def show_probability(self):
title = TexMobject(
"P(\\text{triangle contains the center})",
"=", "1/4"
)
title.to_edge(UP, buff = MED_SMALL_BUFF)
title.highlight_by_tex("1/4", BLUE)
four = title[-1][-1]
four_circle = Circle(color = YELLOW)
four_circle.replace(four, dim_to_match = 1)
four_circle.scale_in_place(1.2)
self.n_in = 0
self.n_out = 0
frac = TexMobject(
"{0", "\\over", "\\quad 0", "+", "0 \\quad}", "="
)
placeholders = frac.get_parts_by_tex("0")
positions = [ORIGIN, RIGHT, LEFT]
frac.next_to(self.circle, RIGHT, 1.5*LARGE_BUFF)
def place_random_triangles(n, dither_time):
for x in range(n):
self.change_point_mobs_randomly(run_time = 0)
contain_center = self.points_contain_center(
[pm.get_center() for pm in self.point_mobs]
)
if contain_center:
self.n_in += 1
else:
self.n_out += 1
nums = map(Integer, [self.n_in, self.n_in, self.n_out])
VGroup(*nums[:2]).highlight(self.positive_triangle_color)
VGroup(*nums[2:]).highlight(self.negative_triangle_color)
for num, placeholder, position in zip(nums, placeholders, positions):
num.move_to(placeholder, position)
decimal = DecimalNumber(float(self.n_in)/(self.n_in + self.n_out))
decimal.next_to(frac, RIGHT, SMALL_BUFF)
self.add(decimal, *nums)
self.dither(dither_time)
self.remove(decimal, *nums)
return VGroup(decimal, *nums)
self.play(Write(title))
self.add(frac)
self.remove(*placeholders)
place_random_triangles(10, 0.25)
nums = place_random_triangles(self.n_random_trials, 0.05)
self.add(nums)
self.dither()
self.play(*map(FadeOut, [frac, nums, title]))
def construct(self):
scale_factor = 0.7
sick = "\\text{sick}"
positive = "\\text{positive}"
formula = TexMobject("P(", sick, "\\,|\\,", positive, ")", "=",
"{\\quad P(", sick, "\\text{ and }", positive,
") \\quad", "\\over", "P(", positive, ")}", "=",
"{1/1{,}000", "\\over", "1/1{,}000", "+",
"(999/1{,}000)(0.01)}")
formula.scale(scale_factor)
formula.next_to(self.pi_creatures, UP, LARGE_BUFF)
formula.shift_onto_screen(buff=MED_LARGE_BUFF)
equals_group = formula.get_parts_by_tex("=")
equals_indices = [
formula.index_of_part(equals) for equals in equals_group
]
lhs = VGroup(*formula[:equals_indices[0]])
initial_formula = VGroup(*formula[:equals_indices[1]])
initial_formula.save_state()
initial_formula.shift(3 * RIGHT)
over = formula.get_part_by_tex("\\over")
num_start_index = equals_indices[0] + 1
num_end_index = formula.index_of_part(over)
numerator = VGroup(*formula[num_start_index:num_end_index])
numerator_rect = SurroundingRectangle(numerator)
alt_numerator = TexMobject("P(", sick, ")", "P(", positive, "\\,|\\,",
sick, ")")
alt_numerator.scale(scale_factor)
alt_numerator.move_to(numerator)
number_fraction = VGroup(*formula[equals_indices[-1]:])
rhs = TexMobject("\\approx 0.09")
rhs.scale(scale_factor)
rhs.move_to(equals_group[-1], LEFT)
rhs.highlight(YELLOW)
for mob in formula, alt_numerator:
mob.highlight_by_tex(sick, SICKLY_GREEN)
mob.highlight_by_tex(positive, YELLOW)
#Ask question
self.student_says("What does the \\\\ formula look like here?")
self.play(self.teacher.change, "happy")
self.dither()
self.play(
Write(lhs),
RemovePiCreatureBubble(
self.students[1],
target_mode="pondering",
),
self.teacher.change,
"raise_right_hand",
self.students[0].change,
"pondering",
self.students[2].change,
"pondering",
)
self.dither()
#Show initial formula
lhs_copy = lhs.copy()
self.play(
LaggedStart(FadeIn, initial_formula, lag_ratio=0.7),
Animation(lhs_copy, remover=True),
)
self.dither(2)
self.play(ShowCreation(numerator_rect))
self.play(FadeOut(numerator_rect))
self.dither()
self.play(Transform(numerator, alt_numerator))
initial_formula.add(*numerator)
formula.add(*numerator)
self.dither(3)
#Show number_fraction
self.play(initial_formula.move_to, initial_formula.saved_state,
FadeIn(VGroup(*number_fraction[:3])))
self.dither(2)
self.play(
LaggedStart(FadeIn,
VGroup(*number_fraction[3:]),
run_time=3,
lag_ratio=0.7))
self.dither(2)
#Show rhs
self.play(formula.shift, UP)
self.play(Write(rhs))
self.change_student_modes(*["happy"] * 3)
self.look_at(rhs)
self.dither(2)
def construct(self):
clunky_deriv = TexMobject(
"{d", "\\big(", "{df", "\\over", "dx}", "\\big)",
"\\over", "dx }"
)
over_index = clunky_deriv.index_of_part(
clunky_deriv.get_parts_by_tex("\\over")[1]
)
numerator = VGroup(*clunky_deriv[:over_index])
denominator = VGroup(*clunky_deriv[over_index+1:])
rp = clunky_deriv.get_part_by_tex("(")
lp = clunky_deriv.get_part_by_tex(")")
dfs, overs, dxs = map(clunky_deriv.get_parts_by_tex, [
"df", "over", "dx"
])
df_over_dx = VGroup(dfs[0], overs[0], dxs[0])
d = clunky_deriv.get_part_by_tex("d")
d_over_dx = VGroup(d, overs[1], dxs[1])
d2f_over_dx2 = TexMobject("{d^2 f", "\\over", "dx", "^2}")
d2f_over_dx2.highlight_by_tex("dx", YELLOW)
for mob in clunky_deriv, d2f_over_dx2:
mob.next_to(self.teacher, UP+LEFT)
for mob in numerator, denominator:
circle = Circle(color = YELLOW)
circle.replace(mob, stretch = True)
circle.scale_in_place(1.3)
mob.circle = circle
dx_to_zero = TexMobject("dx \\to 0")
dx_to_zero.highlight(YELLOW)
dx_to_zero.next_to(clunky_deriv, UP+LEFT)
self.student_says(
"What's that notation?",
target_mode = "raise_left_hand"
)
self.change_student_modes("confused", "raise_left_hand", "confused")
self.play(
FadeIn(
clunky_deriv,
run_time = 2,
submobject_mode = "lagged_start"
),
RemovePiCreatureBubble(self.get_students()[1]),
self.teacher.change_mode, "raise_right_hand"
)
self.dither()
self.play(ShowCreation(numerator.circle))
self.dither()
self.play(ReplacementTransform(
numerator.circle,
denominator.circle,
))
self.dither()
self.play(
FadeOut(denominator.circle),
Write(dx_to_zero),
dxs.highlight, YELLOW
)
self.dither()
self.play(
FadeOut(dx_to_zero),
*[ApplyMethod(pi.change, "plain") for pi in self.get_pi_creatures()]
)
self.play(
df_over_dx.scale, dxs[1].get_height()/dxs[0].get_height(),
df_over_dx.move_to, d_over_dx, RIGHT,
FadeOut(VGroup(lp, rp)),
d_over_dx.shift, 0.8*LEFT + 0.05*UP,
)
self.dither()
self.play(*[
ReplacementTransform(
group,
VGroup(d2f_over_dx2.get_part_by_tex(tex))
)
for group, tex in [
(VGroup(d, dfs[0]), "d^2"),
(overs, "over"),
(dxs, "dx"),
(VGroup(dxs[1].copy()), "^2}"),
]
])
self.dither(2)
self.student_says(
"How does one... \\\\ read that?",
student_index = 0,
)
self.play(self.teacher.change, "happy")
self.dither(2)
def construct(self):
clunky_deriv = TexMobject(
"{d", "\\big(", "{df", "\\over", "dx}", "\\big)",
"\\over", "dx }"
)
over_index = clunky_deriv.index_of_part(
clunky_deriv.get_parts_by_tex("\\over")[1]
)
numerator = VGroup(*clunky_deriv[:over_index])
denominator = VGroup(*clunky_deriv[over_index+1:])
rp = clunky_deriv.get_part_by_tex("(")
lp = clunky_deriv.get_part_by_tex(")")
dfs, overs, dxs = map(clunky_deriv.get_parts_by_tex, [
"df", "over", "dx"
])
df_over_dx = VGroup(dfs[0], overs[0], dxs[0])
d = clunky_deriv.get_part_by_tex("d")
d_over_dx = VGroup(d, overs[1], dxs[1])
d2f_over_dx2 = TexMobject("{d^2 f", "\\over", "dx", "^2}")
d2f_over_dx2.highlight_by_tex("dx", YELLOW)
for mob in clunky_deriv, d2f_over_dx2:
mob.next_to(self.teacher, UP+LEFT)
for mob in numerator, denominator:
circle = Circle(color = YELLOW)
circle.replace(mob, stretch = True)
circle.scale_in_place(1.3)
mob.circle = circle
dx_to_zero = TexMobject("dx \\to 0")
dx_to_zero.highlight(YELLOW)
dx_to_zero.next_to(clunky_deriv, UP+LEFT)
self.student_says(
"What's that notation?",
target_mode = "raise_left_hand"
)
self.change_student_modes("confused", "raise_left_hand", "confused")
self.play(
FadeIn(
clunky_deriv,
run_time = 2,
submobject_mode = "lagged_start"
),
RemovePiCreatureBubble(self.get_students()[1]),
self.teacher.change_mode, "raise_right_hand"
)
self.wait()
self.play(ShowCreation(numerator.circle))
self.wait()
self.play(ReplacementTransform(
numerator.circle,
denominator.circle,
))
self.wait()
self.play(
FadeOut(denominator.circle),
Write(dx_to_zero),
dxs.highlight, YELLOW
)
self.wait()
self.play(
FadeOut(dx_to_zero),
*[ApplyMethod(pi.change, "plain") for pi in self.get_pi_creatures()]
)
self.play(
df_over_dx.scale, dxs[1].get_height()/dxs[0].get_height(),
df_over_dx.move_to, d_over_dx, RIGHT,
FadeOut(VGroup(lp, rp)),
d_over_dx.shift, 0.8*LEFT + 0.05*UP,
)
self.wait()
self.play(*[
ReplacementTransform(
group,
VGroup(d2f_over_dx2.get_part_by_tex(tex))
)
for group, tex in [
(VGroup(d, dfs[0]), "d^2"),
(overs, "over"),
(dxs, "dx"),
(VGroup(dxs[1].copy()), "^2}"),
]
])
self.wait(2)
self.student_says(
"How does one... \\\\ read that?",
student_index = 0,
)
self.play(self.teacher.change, "happy")
self.wait(2)
def reminder_of_weights_and_bias(self):
neuron = self.neuron
layer0 = self.network_mob.layers[0]
active_layer0 = self.network_mob.get_active_layer(
0, np.random.random(len(layer0.neurons)))
prev_neurons = layer0.neurons
weights = 4 * (np.random.random(len(neuron.edges_in)) - 0.5)
weighted_edges = VGroup(*[
edge.copy().set_stroke(color=GREEN if w > 0 else RED, width=abs(w))
for w, edge in zip(weights, neuron.edges_in)
])
formula = TexMobject("=", "\\sigma(", "w_1", "a_1", "+", "w_2", "a_2",
"+", "\\cdots", "+", "w_n", "a_n", "+", "b", ")")
w_labels = formula.get_parts_by_tex("w_")
a_labels = formula.get_parts_by_tex("a_")
b = formula.get_part_by_tex("b")
sigma = VGroup(
formula.get_part_by_tex("\\sigma"),
formula.get_part_by_tex(")"),
)
symbols = VGroup(
*[formula.get_parts_by_tex(tex) for tex in "=", "+", "dots"])
w_labels.highlight(GREEN)
b.highlight(BLUE)
sigma.highlight(YELLOW)
# formula.to_edge(UP)
formula.next_to(neuron, RIGHT)
weights_word = TextMobject("Weights")
weights_word.next_to(neuron.edges_in, RIGHT, aligned_edge=UP)
weights_word.highlight(GREEN)
weights_arrow = Arrow(weights_word.get_bottom(),
neuron.edges_in[0].get_center(),
color=GREEN)
alt_weights_arrows = VGroup(*[
Arrow(weights_word.get_bottom(), w_label.get_top(), color=GREEN)
for w_label in w_labels
])
bias_word = TextMobject("Bias")
bias_arrow = Vector(DOWN, color=BLUE)
bias_arrow.next_to(b, UP, SMALL_BUFF)
bias_word.next_to(bias_arrow, UP, SMALL_BUFF)
bias_word.highlight(BLUE)
self.revert_to_original_skipping_status()
self.play(Transform(layer0, active_layer0),
FadeIn(a_labels),
FadeIn(symbols),
run_time=2,
submobject_mode="lagged_start")
self.play(
Write(weights_word),
GrowArrow(weights_arrow),
Transform(neuron.edges_in, weighted_edges),
run_time=1,
)
self.dither()
self.play(
ReplacementTransform(
weighted_edges.copy(),
w_labels,
), ReplacementTransform(VGroup(weights_arrow), alt_weights_arrows))
self.dither()
self.play(Write(b),
Write(bias_word),
GrowArrow(bias_arrow),
run_time=1)
self.play(Write(sigma))
self.dither(2)
