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finished area model scene 2 (normal dist)
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Ben Hambrecht
parent
83bebfb109
commit
ad6b1fee20
1 changed files with 75 additions and 55 deletions
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@ -740,95 +740,115 @@ class IllustrateAreaModel1(Scene):
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class IllustrateAreaModel2(GraphScene):
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CONFIG = {
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"x_min" : -3.5,
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"x_max" : 3.5,
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"y_min" : -0,
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"y_max" : 0.6,
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"graph_origin": 3*DOWN,
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"num_rects": 20,
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"x_min" : -3.0,
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"x_max" : 3.0,
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"y_min" : 0,
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"y_max" : 1.0,
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"num_rects": 400,
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"y_axis_label" : "",
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"x_axis_label" : "",
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"variable_point_label" : "x",
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"y_axis_height" : 4,
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"graph_origin": 2.5 * DOWN + 3 * LEFT,
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"variable_point_label" : "a",
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"graph_origin": 2.5 * DOWN + 4 * RIGHT,
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"x_axis_width": 5,
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"y_axis_height": 3
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"y_axis_height": 5
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}
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def construct(self):
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x_max_1 = 0
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x_min_1 = -x_max_1
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x_max_2 = 3.5
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x_min_2 = -x_max_2
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# integral bounds
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x_min_1 = -0.0001
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x_max_1 = 0.0001
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x_min_2 = self.x_min
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x_max_2 = self.x_max
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self.setup_axes()
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graph = self.get_graph(lambda x: np.exp(-x**2) / ((0.5 * TAU) ** 0.5))
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self.remove(self.x_axis, self.y_axis)
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graph = self.get_graph(lambda x: np.exp(-x**2) * 2.0 / TAU ** 0.5)
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area = self.area = self.get_area(graph, x_min_1, x_max_1)
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self.add(graph)
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cdf_formula = TexMobject("P(|X-\mu| < x) = \int_{-x}^x {\exp(-{1\over 2}({t\over \sigma})^2) \over \sigma\sqrt{2\pi}} dt")
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cdf_formula.set_color_by_tex("x", YELLOW)
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cdf_formula.next_to(graph, RIGHT, buff = -1)
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self.add(cdf_formula)
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pdf_formula = TexMobject("p(x) = {1\over \sigma\sqrt{2\pi}}e^{-{1\over 2}({x\over\sigma})^2}")
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pdf_formula.set_color(graph.color)
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cdf_formula = TexMobject("P(|X| < ", "a", ") = \int", "_{-a}", "^a", "p(x) dx")
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cdf_formula.set_color_by_tex("a", YELLOW)
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cdf_formula.next_to(graph, LEFT, buff = 2)
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pdf_formula.next_to(cdf_formula, UP)
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formulas = VGroup(pdf_formula, cdf_formula)
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self.play(Write(pdf_formula))
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self.play(Write(cdf_formula))
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self.wait()
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self.play(ShowCreation(self.x_axis))
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self.play(ShowCreation(graph))
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self.play(FadeIn(area))
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self.v_graph = graph
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self.add_T_label(x_min_1, color = YELLOW, animated = False)
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self.add_T_label(
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x_min_1,
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label = "-a",
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side = LEFT,
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color = YELLOW,
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animated = False
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)
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self.add_T_label(
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x_max_1,
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label = "a",
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side = RIGHT,
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color = YELLOW,
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animated = False
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)
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self.remove(self.T_label_group, self.right_v_line)
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#self.T_label_group[0].set_fill(opacity = 0).set_stroke(width = 0)
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#self.T_label_group[1].set_fill(opacity = 0).set_stroke(width = 0)
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#self.right_v_line.set_fill(opacity = 0).set_stroke(width = 0)
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#self.add(self.T_label_group)
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area = self.area = self.get_area(graph, x_min_1, x_max_1)
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right_bound_label = TexMobject("x", color = YELLOW)
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right_bound_label.next_to(self.coords_to_point(0,0), DOWN)
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right_bound_label.target = right_bound_label.copy().next_to(self.coords_to_point(self.x_max,0), DOWN)
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right_bound_label.set_fill(opacity = 0).set_stroke(width = 0)
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left_bound_label = TexMobject("-x", color = YELLOW)
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left_bound_label.next_to(self.coords_to_point(0,0), DOWN)
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left_bound_label.target = right_bound_label.copy().next_to(self.coords_to_point(self.x_min,0), DOWN)
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left_bound_label.set_fill(opacity = 0).set_stroke(width = 0)
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#integral = self.get_riemann_rectangles(
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#graph,x_min = self.x_min, x_max = x_max_1)
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self.add(area)
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def integral_update_func(t):
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return 100 * scipy.special.erf(
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return scipy.special.erf(
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self.point_to_coords(self.right_v_line.get_center())[0]
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)
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cdf_value = DecimalNumber(0, unit = "\%")
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cdf_value.move_to(self.coords_to_point(0,0.2))
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def integral_update_func_percent(t):
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return 100 * integral_update_func(t)
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equals_sign = TexMobject("=").next_to(cdf_formula, buff = MED_LARGE_BUFF)
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cdf_value = DecimalNumber(0, color = graph.color, num_decimal_points = 3)
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cdf_value.next_to(equals_sign)
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self.play(
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FadeIn(equals_sign),
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FadeIn(cdf_value)
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)
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self.add_foreground_mobject(cdf_value)
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cdf_percentage = DecimalNumber(0, unit = "\%")
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cdf_percentage.move_to(self.coords_to_point(0,0.2))
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self.add_foreground_mobject(cdf_percentage)
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self.add(ContinualChangingDecimal(
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decimal_number_mobject = cdf_value,
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number_update_func = integral_update_func,
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num_decimal_points = 3
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))
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self.add(ContinualChangingDecimal(
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decimal_number_mobject = cdf_percentage,
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number_update_func = integral_update_func_percent,
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num_decimal_points = 1
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))
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anim = self.get_animation_integral_bounds_change(
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graph, x_min_2, x_max_2, run_time = 3)
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# changing_cdf_value = ChangingDecimal(
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# decimal_number_mobject = cdf_value,
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# number_update_func = integral_update_func,
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# num_decimal_points = 1
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# )
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anim = self.get_animation_integral_bounds_change(
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graph, x_min_2, x_max_2,
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run_time = 3)
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self.play(
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anim
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)
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rect = SurroundingRectangle(formulas, buff = 0.5 * MED_LARGE_BUFF)
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self.play(ShowCreation(rect))
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