finished area model scene 2 (normal dist)

active_projects/eop/chapter1.py

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