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https://github.com/3b1b/manim.git
synced 2025-07-28 12:32:36 +08:00
Move gradient and mvrc to old_projects
This commit is contained in:
Grant Sanderson
393
old_projects/gradient.py
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393
old_projects/gradient.py
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@ -0,0 +1,393 @@
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from big_ol_pile_of_manim_imports import *
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class GradientDescentWrapper(Scene):
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def construct(self):
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title = TextMobject("Gradient descent")
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title.to_edge(UP)
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rect = ScreenRectangle(height=6)
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rect.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(rect))
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self.wait()
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class ShowSimpleMultivariableFunction(Scene):
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def construct(self):
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scale_val = 1.5
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func_tex = TexMobject(
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"C(", "x_1,", "x_2,", "\\dots,", "x_n", ")", "=",
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)
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func_tex.scale(scale_val)
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func_tex.shift(2 * LEFT)
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alt_func_tex = TexMobject(
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"C(", "x,", "y", ")", "="
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)
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alt_func_tex.scale(scale_val)
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for tex in func_tex, alt_func_tex:
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tex.set_color_by_tex_to_color_map({
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"C(": RED,
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")": RED,
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})
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alt_func_tex.move_to(func_tex, RIGHT)
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inputs = func_tex[1:-2]
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self.add(func_tex)
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many_inputs = TexMobject(*[
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"x_{%d}, " % d for d in range(1, 25)
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])
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many_inputs.scale_to_fit_width(FRAME_WIDTH)
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many_inputs.to_edge(UL)
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inputs_brace = Brace(inputs, UP)
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inputs_brace_text = inputs_brace.get_text("Multiple inputs")
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decimal = DecimalNumber(0)
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decimal.scale(scale_val)
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decimal.next_to(tex, RIGHT)
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value_tracker = ValueTracker(0)
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self.add(ContinualMovement(value_tracker, rate=0.5))
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decimal_change = ContinualChangingDecimal(
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decimal,
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lambda a: 1 + np.sin(value_tracker.get_value())
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)
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self.add(decimal_change)
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output_brace = Brace(decimal, DOWN)
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output_brace_text = output_brace.get_text("Single output")
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self.wait(2)
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self.play(GrowFromCenter(inputs_brace))
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self.play(Write(inputs_brace_text))
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self.play(GrowFromCenter(output_brace))
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self.play(Write(output_brace_text))
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self.wait(3)
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self.play(
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ReplacementTransform(
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inputs,
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many_inputs[:len(inputs)]
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),
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LaggedStart(
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FadeIn,
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many_inputs[len(inputs):]
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),
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FadeOut(inputs_brace),
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FadeOut(inputs_brace_text),
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)
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self.wait()
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self.play(
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ReplacementTransform(
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func_tex[0], alt_func_tex[0]
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),
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Write(alt_func_tex[1:3]),
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LaggedStart(FadeOutAndShiftDown, many_inputs)
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)
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self.wait(3)
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class ShowGraphWithVectors(ExternallyAnimatedScene):
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pass
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class ShowFunction(Scene):
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def construct(self):
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func = TexMobject(
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"f(x, y) = e^{-x^2 + \\cos(2y)}",
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tex_to_color_map={
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"x": BLUE,
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"y": RED,
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}
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)
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func.scale(1.5)
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self.play(FadeInFromDown(func))
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self.wait()
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class ShowExampleFunctionGraph(ExternallyAnimatedScene):
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pass
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class ShowGradient(Scene):
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def construct(self):
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lhs = TexMobject(
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"\\nabla f(x, y)=",
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tex_to_color_map={"x": BLUE, "y": RED}
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)
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vector = Matrix([
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["\\partial f / \\partial x"],
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["\\partial f / \\partial y"],
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], v_buff=1)
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gradient = VGroup(lhs, vector)
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gradient.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
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gradient.scale(1.5)
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del_x, del_y = partials = vector.get_entries()
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background_rects = VGroup()
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for partial, color in zip(partials, [BLUE, RED]):
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partial[-1].set_color(color)
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partial.rect = SurroundingRectangle(
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partial, buff=MED_SMALL_BUFF
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)
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partial.rect.set_stroke(width=0)
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partial.rect.set_fill(color=color, opacity=0.5)
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background_rects.add(partial.rect.copy())
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background_rects.set_fill(opacity=0.1)
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partials.set_fill(opacity=0)
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self.play(
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LaggedStart(FadeIn, gradient),
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LaggedStart(
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FadeIn, background_rects,
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rate_func=squish_rate_func(smooth, 0.5, 1)
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)
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)
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self.wait()
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for partial in partials:
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self.play(DrawBorderThenFill(partial.rect))
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self.wait()
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self.play(FadeOut(partial.rect))
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self.wait()
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for partial in partials:
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self.play(Write(partial))
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self.wait()
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class ExampleGraphHoldXConstant(ExternallyAnimatedScene):
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pass
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class ExampleGraphHoldYConstant(ExternallyAnimatedScene):
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pass
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class TakePartialDerivatives(Scene):
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def construct(self):
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tex_to_color_map = {
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"x": BLUE,
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"y": RED,
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}
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func_tex = TexMobject(
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"f", "(", "x", ",", "y", ")", "=",
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"e^{", "-x^2", "+ \\cos(2y)}",
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tex_to_color_map=tex_to_color_map
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)
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partial_x = TexMobject(
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"{\\partial", "f", "\\over", "\\partial", "x}", "=",
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"\\left(", "e^", "{-x^2", "+ \\cos(2y)}", "\\right)",
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"(", "-2", "x", ")",
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tex_to_color_map=tex_to_color_map,
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)
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partial_y = TexMobject(
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"{\\partial", "f", "\\over", "\\partial", "y}", "=",
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"\\left(", "e^", "{-x^2", "+ \\cos(", "2", "y)}", "\\right)",
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"(", "-\\sin(", "2", "y)", "\\cdot 2", ")",
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tex_to_color_map=tex_to_color_map,
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)
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partials = VGroup(partial_x, partial_y)
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for mob in func_tex, partials:
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mob.scale(1.5)
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func_tex.move_to(2 * UP + 3 * LEFT)
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for partial in partials:
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partial.next_to(func_tex, DOWN, buff=LARGE_BUFF)
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top_eq_x = func_tex.get_part_by_tex("=").get_center()[0]
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low_eq_x = partial.get_part_by_tex("=").get_center()[0]
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partial.shift((top_eq_x - low_eq_x) * RIGHT)
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index = func_tex.index_of_part_by_tex("e^")
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exp_rect = SurroundingRectangle(func_tex[index + 1:], buff=0)
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exp_rect.set_stroke(width=0)
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exp_rect.set_fill(GREEN, opacity=0.5)
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xs = func_tex.get_parts_by_tex("x", substring=False)
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ys = func_tex.get_parts_by_tex("y", substring=False)
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for terms in xs, ys:
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terms.rects = VGroup(*[
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SurroundingRectangle(term, buff=0.5 * SMALL_BUFF)
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for term in terms
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])
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terms.arrows = VGroup(*[
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Vector(0.5 * DOWN).next_to(rect, UP, SMALL_BUFF)
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for rect in terms.rects
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])
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treat_as_constant = TextMobject("Treat as a constant")
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treat_as_constant.next_to(ys.arrows[1], UP)
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# Start to show partial_x
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self.play(FadeInFromDown(func_tex))
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self.wait()
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self.play(
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ReplacementTransform(func_tex[0].copy(), partial_x[1]),
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Write(partial_x[0]),
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Write(partial_x[2:4]),
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Write(partial_x[6]),
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)
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self.play(
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ReplacementTransform(func_tex[2].copy(), partial_x[4])
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)
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self.wait()
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# Label y as constant
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self.play(LaggedStart(ShowCreation, ys.rects))
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self.play(
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LaggedStart(GrowArrow, ys.arrows, lag_ratio=0.8),
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Write(treat_as_constant)
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)
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self.wait(2)
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# Perform partial_x derivative
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self.play(FadeIn(exp_rect), Animation(func_tex))
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self.wait()
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pxi1 = 8
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pxi2 = 15
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self.play(
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ReplacementTransform(
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func_tex[7:].copy(),
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partial_x[pxi1:pxi2],
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),
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FadeIn(partial_x[pxi1 - 1:pxi1]),
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FadeIn(partial_x[pxi2]),
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)
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self.wait(2)
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self.play(
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ReplacementTransform(
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partial_x[10:12].copy(),
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partial_x[pxi2 + 2:pxi2 + 4],
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path_arc=-(TAU / 4)
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),
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FadeIn(partial_x[pxi2 + 1]),
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FadeIn(partial_x[-1]),
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)
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self.wait(2)
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# Swap out partial_x for partial_y
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self.play(
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FadeOutAndShiftDown(partial_x),
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FadeOut(ys.rects),
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FadeOut(ys.arrows),
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FadeOut(treat_as_constant),
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FadeOut(exp_rect),
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Animation(func_tex)
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)
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self.play(FadeInFromDown(partial_y[:7]))
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self.wait()
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treat_as_constant.next_to(xs.arrows[1], UP, SMALL_BUFF)
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self.play(
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LaggedStart(ShowCreation, xs.rects),
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LaggedStart(GrowArrow, xs.arrows),
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Write(treat_as_constant),
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lag_ratio=0.8
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)
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self.wait()
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# Show same outer derivative
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self.play(
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ReplacementTransform(
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func_tex[7:].copy(),
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partial_x[pxi1:pxi2],
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),
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FadeIn(partial_x[pxi1 - 2:pxi1]),
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FadeIn(partial_x[pxi2]),
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)
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self.wait()
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self.play(
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ReplacementTransform(
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partial_y[12:16].copy(),
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partial_y[pxi2 + 3:pxi2 + 7],
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path_arc=-(TAU / 4)
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),
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FadeIn(partial_y[pxi2 + 2]),
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FadeIn(partial_y[-1]),
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)
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self.wait()
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self.play(ReplacementTransform(
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partial_y[-5].copy(),
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partial_y[-2],
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path_arc=-PI
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))
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self.wait()
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class ShowDerivativeAtExamplePoint(Scene):
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def construct(self):
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tex_to_color_map = {
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"x": BLUE,
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"y": RED,
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}
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func_tex = TexMobject(
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"f", "(", "x", ",", "y", ")", "=",
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"e^{", "-x^2", "+ \\cos(2y)}",
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tex_to_color_map=tex_to_color_map
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)
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gradient_tex = TexMobject(
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"\\nabla", "f", "(", "x", ",", "y", ")", "=",
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tex_to_color_map=tex_to_color_map
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)
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partial_vect = Matrix([
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["{\\partial f / \\partial x}"],
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["{\\partial f / \\partial y}"],
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])
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partial_vect.get_mob_matrix()[0, 0][-1].set_color(BLUE)
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partial_vect.get_mob_matrix()[1, 0][-1].set_color(RED)
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result_vector = self.get_result_vector("x", "y")
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gradient = VGroup(
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gradient_tex,
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partial_vect,
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TexMobject("="),
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result_vector
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)
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gradient.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
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func_tex.to_edge(UP)
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gradient.next_to(func_tex, DOWN, buff=LARGE_BUFF)
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example_lhs = TexMobject(
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"\\nabla", "f", "(", "1", ",", "3", ")", "=",
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tex_to_color_map={"1": BLUE, "3": RED},
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)
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example_result_vector = self.get_result_vector("1", "3")
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example_rhs = DecimalMatrix([[-1.92], [0.54]])
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example = VGroup(
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example_lhs,
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example_result_vector,
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TexMobject("="),
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example_rhs,
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)
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example.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
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example.next_to(gradient, DOWN, LARGE_BUFF)
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self.add(func_tex, gradient)
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self.wait()
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self.play(
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ReplacementTransform(gradient_tex.copy(), example_lhs),
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ReplacementTransform(result_vector.copy(), example_result_vector),
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)
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self.wait()
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self.play(Write(example[2:]))
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self.wait()
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def get_result_vector(self, x, y):
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result_vector = Matrix([
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["e^{-%s^2 + \\cos(2\\cdot %s)} (-2\\cdot %s)" % (x, y, x)],
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["e^{-%s^2 + \\cos(2\\cdot %s)} \\big(-\\sin(2\\cdot %s) \\cdot 2\\big)" % (x, y, y)],
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], v_buff=1.2, element_alignment_corner=ORIGIN)
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x_terms = VGroup(
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result_vector.get_mob_matrix()[0, 0][2],
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result_vector.get_mob_matrix()[1, 0][2],
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result_vector.get_mob_matrix()[0, 0][-2],
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)
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y_terms = VGroup(
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result_vector.get_mob_matrix()[0, 0][11],
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result_vector.get_mob_matrix()[1, 0][11],
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result_vector.get_mob_matrix()[1, 0][-5],
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)
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x_terms.set_color(BLUE)
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y_terms.set_color(RED)
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return result_vector
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