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Beginning of ShowPlan in Uncertainty
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Grant Sanderson
parent
6f829c98fb
commit
3b8bbbccab
1 changed files with 139 additions and 47 deletions
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@ -39,55 +39,46 @@ class GaussianDistributionWrapper(Line):
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"""
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This is meant to encode a 2d normal distribution as
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a mobject (so as to be able to have it be interpolated
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during animations). It is a line whose start_point coordinates
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encode the coordinates of mu, and whose end_point - start_point
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encodes the coordinates of sigma.
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during animations). It is a line whose center is the mean
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mu of a distribution, and whose radial vector (center to end)
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is the distribution's standard deviation
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"""
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CONFIG = {
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"stroke_width" : 0,
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"mu_x" : 0,
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"sigma_x" : 1,
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"mu_y" : 0,
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"sigma_y" : 0,
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"mu" : ORIGIN,
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"sigma" : RIGHT,
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}
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def __init__(self, **kwargs):
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Line.__init__(self, ORIGIN, RIGHT, **kwargs)
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self.change_parameters(self.mu_x, self.mu_y, self.sigma_x, self.sigma_y)
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self.change_parameters(self.mu, self.sigma)
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def change_parameters(self, mu_x = None, mu_y = None, sigma_x = None, sigma_y = None):
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curr_parameters = self.get_parameteters()
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args = [mu_x, mu_y, sigma_x, sigma_y]
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new_parameters = [
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arg or curr
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for curr, arg in zip(curr_parameters, args)
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]
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mu_x, mu_y, sigma_x, sigma_y = new_parameters
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mu_point = mu_x*RIGHT + mu_y*UP
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sigma_vect = sigma_x*RIGHT + sigma_y*UP
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self.put_start_and_end_on(mu_point, mu_point + sigma_vect)
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def change_parameters(self, mu = None, sigma = None):
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curr_mu, curr_sigma = self.get_parameters()
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mu = mu if mu is not None else curr_mu
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sigma = sigma if sigma is not None else curr_sigma
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self.put_start_and_end_on(mu - sigma, mu + sigma)
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return self
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def get_parameteters(self):
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def get_parameters(self):
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""" Return mu_x, mu_y, sigma_x, sigma_y"""
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start, end = self.get_start_and_end()
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return tuple(it.chain(start[:2], (end - start)[:2]))
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center, end = self.get_center(), self.get_end()
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return center, end-center
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def get_random_points(self, size = 1):
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mu_x, mu_y, sigma_x, sigma_y = self.get_parameteters()
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x_vals = np.random.normal(mu_x, sigma_x, size)
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y_vals = np.random.normal(mu_y, sigma_y, size)
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mu, sigma = self.get_parameters()
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return np.array([
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x*RIGHT + y*UP
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for x, y in zip(x_vals, y_vals)
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np.array([
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np.random.normal(mu_coord, sigma_coord)
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for mu_coord, sigma_coord in zip(mu, sigma)
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])
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for x in range(size)
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])
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class ProbabalisticMobjectCloud(ContinualAnimation):
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CONFIG = {
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"fill_opacity" : 0.25,
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"n_copies" : 100,
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"gaussian_distribution_wrapper_config" : {
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"sigma_x" : 1,
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}
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"gaussian_distribution_wrapper_config" : {}
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}
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def __init__(self, prototype, **kwargs):
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digest_config(self, kwargs)
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@ -142,6 +133,14 @@ class ProbabalisticVectorCloud(ProbabalisticMobjectCloud):
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point
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)
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class RadarDish(SVGMobject):
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CONFIG = {
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"file_name" : "radar_dish",
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"color" : LIGHT_GREY,
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}
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###################
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class MentionUncertaintyPrinciple(TeacherStudentsScene):
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@ -152,32 +151,33 @@ class MentionUncertaintyPrinciple(TeacherStudentsScene):
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dot_cloud = ProbabalisticDotCloud()
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vector_cloud = ProbabalisticVectorCloud(
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gaussian_distribution_wrapper_config = {"sigma_x" : 0.2},
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center_func = dot_cloud.gaussian_distribution_wrapper.get_start,
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center_func = lambda : dot_cloud.gaussian_distribution_wrapper.get_parameters()[0],
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)
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for cloud in dot_cloud, vector_cloud:
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gdw = cloud.gaussian_distribution_wrapper
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gdw.move_to(title.get_center(), LEFT)
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gdw.shift(2*DOWN)
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cloud.gaussian_distribution_wrapper.next_to(
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title, DOWN, 2*LARGE_BUFF
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)
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vector_cloud.gaussian_distribution_wrapper.shift(3*RIGHT)
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def get_brace_text_group_update(gdw, vect, text):
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def get_brace_text_group_update(gdw, vect, text, color):
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brace = Brace(gdw, vect)
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text = brace.get_tex("\\sigma_{\\text{%s}}"%text, buff = SMALL_BUFF)
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text = brace.get_tex("2\\sigma_{\\text{%s}}"%text, buff = SMALL_BUFF)
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group = VGroup(brace, text)
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def update_group(group):
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brace, text = group
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brace.match_width(gdw, stretch = True)
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brace.next_to(gdw, vect)
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text.next_to(brace, vect, buff = SMALL_BUFF)
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group.highlight(color)
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return ContinualUpdateFromFunc(group, update_group)
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dot_brace_anim = get_brace_text_group_update(
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dot_cloud.gaussian_distribution_wrapper,
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DOWN, "position",
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DOWN, "position", dot_cloud.color
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)
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vector_brace_anim = get_brace_text_group_update(
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vector_cloud.gaussian_distribution_wrapper,
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UP, "momentum",
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UP, "momentum", vector_cloud.color
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)
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self.add(title)
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@ -195,7 +195,7 @@ class MentionUncertaintyPrinciple(TeacherStudentsScene):
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# self.wait(2)
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self.play(
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dot_cloud.gaussian_distribution_wrapper.change_parameters,
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{"sigma_x" : 0.1},
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{"sigma" : 0.1*RIGHT},
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run_time = 2,
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)
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self.wait()
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@ -206,7 +206,7 @@ class MentionUncertaintyPrinciple(TeacherStudentsScene):
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self.add(vector_brace_anim)
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self.play(
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vector_cloud.gaussian_distribution_wrapper.change_parameters,
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{"sigma_x" : 1},
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{"sigma" : RIGHT},
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self.get_student_changes(*3*["confused"]),
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run_time = 3,
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)
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@ -214,17 +214,17 @@ class MentionUncertaintyPrinciple(TeacherStudentsScene):
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for x in range(2):
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self.play(
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dot_cloud.gaussian_distribution_wrapper.change_parameters,
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{"sigma_x" : 2},
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{"sigma" : 2*RIGHT},
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vector_cloud.gaussian_distribution_wrapper.change_parameters,
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{"sigma_x" : 0.1},
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{"sigma" : 0.1*RIGHT},
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run_time = 3,
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)
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self.change_student_modes("thinking", "erm", "sassy")
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self.play(
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dot_cloud.gaussian_distribution_wrapper.change_parameters,
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{"sigma_x" : 0.1},
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{"sigma" : 0.1*RIGHT},
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vector_cloud.gaussian_distribution_wrapper.change_parameters,
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{"sigma_x" : 1},
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{"sigma" : 1*RIGHT},
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run_time = 3,
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)
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self.wait()
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@ -299,7 +299,8 @@ class FourierTradeoff(Scene):
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t_min = time_mean - time_radius,
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t_max = time_mean + time_radius,
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n_samples = 2*time_radius*17,
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complex_to_real_func = abs,
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# complex_to_real_func = abs,
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complex_to_real_func = lambda z : z.real,
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color = FREQUENCY_COLOR,
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)
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@ -351,8 +352,99 @@ class FourierTradeoff(Scene):
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self.wait()
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self.wait()
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class ShowPlan(PiCreatureScene):
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def construct(self):
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self.add_title()
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words = self.get_words()
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self.play_sound_anims(words[0])
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self.play_doppler_anims(words[1], words[0])
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self.play_quantum_anims(words[2], words[1])
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def add_title(self):
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title = TextMobject("The plan")
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title.scale(1.5)
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT).scale(SPACE_WIDTH)
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h_line.next_to(title, DOWN)
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self.add(title, h_line)
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def get_words(self):
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colors = [YELLOW, GREEN, BLUE]
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topics = ["sound waves", "Doppler radar", "quantum particles"]
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words = VGroup()
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for topic, color in zip(topics, colors):
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word = TextMobject("Uncertainty for", topic)
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word[1].highlight(color)
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words.add(word)
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words.arrange_submobjects(DOWN, aligned_edge = LEFT, buff = LARGE_BUFF)
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words.to_edge(LEFT)
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return words
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def play_sound_anims(self, word):
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morty = self.pi_creature
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wave = FunctionGraph(
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lambda x : 0.3*np.sin(15*x)*np.sin(0.5*x),
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x_min = 0, x_max = 30,
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num_anchor_points = 500,
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)
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wave.next_to(word, RIGHT)
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rect = BackgroundRectangle(wave, fill_opacity = 1)
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rect.stretch(2, 1)
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rect.next_to(wave, LEFT, buff = 0)
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wave_shift = AmbientMovement(
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wave, direction = LEFT, rate = 5
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)
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wave_fader = UpdateFromAlphaFunc(
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wave,
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lambda w, a : w.set_stroke(width = 3*a)
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)
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checkmark = self.get_checkmark(word)
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self.add(wave_shift)
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self.add_foreground_mobjects(rect, word)
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self.play(
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Animation(word),
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wave_fader,
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morty.change, "raise_right_hand", word
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)
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self.wait(2)
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wave_fader.rate_func = lambda a : 1-smooth(a)
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self.add_foreground_mobjects(checkmark)
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self.play(
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Write(checkmark),
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morty.change, "happy",
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wave_fader,
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)
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self.remove_foreground_mobjects(rect, word)
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self.add(word)
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self.wait()
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def play_doppler_anims(self, word, to_fade):
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morty = self.pi_creature
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radar_dish = RadarDish()
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radar_dish.next_to(to_fade, RIGHT)
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self.add(radar_dish)
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self.play(
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to_fade.fade, 0.5,
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Write(word),
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morty.change, "pondering",
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run_time = 1
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)
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def play_quantum_anims(self, word, to_fade):
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pass
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##
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def get_checkmark(self, word):
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checkmark = TexMobject("\\checkmark")
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checkmark.highlight(GREEN)
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checkmark.scale(1.5)
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checkmark.next_to(word, UP+RIGHT, buff = 0)
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return checkmark
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