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https://github.com/3b1b/manim.git
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End of EoLA
This commit is contained in:
Grant Sanderson
@ -1643,6 +1643,8 @@ class IntroducePolynomialSpace(Scene):
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def show_example_coordinates(self):
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coords = Matrix(["5", "3", "1", "0", "0", "\\vdots"])
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for i, color in enumerate([X_COLOR, Y_COLOR, Z_COLOR]):
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coords[i].highlight(color)
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self.poly1.generate_target()
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equals = TexMobject("=").next_to(coords, LEFT)
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self.poly1.target.next_to(equals, LEFT)
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@ -1714,34 +1716,32 @@ class IntroducePolynomialSpace(Scene):
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rate_func = there_and_back
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)
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self.remove(*self.get_mobjects_from_last_animation())
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self.add(self.poly2)
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self.dither()
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self.play(*map(FadeOut, [self.poly2, coords, equals]))
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def derivative_as_matrix(self):
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matrix = Matrix([
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["?"]*4 + ["\\cdots"]
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for x in range(4)
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[
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str(j) if j == i+1 else "0"
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for j in range(4)
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] + ["\\cdots"]
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for i in range(4)
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] + [
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["\\vdots"]*4 + ["\\ddots"]
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])
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matrix.shift(2*LEFT)
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matrix.get_entries().gradient_highlight(GREEN, YELLOW, MAROON_B)
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mob_matrix = matrix.get_mob_matrix()
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diag_entries = VGroup(*[
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matrix.get_mob_matrix()[i, i+1]
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for i in range(3)
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])
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##Horrible
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last_col = VGroup(*mob_matrix[:,-1])
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last_col = VGroup(*matrix.get_mob_matrix()[:,-1])
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last_col_top = last_col.get_top()
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last_col.arrange_submobjects(DOWN, buff = 0.83)
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last_col.move_to(last_col_top, aligned_edge = UP+RIGHT)
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##End horrible
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colors = [X_COLOR, Y_COLOR, Z_COLOR, MAROON_B, YELLOW]
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for i, j in it.product(*[range(4)]*2):
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entry = mob_matrix[i, j]
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if j == i+1:
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entry.target = TexMobject(str(j))
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else:
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entry.target = TexMobject("0")
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entry.target.scale(0.8).move_to(entry)
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entry.target.highlight(colors[j])
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matrix.highlight_columns(X_COLOR, Y_COLOR, Z_COLOR, MAROON_B)
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deriv = TexMobject("\\dfrac{d}{dx}")
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equals = TexMobject("=")
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@ -1751,85 +1751,140 @@ class IntroducePolynomialSpace(Scene):
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self.play(FadeIn(deriv), FadeIn(equals))
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self.play(Write(matrix))
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self.dither()
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basis_derivatives = [
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"0",
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"1",
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"2x",
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"3x^2",
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]
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arrays = [
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["0", "0", "0", "0", "\\vdots"],
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["1", "0", "0", "0", "\\vdots"],
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["0", "2", "0", "0", "\\vdots"],
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["0", "0", "3", "0", "\\vdots"],
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]
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qunits = zip(
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it.count(),
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self.basis,
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self.basis_functions,
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basis_derivatives,
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arrays
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)
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for j, basis, basis_func, basis_deriv_tex, arr in qunits:
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matrix.save_state()
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matrix.generate_target()
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matrix.target.scale(0.35)
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matrix.target.to_corner(UP+LEFT)
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func, func_equals = basis_func
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deriv_copy = deriv.copy()
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movers = [func, equals, deriv_copy, basis, func_equals]
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for mob in movers:
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mob.generate_target()
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mob.save_state()
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lp, rp = TexMobject("()")
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basis_deriv = TexMobject(basis_deriv_tex)
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new_equals = TexMobject("=")
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coords = Matrix(arr)
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coords.highlight(basis.get_color())
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basis_deriv.highlight(basis.get_color())
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group = VGroup(
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func.target, equals.target, deriv_copy.target,
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lp, basis.target, rp, func_equals.target,
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basis_deriv, new_equals, coords
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)
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group.arrange_submobjects()
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group.next_to(deriv)
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self.play(*it.chain(
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map(MoveToTarget, [
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matrix, func, equals,
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deriv_copy, basis, func_equals
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]),
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map(Write, [lp, rp])
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))
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self.dither()
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self.play(*map(Write, [basis_deriv, new_equals, coords]))
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self.dither()
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self.play(*it.chain(
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[mob.restore for mob in movers+[matrix]],
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map(FadeOut, [lp, rp, basis_deriv, new_equals]),
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[coords.to_edge, RIGHT, 4]
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))
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column = VGroup(*[
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mob_matrix[i,j]
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for i in range(4)
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])
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column_target = VGroup(*[
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mob.target
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for mob in column
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])
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entries = VGroup(*coords.get_entries()[:4])
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diag_entries.save_state()
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diag_entries.generate_target()
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diag_entries.target.scale_in_place(1.2)
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diag_entries.target.highlight(YELLOW)
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for anim in MoveToTarget(diag_entries), diag_entries.restore:
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self.play(
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Transform(entries, column_target),
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FadeOut(coords.get_brackets()),
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FadeOut(coords.get_entries()[-1]),
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Transform(column, column_target)
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anim,
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submobject_mode = "lagged_start",
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run_time = 1.5,
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)
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self.remove(coords)
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self.dither()
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matrix.generate_target()
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matrix.target.to_corner(DOWN+LEFT).shift(0.25*UP)
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deriv.generate_target()
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deriv.target.next_to(
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matrix.target, UP,
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buff = MED_BUFF,
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aligned_edge = LEFT
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)
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deriv.target.shift(0.25*RIGHT)
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self.play(
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FadeOut(equals),
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*map(MoveToTarget, [matrix, deriv])
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)
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poly = TexMobject(
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"(", "1", "x^3", "+",
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"5", "x^2", "+",
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"4", "x", "+",
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"5", ")"
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)
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coefs = VGroup(*np.array(poly)[[10, 7, 4, 1]])
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VGroup(*poly[1:3]).highlight(MAROON_B)
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VGroup(*poly[4:6]).highlight(Z_COLOR)
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VGroup(*poly[7:9]).highlight(Y_COLOR)
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VGroup(*poly[10:11]).highlight(X_COLOR)
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poly.next_to(deriv)
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self.play(FadeIn(poly))
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array = Matrix(list(coefs.copy()) + [TexMobject("\\vdots")])
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array.next_to(matrix, RIGHT)
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self.play(Write(array.get_brackets()))
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to_remove = []
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for coef, entry in zip(coefs, array.get_entries()):
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self.play(Transform(coef.copy(), entry))
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to_remove += self.get_mobjects_from_last_animation()
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self.play(Write(array.get_entries()[-1]))
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to_remove += self.get_mobjects_from_last_animation()
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self.remove(*to_remove)
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self.add(array)
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eq1, eq2 = TexMobject("="), TexMobject("=")
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eq1.next_to(poly)
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eq2.next_to(array)
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poly_result = TexMobject(
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"3", "x^2", "+",
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"10", "x", "+",
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"4"
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)
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poly_result.next_to(eq1)
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brace = Brace(poly_result, buff = 0)
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self.play(*map(Write, [eq1, eq2, brace]))
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result_coefs = VGroup(*np.array(poly_result)[[6, 3, 0]])
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VGroup(*poly_result[0:2]).highlight(MAROON_B)
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VGroup(*poly_result[3:5]).highlight(Z_COLOR)
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VGroup(*poly_result[6:]).highlight(Y_COLOR)
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result_terms = [
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VGroup(*poly_result[6:]),
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VGroup(*poly_result[3:6]),
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VGroup(*poly_result[0:3]),
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]
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relevant_entries = VGroup(*array.get_entries()[1:4])
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dots = [TexMobject("\\cdot") for x in range(3)]
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result_entries = []
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for entry, diag_entry, dot in zip(relevant_entries, diag_entries, dots):
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entry.generate_target()
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diag_entry.generate_target()
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group = VGroup(diag_entry.target, dot, entry.target)
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group.arrange_submobjects()
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result_entries.append(group)
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result_array = Matrix(
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result_entries + [
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TexMobject("0"),
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TexMobject("\\vdots")
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]
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)
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result_array.next_to(eq2)
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rects = [
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Rectangle(
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color = YELLOW
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).replace(
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VGroup(*matrix.get_mob_matrix()[i,:]),
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stretch = True
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).stretch_in_place(1.1, 0).stretch_in_place(1.3, 1)
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for i in range(3)
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]
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vert_rect = Rectangle(color = YELLOW)
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vert_rect.replace(array.get_entries(), stretch = True)
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vert_rect.stretch_in_place(1.1, 1)
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vert_rect.stretch_in_place(1.5, 0)
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tuples = zip(
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relevant_entries,
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diag_entries,
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result_entries,
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rects,
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result_terms,
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coefs[1:]
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)
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self.play(Write(result_array.get_brackets()))
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for entry, diag_entry, result_entry, rect, result_term, coef in tuples:
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self.play(FadeIn(rect), FadeIn(vert_rect))
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self.dither()
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self.play(
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entry.scale_in_place, 1.2,
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diag_entry.scale_in_place, 1.2,
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)
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diag_entry_target, dot, entry_target = result_entry
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self.play(
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Transform(entry.copy(), entry_target),
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Transform(diag_entry.copy(), diag_entry_target),
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entry.scale_in_place, 1/1.2,
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diag_entry.scale_in_place, 1/1.2,
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Write(dot)
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)
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self.dither()
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self.play(Transform(coef.copy(), VGroup(result_term)))
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self.dither()
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self.play(FadeOut(rect), FadeOut(vert_rect))
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self.play(*map(Write, result_array.get_entries()[3:]))
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self.dither()
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class MatrixVectorMultiplicationAndDerivative(TeacherStudentsScene):
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def construct(self):
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@ -2046,20 +2101,21 @@ class ShowVectorSpaces(Scene):
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return arrays
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def get_functions(self):
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axes = Axes()
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axes.scale(0.3)
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functions = VGroup(*[
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TexMobject(poly)
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for poly in [
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"x^2+3x+5",
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"4x^7-5x^2",
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"x^{100}+2x^{99}+3x^{98}",
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"3x-7",
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"x^{1{,}000{,}000{,}000}+1",
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"\\vdots",
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FunctionGraph(func, x_min = -4, x_max = 4)
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for func in [
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lambda x : x**3 - 9*x,
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lambda x : x**3 - 4*x,
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lambda x : x**2 - 1,
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]
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])
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functions.arrange_submobjects(DOWN, buff = MED_BUFF)
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functions.stretch_to_fit_width(SPACE_WIDTH/2.)
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functions.stretch_to_fit_height(6)
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functions.gradient_highlight(YELLOW, MAROON_B)
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return functions
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functions.center()
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return VGroup(axes, functions)
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class ToolsOfLinearAlgebra(Scene):
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def construct(self):
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@ -253,14 +253,18 @@ class Mobject(object):
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self.to_edge(vect, **kwargs)
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return self
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def stretch_in_place(self, factor, dim):
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self.do_in_place(self.stretch, factor, dim)
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return self
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def stretch_to_fit(self, length, dim, stretch = True):
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old_length = self.length_over_dim(dim)
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if old_length == 0:
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return self
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if stretch:
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self.do_in_place(self.stretch, length/old_length, dim)
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self.stretch_in_place(length/old_length, dim)
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else:
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self.do_in_place(self.scale, length/old_length)
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self.scale_in_place(length/old_length)
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return self
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def stretch_to_fit_width(self, width):
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@ -497,9 +501,6 @@ class Mobject(object):
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def __iter__(self):
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return iter(self.split())
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def __len__(self):
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return len(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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return result + self.submobjects
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