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improved area model examples 1 and 2
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Ben Hambrecht
parent
8e7f33c65a
commit
dca4400b09
1 changed files with 107 additions and 74 deletions
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@ -1,6 +1,8 @@
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from big_ol_pile_of_manim_imports import *
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from big_ol_pile_of_manim_imports import *
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from old_projects.eoc.chapter8 import *
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from old_projects.eoc.chapter8 import *
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import scipy.special
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COIN_RADIUS = 0.3
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COIN_RADIUS = 0.3
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COIN_THICKNESS = 0.4 * COIN_RADIUS
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COIN_THICKNESS = 0.4 * COIN_RADIUS
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COIN_FORESHORTENING = 0.3
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COIN_FORESHORTENING = 0.3
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@ -665,19 +667,35 @@ class IllustrateAreaModel1(Scene):
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label_B_knowing_A = label_B
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label_B_knowing_A = label_B
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self.play(FadeOut(label_B_copy))
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self.play(FadeOut(label_B_copy))
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self.remove(indep_formula.get_part_by_tex("P(B)"))
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label_B_knowing_A_copy = label_B_knowing_A.copy()
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label_B_knowing_A_copy = label_B_knowing_A.copy()
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self.add(label_B_knowing_A_copy)
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self.add(label_B_knowing_A_copy)
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self.play(
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self.play(
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label_B_knowing_A_copy.next_to, indep_formula[-2], RIGHT
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label_B_knowing_A_copy.next_to, indep_formula.get_part_by_tex("\cdot"), RIGHT,
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)
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)
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# solve formula for P(B|A)
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rearranged_formula = TexMobject(["P(B\mid A)", "=", "{P(A\\text{ and }B) \over P(A)}"])
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rearranged_formula.move_to(indep_formula)
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self.wait()
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self.wait()
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self.play(
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# in some places get_part_by_tex does not find the correct part
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# so I picked out fitting indices
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label_B_knowing_A_copy.move_to, rearranged_formula.get_part_by_tex("P(B\mid A)"),
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label_A_copy.move_to, rearranged_formula[-1][10],
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label_A_and_B_copy.move_to, rearranged_formula[-1][3],
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indep_formula.get_part_by_tex("=").move_to, rearranged_formula.get_part_by_tex("="),
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Transform(indep_formula.get_part_by_tex("\cdot"), rearranged_formula[-1][8]),
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)
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# # # # # # # # # # # # # # # # #
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# Old version with SampleSpace #
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# # # # # # # # # # # # # # # # #
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# def show_independent_events(self):
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# def show_independent_events(self):
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# sample_space = SampleSpace(
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# sample_space = SampleSpace(
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@ -747,63 +765,108 @@ class IllustrateAreaModel1(Scene):
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def color_label(self, label):
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# def color_label(self, label):
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label.set_color_by_tex("B", RED)
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# label.set_color_by_tex("B", RED)
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label.set_color_by_tex("I", GREEN)
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# label.set_color_by_tex("I", GREEN)
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class IllustrateAreaModel2(GraphScene):
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class IllustrateAreaModel2(AreaIsDerivative):
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CONFIG = {
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CONFIG = {
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"y_max" : 4,
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"x_min" : -5,
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"y_min" : -4,
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"x_max" : 5,
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"num_iterations" : 7,
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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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"y_axis_label" : "",
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"y_axis_label" : "",
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"num_rects" : 50,
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"x_axis_label" : "",
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"dT" : 0.25,
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"variable_point_label" : "x",
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"variable_point_label" : "T",
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"y_axis_height" : 4
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"area_opacity" : 0.8,
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}
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}
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def construct(self):
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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 = 5
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x_min_2 = -x_max_2
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self.setup_axes()
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self.setup_axes()
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self.introduce_variable_area()
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graph = self.get_graph(lambda x: np.exp(-x**2) / ((0.5 * TAU) ** 0.5))
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return
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self.add(graph)
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graph, label = self.get_v_graph_and_label()
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rect_list = self.get_riemann_rectangles_list(
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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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graph, self.num_iterations
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cdf_formula.set_color_by_tex("x", YELLOW)
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cdf_formula.next_to(graph, UP, buff = 1)
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self.add(cdf_formula)
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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.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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self.point_to_coords(self.right_v_line.get_center())[0]
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)
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)
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VGroup(*rect_list).set_fill(opacity = 0.8)
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rects = rect_list[0]
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self.play(ShowCreation(graph))
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cdf_value = DecimalNumber(0, unit = "\%")
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self.play(Write(rects))
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cdf_value.move_to(self.coords_to_point(0,0.2))
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for new_rects in rect_list[1:]:
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self.add_foreground_mobject(cdf_value)
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rects.align_submobjects(new_rects)
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for every_other_rect in rects[::2]:
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self.add(ContinualChangingDecimal(
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every_other_rect.set_fill(opacity = 0)
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decimal_number_mobject = cdf_value,
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self.play(Transform(
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number_update_func = integral_update_func,
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rects, new_rects,
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num_decimal_points = 1
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run_time = 2,
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submobject_mode = "lagged_start"
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))
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))
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self.wait()
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# self.play(FadeOut(self.x_axis.numbers))
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anim = self.get_animation_integral_bounds_change(
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self.add_T_label(6)
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graph, x_min_2, x_max_2, run_time = 3)
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self.change_area_bounds(
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new_t_max = 4,
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# changing_cdf_value = ChangingDecimal(
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rate_func = there_and_back,
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# decimal_number_mobject = cdf_value,
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run_time = 2
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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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self.play(
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anim
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)
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)
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def func(self, x):
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return np.exp(-x**2/2)
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class AreaSplitting(Scene):
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class AreaSplitting(Scene):
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@ -936,36 +999,6 @@ class AreaSplitting(Scene):
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class Test(GraphScene):
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CONFIG = {
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"x_min" : -3,
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"x_max" : 3,
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"y_min" : -0.2,
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"y_max" : 2.0,
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"graph_origin": 3*DOWN,
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"num_rects": 100
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}
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def construct(self):
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x_max_1 = -2.99
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x_max_2 = 3.0
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self.setup_axes()
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graph = self.get_graph(lambda x: np.exp(-x**2/2))
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self.add(graph)
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area = self.area = self.get_area(graph,self.x_min, x_max_1)
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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(integral)
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anim = self.get_animation_integral_bounds_change(
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graph, self.x_min, x_max_2, run_time = 3)
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self.play(anim)
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