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middle of massive restructure, everything still broken
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Grant Sanderson
254
old_projects/complex_multiplication_article.py
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254
old_projects/complex_multiplication_article.py
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#!/usr/bin/env python
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import numpy as np
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import itertools as it
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from copy import deepcopy
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import sys
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from animation import *
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from mobject import *
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from constants import *
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from region import *
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from scene import Scene
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from topics.complex_numbers import *
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DEFAULT_PLANE_CONFIG = {
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"point_thickness" : 2*DEFAULT_POINT_THICKNESS
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class SuccessiveComplexMultiplications(ComplexMultiplication):
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args_list = [
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(complex(1, 2), complex(1, -2)),
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(complex(-2, 1), complex(-2, -1)),
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]
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@staticmethod
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def args_to_string(*multipliers):
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return "_".join([str(m)[1:-1] for m in multipliers])
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@staticmethod
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def string_to_args(arg_string):
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args_string.replac("i", "j")
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return map(copmlex, arg_string.split())
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def construct(self, *multipliers):
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norm = abs(reduce(op.mul, multipliers, 1))
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shrink_factor = SPACE_WIDTH/max(SPACE_WIDTH, norm)
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plane_config = {
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"density" : norm*DEFAULT_POINT_DENSITY_1D,
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"unit_to_spatial_width" : shrink_factor,
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"x_radius" : shrink_factor*SPACE_WIDTH,
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"y_radius" : shrink_factor*SPACE_HEIGHT,
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}
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ComplexMultiplication.construct(self, multipliers[0], **plane_config)
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one_dot = self.draw_dot("1", 1, True)
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one_dot_copy = deepcopy(one_dot)
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for multiplier, count in zip(multipliers, it.count()):
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if multiplier == multipliers[0]:
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tex = "z"
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elif np.conj(multiplier) == multipliers[0]:
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tex = "\\bar z"
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else:
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tex = "z_%d"%count
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self.draw_dot(tex, multiplier)
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for multiplier in multipliers:
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self.multiplier = multiplier
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self.apply_multiplication()
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new_one = deepcopy(one_dot_copy)
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self.mobjects_to_move_without_molding.append(new_one)
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class ShowComplexPower(SuccessiveComplexMultiplications):
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args_list = [
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(complex(0, 1), 1),
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(complex(0, 1), 2),
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(np.exp(complex(0, 2*np.pi/5)), 1),
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(np.exp(complex(0, 2*np.pi/5)), 5),
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(np.exp(complex(0, 4*np.pi/5)), 5),
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(np.exp(complex(0, -2*np.pi/5)), 5),
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(complex(1, np.sqrt(3)), 1),
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(complex(1, np.sqrt(3)), 3),
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]
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@staticmethod
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def args_to_string(multiplier, num_repeats):
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start = ComplexMultiplication.args_to_string(multiplier)
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return start + "ToThe%d"%num_repeats
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@staticmethod
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def string_to_args(arg_string):
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parts = arg_string.split()
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if len(parts) < 2 or len(parts) > 3:
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raise Exception("Invalid arguments")
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multiplier = complex(parts[0])
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num_repeats = int(parts[1])
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return multiplier, num_repeats
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def construct(self, multiplier, num_repeats):
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SuccessiveComplexMultiplications.construct(
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[multiplier]*num_repeats
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)
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class ComplexDivision(ComplexMultiplication):
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args_list = [
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complex(np.sqrt(3), 1),
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complex(1./3, -1./3),
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complex(1, 2),
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]
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def construct(self, num):
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ComplexMultiplication.construct(self, 1./num)
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self.draw_dot("1", 1, False),
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self.draw_dot("z", num, True)
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self.apply_multiplication()
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class ConjugateDivisionExample(ComplexMultiplication):
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args_list = [
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complex(1, 2),
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]
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def construct(self, num):
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ComplexMultiplication.construct(self, np.conj(num), radius = 2.5*SPACE_WIDTH)
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self.draw_dot("1", 1, True)
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self.draw_dot("\\bar z", self.multiplier)
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self.apply_multiplication()
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self.multiplier = 1./(abs(num)**2)
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self.anim_config["interpolation_function"] = straight_path
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self.apply_multiplication()
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self.dither()
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class DrawSolutionsToZToTheNEqualsW(Scene):
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@staticmethod
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def args_to_string(n, w):
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return str(n) + "_" + complex_string(w)
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@staticmethod
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def string_to_args(args_string):
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parts = args_string.split()
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return int(parts[0]), complex(parts[1])
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def construct(self, n, w):
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w = complex(w)
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plane_config = DEFAULT_PLANE_CONFIG.copy()
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norm = abs(w)
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theta = np.log(w).imag
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radius = norm**(1./n)
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zoom_value = (SPACE_HEIGHT-0.5)/radius
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plane_config["unit_to_spatial_width"] = zoom_value
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plane = ComplexPlane(**plane_config)
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circle = Circle(
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radius = radius*zoom_value,
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point_thickness = plane.point_thickness
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)
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solutions = [
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radius*np.exp(complex(0, 1)*(2*np.pi*k + theta)/n)
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for k in range(n)
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]
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points = map(plane.number_to_point, solutions)
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dots = [
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Dot(point, color = BLUE_B, radius = 0.1)
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for point in points
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]
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lines = [Line(*pair) for pair in adjascent_pairs(points)]
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self.add(plane, circle, *dots+lines)
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self.add(*plane.get_coordinate_labels())
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class DrawComplexAngleAndMagnitude(Scene):
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args_list = [
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(
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("1+i\\sqrt{3}", complex(1, np.sqrt(3)) ),
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("\\frac{\\sqrt{3}}{2} - \\frac{1}{2}i", complex(np.sqrt(3)/2, -1./2)),
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),
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(("1+i", complex(1, 1)),),
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]
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@staticmethod
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def args_to_string(*reps_and_nums):
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return "--".join([
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complex_string(num)
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for rep, num in reps_and_nums
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])
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def construct(self, *reps_and_nums):
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radius = max([abs(n.imag) for r, n in reps_and_nums]) + 1
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plane_config = {
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"color" : "grey",
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"unit_to_spatial_width" : SPACE_HEIGHT / radius,
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}
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plane_config.update(DEFAULT_PLANE_CONFIG)
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self.plane = ComplexPlane(**plane_config)
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coordinates = self.plane.get_coordinate_labels()
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# self.plane.add_spider_web()
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self.add(self.plane, *coordinates)
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for rep, num in reps_and_nums:
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self.draw_number(rep, num)
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self.add_angle_label(num)
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self.add_lines(rep, num)
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def draw_number(self, tex_representation, number):
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point = self.plane.number_to_point(number)
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dot = Dot(point)
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label = tex_mobject(tex_representation)
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max_width = 0.8*self.plane.unit_to_spatial_width
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if label.get_width() > max_width:
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label.scale_to_fit_width(max_width)
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dot_to_label_dir = RIGHT if point[0] > 0 else LEFT
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edge = label.get_edge_center(-dot_to_label_dir)
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buff = 0.1
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label.shift(point - edge + buff*dot_to_label_dir)
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label.highlight(YELLOW)
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self.add_local_mobjects()
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def add_angle_label(self, number):
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arc = PartialCircle(
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np.log(number).imag,
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radius = 0.2
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)
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self.add_local_mobjects()
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def add_lines(self, tex_representation, number):
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point = self.plane.number_to_point(number)
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x_line, y_line, num_line = [
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Line(
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start, end,
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color = color,
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point_thickness = self.plane.point_thickness
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)
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for start, end, color in zip(
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[ORIGIN, point[0]*RIGHT, ORIGIN],
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[point[0]*RIGHT, point, point],
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[BLUE_D, GOLD_E, WHITE]
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)
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]
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# tex_representation.replace("i", "")
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# if "+" in tex_representation:
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# tex_parts = tex_representation.split("+")
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# elif "-" in tex_representation:
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# tex_parts = tex_representation.split("-")
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# x_label, y_label = map(tex_mobject, tex_parts)
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# for label in x_label, y_label:
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# label.scale_to_fit_height(0.5)
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# x_label.next_to(x_line, point[1]*DOWN/abs(point[1]))
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# y_label.next_to(y_line, point[0]*RIGHT/abs(point[0]))
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norm = np.linalg.norm(point)
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brace = underbrace(ORIGIN, ORIGIN+norm*RIGHT)
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if point[1] > 0:
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brace.rotate(np.pi, RIGHT)
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brace.rotate(np.log(number).imag)
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norm_label = tex_mobject("%.1f"%abs(number))
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norm_label.scale(0.5)
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axis = OUT if point[1] > 0 else IN
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norm_label.next_to(brace, rotate_vector(point, np.pi/2, axis))
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self.add_local_mobjects()
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