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from manim import *
import numpy as np
class FullVideo(Scene):
def construct(self):
# Part 1: Introduction
title = Text("Gradients, Optimization, and Bayesian Updating").scale(0.8).to_edge(UP)
intro_text = Text(
"Exploring how gradients guide optimization\nand how beliefs evolve with evidence.",
font_size=24
).next_to(title, DOWN)
self.play(Write(title), Write(intro_text))
self.wait(2)
self.play(FadeOut(intro_text))
# Transition to gradients
self.play(FadeOut(title))
self.wait(0.5)
# Part 2: Understanding Gradients
axes = Axes(
x_range=[0, 10, 1],
y_range=[0, 25, 5],
axis_config={"include_numbers": True},
)
graph = axes.plot(lambda x: (x - 5)**2, color=BLUE)
func_label = MathTex("f(x) = (x - 5)^2").next_to(axes, UP)
self.play(Create(axes), Write(func_label))
self.play(Create(graph))
self.wait(1)
# Gradient descent animation
dot_min = Dot(axes.coords_to_point(7, (7 - 5)**2), color=RED)
self.play(FadeIn(dot_min))
for _ in range(5):
new_x = dot_min.get_center()[0] - 0.5
new_y = (new_x - 5)**2
new_dot = Dot(axes.coords_to_point(new_x, new_y), color=RED)
self.play(Transform(dot_min, new_dot), run_time=0.5)
self.wait(1)
# Zoom effect on the minimum point
self.play(
axes.animate.scale(0.8).shift(LEFT * 2),
dot_min.animate.scale(1.5),
run_time=1.5
)
self.wait(1)
self.play(FadeOut(axes), FadeOut(dot_min), FadeOut(func_label))
# Part 3: Comfort Score Function
axes_3d = ThreeDAxes(
x_range=[60, 80, 5],
y_range=[30, 50, 5],
z_range=[0, 100, 20],
x_length=8,
y_length=8,
z_length=6
)
def comfort_score(t, h):
return 72 - (t - 70)**2 - 2 * (h - 40)**2
surface = Surface(
lambda u, v: axes_3d.c2p(u, v, comfort_score(u, v)),
u_range=[60, 80],
v_range=[30, 50],
resolution=(20, 20),
fill_opacity=0.7
)
surface.set_fill_by_value(
axes=axes_3d,
colors=[(RED, 0), (YELLOW, 50), (GREEN, 100)]
)
# Set camera orientation and animate rotation
self.set_camera_orientation(phi=75 * DEGREES, theta=-45 * DEGREES)
self.add(axes_3d, surface)
self.begin_ambient_camera_rotation(rate=0.2)
self.wait(5)
self.stop_ambient_camera_rotation()
# Zoom into the peak of the surface
self.move_camera(phi=90 * DEGREES, theta=-90 * DEGREES, zoom=1.5, run_time=2)
self.wait(1)
self.play(FadeOut(axes_3d), FadeOut(surface))
# Part 4: Bayesian Updating
prior = [0.3, 0.7]
bar_chart = BarChart(
prior,
max_value=1,
bar_names=["Rain", "No Rain"],
bar_colors=[BLUE, YELLOW]
)
prior_label = Text("Prior Probabilities").next_to(bar_chart, DOWN)
self.play(Create(bar_chart), Write(prior_label))
self.wait(2)
posterior = [0.6, 0.4]
updated_bar_chart = BarChart(
posterior,
max_value=1,
bar_names=["Rain", "No Rain"],
bar_colors=[BLUE, YELLOW]
)
posterior_label = Text("Posterior Probabilities").next_to(updated_bar_chart, DOWN)
self.play(Transform(bar_chart, updated_bar_chart), Transform(prior_label, posterior_label))
self.wait(2)
bayes_formula = MathTex(r"P(H|E) = \frac{P(E|H)P(H)}{P(E)}").next_to(bar_chart, DOWN)
self.play(Write(bayes_formula))
self.wait(2)
# Zoom out for conclusion
self.play(
bar_chart.animate.scale(0.8).shift(LEFT * 2),
bayes_formula.animate.scale(0.8).shift(RIGHT * 2),
run_time=1.5
)
self.wait(1)
# Part 5: Connecting the Dots
self.clear()
conclusion = Text(
"Gradients and Bayesian updating both rely\non iterative refinement to achieve their goals.",
font_size=24
).to_edge(UP)
self.play(Write(conclusion))
self.wait(3)
# Part 6: Call to Action
call_to_action = Text(
"Explore more about optimization and Bayesian methods!",
font_size=24
).next_to(conclusion, DOWN)
self.play(Write(call_to_action))
self.wait(3) |