mirror of
https://github.com/3b1b/manim.git
synced 2025-08-03 04:04:36 +08:00
75% of Chapter 6
This commit is contained in:
Grant Sanderson
343
eola/chapter6.py
343
eola/chapter6.py
@ -234,6 +234,24 @@ class MachineLearningNetwork(Scene):
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self.play(Write(mob), run_time = 2)
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self.dither()
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class ComplicatedSystem(Scene):
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def construct(self):
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system = TexMobject("""
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\\begin{align*}
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\\dfrac{1}{1-e^{2x-3y+4z}} &= 1 \\\\ \\\\
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\\sin(xy) + z^2 &= \\sqrt{y} \\\\ \\\\
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x^2 + y^2 &= e^{-z}
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\\end{align*}
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""")
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system.to_edge(UP)
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randy = Randolph().to_corner(DOWN+LEFT)
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self.add(randy)
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self.play(Write(system, run_time = 1))
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self.play(randy.change_mode, "sassy")
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self.play(Blink(randy))
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self.dither()
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class SystemOfEquations(Scene):
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def construct(self):
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equations = self.get_equations()
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@ -671,7 +689,6 @@ class LabeledExample(LinearSystemTransformationScene):
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self.title = title
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def construct(self):
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self.setup()
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self.dither()
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self.apply_transposed_matrix(self.t_matrix)
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self.dither()
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@ -714,26 +731,42 @@ class PlayInReverse(FullRankExmapleDet):
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class DescribeInverse(LinearTransformationScene):
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CONFIG = {
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"show_matrix" : False
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"show_actual_inverse" : False,
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"matrix_label" : "$A$",
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"inv_label" : "$A^{-1}$",
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}
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def construct(self):
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self.setup()
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title = TextMobject("Transformation:")
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new_title = TextMobject("Inverse transformation:")
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if self.show_matrix:
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matrix = Matrix(self.t_matrix.T)
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inv_matrix = Matrix(np.linalg.inv(self.t_matrix.T).astype('int'))
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matrix = Matrix(self.t_matrix.T)
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if not self.show_actual_inverse:
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inv_matrix = matrix.copy()
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neg_1 = TexMobject("-1")
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neg_1.move_to(
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inv_matrix.get_corner(UP+RIGHT),
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side_to_align = LEFT
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)
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neg_1.shift(0.1*RIGHT)
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inv_matrix.add(neg_1)
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matrix.add(VectorizedPoint(matrix.get_corner(UP+RIGHT)))
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else:
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matrix, inv_matrix = map(TexMobject, ["A", "A^{-1}"])
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inv_matrix = Matrix(np.linalg.inv(self.t_matrix.T).astype('int'))
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matrix.label = self.matrix_label
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inv_matrix.label = self.inv_label
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for m, text in (matrix, title), (inv_matrix, new_title):
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m.rect = BackgroundRectangle(m)
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m = VMobject(m.rect, m)
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m.add_to_back(BackgroundRectangle(m))
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text.add_background_rectangle()
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m.next_to(text, RIGHT)
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brace = Brace(m)
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label_mob = brace.get_text(m.label)
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label_mob.add_background_rectangle()
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m.add(brace, label_mob)
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text.add(m)
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if text.get_width() > 2*SPACE_WIDTH-1:
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text.scale_to_fit_width(2*SPACE_WIDTH-1)
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text.center().to_edge(UP)
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text.center().to_corner(UP+RIGHT)
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matrix.highlight(PINK)
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inv_matrix.highlight(YELLOW)
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self.add_foreground_mobject(title)
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self.apply_transposed_matrix(self.t_matrix)
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@ -745,13 +778,17 @@ class DescribeInverse(LinearTransformationScene):
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class ClockwiseCounterclockwise(DescribeInverse):
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CONFIG = {
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"t_matrix" : [[0, 1], [-1, 0]],
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"show_matrix" : True,
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"show_actual_inverse" : True,
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"matrix_label" : "$90^\\circ$ Couterclockwise",
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"inv_label" : "$90^\\circ$ Clockwise",
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}
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class ShearInverseShear(DescribeInverse):
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CONFIG = {
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"t_matrix" : [[1, 0], [1, 1]],
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"show_matrix" : True,
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"show_actual_inverse" : True,
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"matrix_label" : "Rightward shear",
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"inv_label" : "Leftward shear",
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}
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class MultiplyToIdentity(LinearTransformationScene):
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@ -810,18 +847,276 @@ class MultiplyToIdentity(LinearTransformationScene):
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self.play(Write(col2))
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self.dither()
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class TwoDInverseFormula(Scene):
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def construct(self):
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title = TextMobject("If you're curious...")
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title.highlight(YELLOW)
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title.to_edge(UP)
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morty = Mortimer().to_corner(DOWN+RIGHT)
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self.add(title, morty)
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matrix = [["a", "b"], ["c", "d"]]
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scaled_inv = [["d", "-b"], ["-c", "a"]]
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formula = TexMobject("""
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%s^{-1} = \\dfrac{1}{ad-bc} %s
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"""%(
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matrix_to_tex_string(matrix),
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matrix_to_tex_string(scaled_inv)
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))
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self.play(Write(formula))
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self.play(morty.change_mode, "confused")
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self.play(Blink(morty))
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class SymbolicInversion(Scene):
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def construct(self):
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vec = lambda s : "\\vec{\\textbf{%s}}"%s
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words = TextMobject("Once you have this:")
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words.to_edge(UP, buff = 2)
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inv = TexMobject("A^{-1}")
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inv.highlight(GREEN)
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inv.next_to(words.split()[-1], RIGHT, aligned_edge = DOWN)
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inv2 = inv.copy()
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start = TexMobject("A", vec("x"), "=", vec("v"))
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interim = TexMobject("A^{-1}", "A", vec("x"), "=", "A^{-1}", vec("v"))
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end = TexMobject(vec("x"), "=", "A^{-1}", vec("v"))
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A, x, eq, v = start.split()
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x.highlight(PINK)
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v.highlight(YELLOW)
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interim_mobs = [inv, A, x, eq, inv2, v]
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for i, mob in enumerate(interim_mobs):
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mob.interim = mob.copy().move_to(interim.split()[i])
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self.add(start)
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self.play(Write(words), FadeIn(inv), run_time = 1)
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self.dither()
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self.play(
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FadeOut(words),
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*[Transform(m, m.interim) for m in interim_mobs]
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)
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self.dither()
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product = VMobject(A, inv)
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product.brace = Brace(product)
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product.words = product.brace.get_text(
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"The ``do nothing'' matrix"
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)
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product.words.highlight(BLUE)
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self.play(
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GrowFromCenter(product.brace),
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Write(product.words, run_time = 1),
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product.highlight, BLUE
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)
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self.dither()
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self.play(*[
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ApplyMethod(m.highlight, BLACK)
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for m in product, product.brace, product.words
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])
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self.dither()
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self.play(ApplyFunction(
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lambda m : m.center().to_edge(UP),
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VMobject(x, eq, inv2, v)
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))
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self.dither()
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class PlayInReverseWithSolution(PlayInReverse):
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def setup(self):
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LinearTransformationScene.setup(self)
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equation = TexMobject([
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"\\vec{\\textbf{x}}",
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"=",
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"A^{-1}",
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"\\vec{\\textbf{v}}",
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])
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equation.to_edge(UP)
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equation.add_background_rectangle()
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self.add_foreground_mobject(equation)
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self.equation = equation
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self.x, eq, self.inv, self.v = equation.split()[1].split()
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self.x.highlight(PINK)
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self.v.highlight(YELLOW)
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self.inv.highlight(GREEN)
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class OneUniqueSolution(Scene):
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def construct(self):
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system = TexMobject("""
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\\begin{align*}
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ax + cy &= e \\\\
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bx + dy &= f
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\\end{align*}
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""")
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VMobject(*np.array(system.split())[[1, 8]]).highlight(X_COLOR)
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VMobject(*np.array(system.split())[[4, 11]]).highlight(Y_COLOR)
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brace = Brace(system, UP)
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brace.highlight(YELLOW)
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words = brace.get_text("One unique solution \\dots", "probably")
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words.highlight(YELLOW)
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words.split()[1].highlight(GREEN)
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self.add(system)
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self.dither()
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self.play(
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GrowFromCenter(brace),
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Write(words.split()[0])
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)
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self.dither()
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self.play(Write(words.split()[1], run_time = 1))
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self.dither()
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class ThreeDTransformAndReverse(Scene):
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pass
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class InversesDontAlwaysExist(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("$A^{-1}$ doesn't always exist")
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self.random_blink()
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self.dither()
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self.random_blink()
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class InvertNonInvertable(LinearTransformationScene):
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CONFIG = {
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"t_matrix" : [[2, 1], [-2, -1]]
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}
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def setup(self):
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LinearTransformationScene.setup(self)
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det_text = TexMobject("\\det(A) = 0")
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det_text.scale(1.5)
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det_text.to_corner(UP+LEFT)
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det_text.add_background_rectangle()
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self.add_foreground_mobject(det_text)
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def construct(self):
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no_func = TextMobject("No function does this")
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no_func.shift(2*UP)
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no_func.highlight(RED)
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no_func.add_background_rectangle()
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grid = VMobject(self.plane, self.i_hat, self.j_hat)
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grid.save_state()
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self.apply_transposed_matrix(self.t_matrix, path_arc = 0)
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self.dither()
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self.play(Write(no_func, run_time = 1))
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self.add_foreground_mobject(no_func)
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self.play(
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grid.restore,
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*map(Animation, self.foreground_mobjects),
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run_time = 3
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)
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self.dither()
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class OneInputMultipleOutputs(InvertNonInvertable):
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def construct(self):
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input_vectors = VMobject(*[
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Vector([x+2, x]) for x in np.arange(-4, 4.5, 0.5)
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])
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input_vectors.submobject_gradient_highlight(PINK, YELLOW)
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output_vector = Vector([4, 2], color = YELLOW)
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grid = VMobject(self.plane, self.i_hat, self.j_hat)
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grid.save_state()
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self.apply_transposed_matrix(self.t_matrix, path_arc = 0)
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self.play(ShowCreation(output_vector))
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single_input = TextMobject("Single vector")
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single_input.add_background_rectangle()
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single_input.next_to(output_vector.get_end(), UP)
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single_input.highlight(YELLOW)
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self.play(Write(single_input))
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self.dither()
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self.remove(single_input, output_vector)
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self.play(
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grid.restore,
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*[
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Transform(output_vector.copy(), input_vector)
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for input_vector in input_vectors.split()
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] + map(Animation, self.foreground_mobjects),
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run_time = 3
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)
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multiple_outputs = TextMobject(
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"Must map to \\\\",
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"multiple vectors"
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)
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multiple_outputs.split()[1].submobject_gradient_highlight(YELLOW, PINK)
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multiple_outputs.next_to(ORIGIN, DOWN).to_edge(RIGHT)
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multiple_outputs.add_background_rectangle()
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self.play(Write(multiple_outputs, run_time = 2))
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self.dither()
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class ThreeDOntoPlane(Scene):
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pass
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class ThreeDOntoLine(Scene):
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pass
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class ThreeDOntoPoint(Scene):
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pass
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class TowDColumnsDontSpan(LinearTransformationScene):
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CONFIG = {
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"t_matrix" : [[2, 1], [-2, -1]]
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}
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def construct(self):
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matrix = Matrix(self.t_matrix.T)
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matrix.highlight_columns(X_COLOR, Y_COLOR)
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matrix.add_to_back(BackgroundRectangle(matrix))
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self.add_foreground_mobject(matrix)
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brace = Brace(matrix)
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words = brace.get_text(
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"Columns don't",
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"span \\\\",
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"full output space"
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)
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words[1].highlight(PINK)
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words.add_background_rectangle()
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VMobject(matrix, brace, words).to_corner(UP+LEFT)
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self.apply_transposed_matrix(self.t_matrix, path_arc = 0)
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self.play(
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GrowFromCenter(brace),
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Write(words, run_time = 2)
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)
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self.dither()
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self.play(ApplyFunction(
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lambda m : m.scale(-1).shift(self.i_hat.get_end()),
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self.j_hat
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))
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for x in range(5):
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i_target, j_target = [
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m.copy().scale(random.uniform(-1.2, 1.2))
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for m in self.i_hat, self.j_hat
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]
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j_target.shift(-j_target.get_start()+i_target.get_end())
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self.play(Transform(
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VMobject(self.i_hat, j_hat, VectorizedPoint()),
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VMobject(i_target, j_target, VectorizedPoint()),
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submobject_mode = "lagged_start"
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))
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self.dither()
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if x == 2:
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self.play(ShowCreation(Vector([2, -1])))
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class ThreeDColumnsDontSpan(Scene):
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def construct(self):
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matrix = Matrix(np.array([
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[1, 1, 0],
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[0, 1, 1],
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[-1, -2, -1],
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]).T)
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matrix.highlight_columns(X_COLOR, Y_COLOR, Z_COLOR)
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brace = Brace(matrix)
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words = brace.get_text(
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"Columns don't",
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"span \\\\",
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"full output space"
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)
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words[1].highlight(PINK)
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self.add(matrix)
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self.play(
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GrowFromCenter(brace),
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Write(words, run_time = 2)
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)
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self.dither()
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@ -260,6 +260,10 @@ class LinearTransformationScene(VectorScene):
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"t_matrix" : np.array([[3, 0], [1, 2]]),
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}
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def setup(self):
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if hasattr(self, "has_setup"):
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return
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self.has_setup = True
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##^This is to not break all the old Scenes
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self.background_mobjects = []
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self.foreground_mobjects = []
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self.transformable_mobjects = []
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@ -454,7 +454,13 @@ class Mobject(object):
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raise Exception("Not implemented")
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## Family matters
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## Family matters
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def __getitem__(self, index):
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return self.split()[index]
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def __iter__(self):
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return iter(self.split())
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def split(self):
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result = [self] if len(self.points) > 0 else []
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@ -43,9 +43,9 @@ class TexMobject(SVGMobject):
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digest_config(self, kwargs, locals())
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##TODO, Eventually remove this
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if len(args) == 1 and isinstance(args[0], list):
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args = args[0]
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self.args = args[0]
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##
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assert(all([isinstance(a, str) for a in args]))
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assert(all([isinstance(a, str) for a in self.args]))
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VMobject.__init__(self, **kwargs)
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self.move_into_position()
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if self.organize_left_to_right:
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@ -133,8 +133,8 @@ class Brace(TexMobject):
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mob.next_to(self, self.direction, **kwargs)
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return self
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def get_text(self, text, **kwargs):
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text_mob = TextMobject(text)
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def get_text(self, *text, **kwargs):
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text_mob = TextMobject(*text)
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self.put_at_tip(text_mob, **kwargs)
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return text_mob
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@ -31,8 +31,12 @@ class Scene(object):
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self.mobjects = []
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self.num_plays = 0
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self.setup()
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self.construct(*self.construct_args)
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def setup(self):
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pass #For any common super classes to set up.
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def construct(self):
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pass #To be implemented in subclasses
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Block a user