 1
elif flip == 1:
tails += 1
else:
raise Exception("That side does not exist on this coin")
new_tally = TallyStack(heads, tails, anchor = ORIGIN)
if tally.nb_heads == 0 and new_tally.nb_heads == 1:
self.play(FadeIn(new_tally.heads_stack))
elif tally.nb_tails == 0 and new_tally.nb_tails == 1:
self.play(FadeIn(new_tally.tails_stack))
else:
self.play(Transform(tally, new_tally))
tally = new_tally

103
active_projects/eop/chapter2.py Normal file
View File

@@ -0,0 +1,103 @@
from big_ol_pile_of_manim_imports import *
def print_permutation(index_list):
n = max(max(index_list), len(index_list))
for i in range(0,n):
if index_list[i] > n - i:
raise Exception("Impossible indices!")
#print "given index list:", index_list
perm_list = n * ["_"]
alphabet = ["A", "B", "C", "D", "E", "F",
"G", "H", "I", "J", "K", "L",
"M", "N", "O", "P", "Q", "R",
"S", "T", "U", "V", "W", "X",
"Y", "Z"]
free_indices = range(n)
free_indices_p1 = range(1,n + 1)
#print perm_list
for i in range(n):
findex = index_list[i] - 1
#print "place next letter at", findex + 1, "th free place"
tindex = free_indices[findex]
#print "so at position", tindex + 1
perm_list[tindex] = alphabet[i]
free_indices.remove(tindex)
free_indices_p1.remove(tindex + 1)
#print "remaining free places:", free_indices_p1
#print perm_list
return "".join(perm_list)
class PermutationGrid(Scene):
def text_box(self, str):
box = TextMobject(str).scale(0.3)
box.add(SurroundingRectangle(box, stroke_color = DARK_GREY))
return box
def construct(self):
N = 5
index_list = []
perm5_box = VGroup()
for i in range(1, N + 1):
index_list.append(i)
perm4_box = VGroup()
for j in range(1, N):
index_list.append(j)
perm3_box = VGroup()
for k in range(1, N - 1):
index_list.append(k)
perm2_box = VGroup()
for l in range(1, N - 2):
index_list.append(l)
index_list.append(1)
perm_box = self.text_box(print_permutation(index_list))
if l > 1:
perm_box.next_to(perm2_box[-1], DOWN, buff = 0)
perm2_box.add(perm_box)
index_list.pop()
index_list.pop()
if k > 1:
perm2_box.next_to(perm3_box[-1], RIGHT, buff = 0.08)
perm3_box.add(perm2_box)
index_list.pop()
perm3_box.add(SurroundingRectangle(perm3_box, buff = 0.12, stroke_color = LIGHT_GRAY))
if j > 1:
perm3_box.next_to(perm4_box[-1], DOWN, buff = 0)
perm4_box.add(perm3_box)
index_list.pop()
if i > 1:
perm4_box.next_to(perm5_box[-1], RIGHT, buff = 0.16)
perm5_box.add(perm4_box)
index_list.pop()
perm5_box.move_to(ORIGIN)
self.add(perm5_box)

73
active_projects/eop/histograms.py
View File

@@ -16,7 +16,8 @@ class Histogram(VMobject):
"end_color" : BLUE,
"x_scale" : 1.0,
"y_scale" : 1.0,
"x_labels" : "auto",
"x_labels" : "auto", # widths, mids, auto, none, [...]
"y_labels" : "auto", # auto, none, [...]
"x_min" : 0
}
@@ -31,18 +32,29 @@ class Histogram(VMobject):
elif mode == "posts" and len(x_values) != len(y_values) + 1:
raise Exception("Array lengths do not match up!")
# preliminaries
self.y_values = np.array(y_values)
if mode == "widths":
self.widths = x_values
self.y_values = y_values
self.x_values = x_values
self.mode = mode
self.process_values()
VMobject.__init__(self, **kwargs)
def process_values(self):
# preliminaries
self.y_values = np.array(self.y_values)
if self.mode == "widths":
self.widths = self.x_values
self.posts = np.cumsum(self.widths)
self.posts = np.insert(self.posts, 0, 0)
self.posts += self.x_min
self.x_max = self.posts[-1]
elif mode == "posts":
self.posts = x_values
self.widths = x_values[1:] - x_values[:-1]
elif self.mode == "posts":
self.posts = self.x_values
self.widths = self.x_values[1:] - self.x_values[:-1]
self.x_min = self.posts[0]
self.x_max = self.posts[-1]
else:
@@ -57,12 +69,14 @@ class Histogram(VMobject):
self.y_values_scaled = self.y_scale * self.y_values
VMobject.__init__(self, **kwargs)
digest_config(self, kwargs)
def generate_points(self):
self.process_values()
for submob in self.submobjects:
self.remove(submob)
def empty_string_array(n):
arr = []
for i in range(n):
@@ -72,21 +86,33 @@ class Histogram(VMobject):
def num_arr_to_string_arr(arr): # converts number array to string array
ret_arr = []
for x in arr:
ret_arr.append(str(x))
if x == np.floor(x):
new_x = int(np.floor(x))
else:
new_x = x
ret_arr.append(str(new_x))
return ret_arr
previous_bar = ORIGIN
self.bars = []
self.bars = VGroup()
self.x_labels_group = VGroup()
self.y_labels_group = VGroup()
outline_points = []
if self.x_labels == "widths":
self.x_labels = num_arr_to_string_arr(self.widths)
elif self.x_labels == "mids":
print self.x_mids
self.x_labels = num_arr_to_string_arr(self.x_mids)
elif self.x_labels == "none":
self.x_labels = empty_string_array(len(self.widths))
print self.x_labels
if self.y_labels == "auto":
self.y_labels = num_arr_to_string_arr(self.y_values)
elif self.y_labels == "none":
self.y_labels = empty_string_array(len(self.y_values))
for (i,x) in enumerate(self.x_mids):
@@ -104,12 +130,15 @@ class Histogram(VMobject):
bar.set_stroke(width = 0)
bar.next_to(previous_bar,RIGHT,buff = 0, aligned_edge = DOWN)
self.add(bar)
self.bars.append(bar)
self.bars.add(bar)
label = TextMobject(self.x_labels[i])
label.next_to(bar,DOWN)
self.add(label)
x_label = TextMobject(self.x_labels[i])
x_label.next_to(bar,DOWN)
self.x_labels_group.add(x_label)
y_label = TextMobject(self.y_labels[i])
y_label.next_to(bar, UP)
self.y_labels_group.add(y_label)
if i == 0:
# start with the lower left
@@ -128,7 +157,9 @@ class Histogram(VMobject):
self.outline = Polygon(*outline_points)
self.outline.set_stroke(color = WHITE)
self.add(self.outline)
self.add(self.bars, self.x_labels_group, self.y_labels_group, self.outline)
print self.submobjects
def get_lower_left_point(self):
return self.bars[0].get_anchors()[-2]