3b1b-manim/active_projects/uncertainty.py

from helpers import *
import scipy

from animation.animation import Animation
from animation.transform import *
from animation.simple_animations import *
from animation.playground import *
from animation.continual_animation import *
from topics.geometry import *
from topics.characters import *
from topics.functions import *
from topics.fractals import *
from topics.number_line import *
from topics.combinatorics import *
from topics.numerals import *
from topics.three_dimensions import *
from topics.objects import *
from topics.probability import *
from topics.complex_numbers import *
from topics.common_scenes import *
from scene import Scene
from scene.reconfigurable_scene import ReconfigurableScene
from scene.zoomed_scene import *
from camera import Camera
from mobject import *
from mobject.image_mobject import *
from mobject.vectorized_mobject import *
from mobject.svg_mobject import *
from mobject.tex_mobject import *
from topics.graph_scene import *

from active_projects.fourier import *


class GaussianDistributionWrapper(Line):
    """
    This is meant to encode a 2d normal distribution as
    a mobject (so as to be able to have it be interpolated
    during animations).  It is a line whose start_point coordinates
    encode the coordinates of mu, and whose end_point - start_point
    encodes the coordinates of sigma.
    """
    CONFIG = {
        "stroke_width" : 0,
        "mu_x" : 0,
        "sigma_x" : 1,
        "mu_y" : 0,
        "sigma_y" : 0,
    }
    def __init__(self, **kwargs):
        Line.__init__(self, ORIGIN, RIGHT, **kwargs)
        self.change_parameters(self.mu_x, self.mu_y, self.sigma_x, self.sigma_y)

    def change_parameters(self, mu_x = None, mu_y = None, sigma_x = None, sigma_y = None):
        curr_parameters = self.get_parameteters()
        args = [mu_x, mu_y, sigma_x, sigma_y]
        new_parameters = [
            arg or curr
            for curr, arg in zip(curr_parameters, args)
        ]
        mu_x, mu_y, sigma_x, sigma_y = new_parameters
        mu_point = mu_x*RIGHT + mu_y*UP
        sigma_vect = sigma_x*RIGHT + sigma_y*UP
        self.put_start_and_end_on(mu_point, mu_point + sigma_vect)
        return self

    def get_parameteters(self):
        """ Return mu_x, mu_y, sigma_x, sigma_y"""
        start, end = self.get_start_and_end()
        return tuple(it.chain(start[:2], (end - start)[:2]))

    def get_random_points(self, size = 1):
        mu_x, mu_y, sigma_x, sigma_y = self.get_parameteters()
        x_vals = np.random.normal(mu_x, sigma_x, size)
        y_vals = np.random.normal(mu_y, sigma_y, size)
        return np.array([
            x*RIGHT + y*UP
            for x, y in zip(x_vals, y_vals)
        ])

class ProbabalisticMobjectCloud(ContinualAnimation):
    CONFIG = {
        "fill_opacity" : 0.25,
        "n_copies" : 100,
        "gaussian_distribution_wrapper_config" : {
            "sigma_x" : 1,
        }
    }
    def __init__(self, prototype, **kwargs):
        digest_config(self, kwargs)
        fill_opacity = self.fill_opacity or prototype.get_fill_opacity()
        self.gaussian_distribution_wrapper = GaussianDistributionWrapper(
            **self.gaussian_distribution_wrapper_config
        )
        group = VGroup(*[
            prototype.copy().set_fill(opacity = fill_opacity)
            for x in range(self.n_copies)
        ])
        ContinualAnimation.__init__(self, group, **kwargs)

    def update_mobject(self, dt):
        group = self.mobject
        points = self.gaussian_distribution_wrapper.get_random_points(len(group))
        for mob, point in zip(group, points):
            self.update_mobject_by_point(mob, point)
        return self

    def update_mobject_by_point(self, mobject, point):
        mobject.move_to(point)
        return self

class ProbabalisticDotCloud(ProbabalisticMobjectCloud):
    CONFIG = {
        "color" : BLUE,
    }
    def __init__(self, **kwargs):
        digest_config(self, kwargs)
        dot = Dot(color = self.color)
        ProbabalisticMobjectCloud.__init__(self, dot)

class ProbabalisticVectorCloud(ProbabalisticMobjectCloud):
    CONFIG = {
        "color" : RED,
        "n_copies" : 20,
        "fill_opacity" : 0.5,
        "center_func" : lambda : ORIGIN,
    }
    def __init__(self, **kwargs):
        digest_config(self, kwargs)
        vector = Vector(
            RIGHT, color = self.color,
            max_tip_length_to_length_ratio = 1,
        )
        ProbabalisticMobjectCloud.__init__(self, vector)

    def update_mobject_by_point(self, vector, point):
        vector.put_start_and_end_on(
            self.center_func(),
            point
        )

###################

class MentionUncertaintyPrinciple(TeacherStudentsScene):
    def construct(self):
        title = TextMobject("Heisenberg Uncertainty Principle")
        title.to_edge(UP)

        dot_cloud = ProbabalisticDotCloud()
        vector_cloud = ProbabalisticVectorCloud(
            gaussian_distribution_wrapper_config = {"sigma_x" : 0.2},
            center_func = dot_cloud.gaussian_distribution_wrapper.get_start,
        )
        for cloud in dot_cloud, vector_cloud:
            gdw = cloud.gaussian_distribution_wrapper
            gdw.move_to(title.get_center(), LEFT)
            gdw.shift(2*DOWN)
        vector_cloud.gaussian_distribution_wrapper.shift(3*RIGHT)

        def get_brace_text_group_update(gdw, vect, text):
            brace = Brace(gdw, vect)
            text = brace.get_tex("\\sigma_{\\text{%s}}"%text, buff = SMALL_BUFF)
            group = VGroup(brace, text)
            def update_group(group):
                brace, text = group
                brace.match_width(gdw, stretch = True)
                brace.next_to(gdw, vect)
                text.next_to(brace, vect, buff = SMALL_BUFF)
            return ContinualUpdateFromFunc(group, update_group)

        dot_brace_anim = get_brace_text_group_update(
            dot_cloud.gaussian_distribution_wrapper,
            DOWN, "position",
        )
        vector_brace_anim = get_brace_text_group_update(
            vector_cloud.gaussian_distribution_wrapper,
            UP, "momentum",
        )

        self.add(title)
        self.add(dot_cloud)
        self.play(
            Write(title),
            self.teacher.change, "raise_right_hand",
            self.get_student_changes(*["pondering"]*3)
        )
        self.play(
            Write(dot_brace_anim.mobject, run_time = 1)
        )
        self.add(dot_brace_anim)
        self.wait()
        # self.wait(2)
        self.play(
            dot_cloud.gaussian_distribution_wrapper.change_parameters, 
            {"sigma_x" : 0.1},
            run_time = 2,
        )
        self.wait()
        self.add(vector_cloud)
        self.play(
            FadeIn(vector_brace_anim.mobject)
        )
        self.add(vector_brace_anim)
        self.play(
            vector_cloud.gaussian_distribution_wrapper.change_parameters,
            {"sigma_x" : 1},
            self.get_student_changes(*3*["confused"]),
            run_time = 3,
        )
        self.wait()
        #Back and forth
        self.play(
            dot_cloud.gaussian_distribution_wrapper.change_parameters,
            {"sigma_x" : 2},
            vector_cloud.gaussian_distribution_wrapper.change_parameters,
            {"sigma_x" : 0.1},
            run_time = 3,
        )
        self.change_student_modes("thinking", "erm", "sassy")
        self.play(
            dot_cloud.gaussian_distribution_wrapper.change_parameters,
            {"sigma_x" : 0.1},
            vector_cloud.gaussian_distribution_wrapper.change_parameters,
            {"sigma_x" : 1},
            run_time = 3,
        )
        self.wait(2)