mirror of
https://github.com/3b1b/manim.git
synced 2025-11-14 08:17:43 +00:00
Moved moved matrix.py to mobject, and pulled out MatrixMultiplicationScene
This commit is contained in:
Grant Sanderson
parent
b37f212349
commit
c82417e008
8 changed files with 284 additions and 282 deletions
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@ -70,7 +70,7 @@ from once_useful_constructs.fractals import *
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from once_useful_constructs.graph_theory import *
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from once_useful_constructs.light import *
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from topics.matrix import *
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from mobject.matrix import *
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from topics.probability import *
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from topics.three_dimensions import *
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from topics.vector_space_scene import *
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@ -216,7 +216,6 @@ def get_module(file_name):
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return get_module_windows(file_name)
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return get_module_posix(file_name)
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def main():
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config = get_configuration()
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module = get_module(config["file"])
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135
mobject/matrix.py
Normal file
135
mobject/matrix.py
Normal file
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@ -0,0 +1,135 @@
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import numpy as np
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from mobject.mobject import Mobject
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from mobject.svg.tex_mobject import TexMobject
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from mobject.types.vectorized_mobject import VGroup
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from mobject.types.vectorized_mobject import VMobject
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from mobject.shape_matchers import BackgroundRectangle
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from constants import *
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VECTOR_LABEL_SCALE_FACTOR = 0.8
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def matrix_to_tex_string(matrix):
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matrix = np.array(matrix).astype("string")
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if matrix.ndim == 1:
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matrix = matrix.reshape((matrix.size, 1))
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n_rows, n_cols = matrix.shape
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prefix = "\\left[ \\begin{array}{%s}"%("c"*n_cols)
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suffix = "\\end{array} \\right]"
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rows = [
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" & ".join(row)
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for row in matrix
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]
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return prefix + " \\\\ ".join(rows) + suffix
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def matrix_to_mobject(matrix):
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return TexMobject(matrix_to_tex_string(matrix))
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def vector_coordinate_label(vector_mob, integer_labels = True,
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n_dim = 2, color = WHITE):
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vect = np.array(vector_mob.get_end())
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if integer_labels:
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vect = np.round(vect).astype(int)
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vect = vect[:n_dim]
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vect = vect.reshape((n_dim, 1))
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label = Matrix(vect, add_background_rectangles = True)
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label.scale(VECTOR_LABEL_SCALE_FACTOR)
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shift_dir = np.array(vector_mob.get_end())
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if shift_dir[0] >= 0: #Pointing right
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shift_dir -= label.get_left() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*LEFT
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else: #Pointing left
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shift_dir -= label.get_right() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*RIGHT
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label.shift(shift_dir)
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label.set_color(color)
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label.rect = BackgroundRectangle(label)
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label.add_to_back(label.rect)
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return label
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class Matrix(VMobject):
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CONFIG = {
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"v_buff" : 0.5,
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"h_buff" : 1,
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"add_background_rectangles" : False
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}
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def __init__(self, matrix, **kwargs):
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"""
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Matrix can either either include numbres, tex_strings,
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or mobjects
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"""
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VMobject.__init__(self, **kwargs)
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matrix = np.array(matrix)
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if matrix.ndim == 1:
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matrix = matrix.reshape((matrix.size, 1))
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if not isinstance(matrix[0][0], Mobject):
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matrix = matrix.astype("string")
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matrix = self.string_matrix_to_mob_matrix(matrix)
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self.organize_mob_matrix(matrix)
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self.add(*matrix.flatten())
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self.add_brackets()
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self.center()
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self.mob_matrix = matrix
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if self.add_background_rectangles:
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for mob in matrix.flatten():
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mob.add_background_rectangle()
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def string_matrix_to_mob_matrix(self, matrix):
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return np.array([
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map(TexMobject, row)
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for row in matrix
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]).reshape(matrix.shape)
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def organize_mob_matrix(self, matrix):
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for i, row in enumerate(matrix):
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for j, elem in enumerate(row):
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mob = matrix[i][j]
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if i == 0 and j == 0:
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continue
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elif i == 0:
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mob.next_to(matrix[i][j-1], RIGHT, self.h_buff)
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else:
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mob.next_to(matrix[i-1][j], DOWN, self.v_buff)
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return self
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def add_brackets(self):
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bracket_pair = TexMobject("\\big[ \\big]")
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bracket_pair.scale(2)
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bracket_pair.stretch_to_fit_height(self.get_height() + 0.5)
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l_bracket, r_bracket = bracket_pair.split()
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l_bracket.next_to(self, LEFT)
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r_bracket.next_to(self, RIGHT)
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self.add(l_bracket, r_bracket)
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self.brackets = VGroup(l_bracket, r_bracket)
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return self
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def set_color_columns(self, *colors):
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for i, color in enumerate(colors):
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VGroup(*self.mob_matrix[:,i]).set_color(color)
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return self
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def add_background_to_entries(self):
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for mob in self.get_entries():
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mob.add_background_rectangle()
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return self
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def get_mob_matrix(self):
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return self.mob_matrix
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def get_entries(self):
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return VGroup(*self.get_mob_matrix().flatten())
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def get_brackets(self):
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return self.brackets
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@ -1,3 +1,5 @@
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from __future__ import absolute_import
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from constants import *
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from mobject.svg.tex_mobject import TexMobject
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140
once_useful_constructs/matrix_multiplication.py
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140
once_useful_constructs/matrix_multiplication.py
Normal file
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@ -0,0 +1,140 @@
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import numpy as np
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from animation.creation import ShowCreation
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from animation.transform import ApplyMethod
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from animation.creation import FadeOut
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from animation.transform import Transform
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from mobject.matrix import Matrix
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from mobject.svg.tex_mobject import TexMobject
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from mobject.types.vectorized_mobject import VGroup
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from scene.scene import Scene
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from mobject.geometry import Circle
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from mobject.geometry import Line
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class NumericalMatrixMultiplication(Scene):
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CONFIG = {
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"left_matrix" : [[1, 2], [3, 4]],
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"right_matrix" : [[5, 6], [7, 8]],
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"use_parens" : True,
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}
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def construct(self):
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left_string_matrix, right_string_matrix = [
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np.array(matrix).astype("string")
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for matrix in self.left_matrix, self.right_matrix
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]
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if right_string_matrix.shape[0] != left_string_matrix.shape[1]:
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raise Exception("Incompatible shapes for matrix multiplication")
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left = Matrix(left_string_matrix)
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right = Matrix(right_string_matrix)
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result = self.get_result_matrix(
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left_string_matrix, right_string_matrix
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)
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self.organize_matrices(left, right, result)
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self.animate_product(left, right, result)
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def get_result_matrix(self, left, right):
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(m, k), n = left.shape, right.shape[1]
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mob_matrix = np.array([VGroup()]).repeat(m*n).reshape((m, n))
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for a in range(m):
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for b in range(n):
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template = "(%s)(%s)" if self.use_parens else "%s%s"
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parts = [
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prefix + template%(left[a][c], right[c][b])
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for c in range(k)
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for prefix in ["" if c == 0 else "+"]
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]
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mob_matrix[a][b] = TexMobject(parts, next_to_buff = 0.1)
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return Matrix(mob_matrix)
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def add_lines(self, left, right):
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line_kwargs = {
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"color" : BLUE,
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"stroke_width" : 2,
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}
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left_rows = [
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VGroup(*row) for row in left.get_mob_matrix()
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]
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h_lines = VGroup()
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for row in left_rows[:-1]:
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h_line = Line(row.get_left(), row.get_right(), **line_kwargs)
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h_line.next_to(row, DOWN, buff = left.v_buff/2.)
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h_lines.add(h_line)
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right_cols = [
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VGroup(*col) for col in np.transpose(right.get_mob_matrix())
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]
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v_lines = VGroup()
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for col in right_cols[:-1]:
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v_line = Line(col.get_top(), col.get_bottom(), **line_kwargs)
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v_line.next_to(col, RIGHT, buff = right.h_buff/2.)
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v_lines.add(v_line)
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self.play(ShowCreation(h_lines))
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self.play(ShowCreation(v_lines))
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self.wait()
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self.show_frame()
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def organize_matrices(self, left, right, result):
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equals = TexMobject("=")
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everything = VGroup(left, right, equals, result)
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everything.arrange_submobjects()
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everything.scale_to_fit_width(FRAME_WIDTH-1)
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self.add(everything)
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def animate_product(self, left, right, result):
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l_matrix = left.get_mob_matrix()
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r_matrix = right.get_mob_matrix()
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result_matrix = result.get_mob_matrix()
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circle = Circle(
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radius = l_matrix[0][0].get_height(),
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color = GREEN
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)
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circles = VGroup(*[
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entry.get_point_mobject()
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for entry in l_matrix[0][0], r_matrix[0][0]
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])
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(m, k), n = l_matrix.shape, r_matrix.shape[1]
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for mob in result_matrix.flatten():
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mob.set_color(BLACK)
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lagging_anims = []
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for a in range(m):
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for b in range(n):
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for c in range(k):
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l_matrix[a][c].set_color(YELLOW)
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r_matrix[c][b].set_color(YELLOW)
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for c in range(k):
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start_parts = VGroup(
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l_matrix[a][c].copy(),
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r_matrix[c][b].copy()
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)
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result_entry = result_matrix[a][b].split()[c]
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new_circles = VGroup(*[
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circle.copy().shift(part.get_center())
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for part in start_parts.split()
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])
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self.play(Transform(circles, new_circles))
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self.play(
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Transform(
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start_parts,
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result_entry.copy().set_color(YELLOW),
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path_arc = -np.pi/2,
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submobject_mode = "all_at_once",
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),
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*lagging_anims
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)
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result_entry.set_color(YELLOW)
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self.remove(start_parts)
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lagging_anims = [
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ApplyMethod(result_entry.set_color, WHITE)
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]
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for c in range(k):
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l_matrix[a][c].set_color(WHITE)
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r_matrix[c][b].set_color(WHITE)
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self.play(FadeOut(circles), *lagging_anims)
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self.wait()
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@ -19,6 +19,9 @@ from utils.color import color_gradient
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from utils.color import invert_color
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from utils.space_ops import angle_of_vector
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# TODO, this should probably reimplemented entirely, especially so as to
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# better reuse code from mobject/coordinate_systems
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class GraphScene(Scene):
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CONFIG = {
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"x_min" : -1,
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277
topics/matrix.py
277
topics/matrix.py
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@ -1,277 +0,0 @@
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import numpy as np
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from animation.creation import ShowCreation
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from animation.creation import Write
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from animation.transform import ApplyFunction
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from animation.transform import ApplyMethod
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from animation.transform import ApplyPointwiseFunction
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from animation.creation import FadeOut
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from animation.transform import Transform
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from mobject.mobject import Mobject
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from mobject.svg.tex_mobject import TexMobject
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from mobject.svg.tex_mobject import TextMobject
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from mobject.types.vectorized_mobject import VGroup
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from mobject.types.vectorized_mobject import VMobject
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from scene.scene import Scene
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from mobject.geometry import Arrow
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from mobject.shape_matchers import BackgroundRectangle
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from mobject.geometry import Circle
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from mobject.geometry import Dot
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from mobject.geometry import Line
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from mobject.geometry import Vector
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from mobject.coordinate_systems import Axes
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from mobject.coordinate_systems import NumberPlane
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from constants import *
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VECTOR_LABEL_SCALE_FACTOR = 0.8
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def matrix_to_tex_string(matrix):
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matrix = np.array(matrix).astype("string")
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if matrix.ndim == 1:
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matrix = matrix.reshape((matrix.size, 1))
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n_rows, n_cols = matrix.shape
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prefix = "\\left[ \\begin{array}{%s}"%("c"*n_cols)
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suffix = "\\end{array} \\right]"
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rows = [
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" & ".join(row)
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for row in matrix
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]
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return prefix + " \\\\ ".join(rows) + suffix
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def matrix_to_mobject(matrix):
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return TexMobject(matrix_to_tex_string(matrix))
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def vector_coordinate_label(vector_mob, integer_labels = True,
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n_dim = 2, color = WHITE):
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vect = np.array(vector_mob.get_end())
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if integer_labels:
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vect = np.round(vect).astype(int)
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vect = vect[:n_dim]
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vect = vect.reshape((n_dim, 1))
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label = Matrix(vect, add_background_rectangles = True)
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label.scale(VECTOR_LABEL_SCALE_FACTOR)
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shift_dir = np.array(vector_mob.get_end())
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if shift_dir[0] >= 0: #Pointing right
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shift_dir -= label.get_left() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*LEFT
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else: #Pointing left
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shift_dir -= label.get_right() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*RIGHT
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label.shift(shift_dir)
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label.set_color(color)
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label.rect = BackgroundRectangle(label)
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label.add_to_back(label.rect)
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return label
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class Matrix(VMobject):
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CONFIG = {
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"v_buff" : 0.5,
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"h_buff" : 1,
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"add_background_rectangles" : False
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}
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def __init__(self, matrix, **kwargs):
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"""
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Matrix can either either include numbres, tex_strings,
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or mobjects
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"""
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VMobject.__init__(self, **kwargs)
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matrix = np.array(matrix)
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if matrix.ndim == 1:
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matrix = matrix.reshape((matrix.size, 1))
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if not isinstance(matrix[0][0], Mobject):
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matrix = matrix.astype("string")
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matrix = self.string_matrix_to_mob_matrix(matrix)
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self.organize_mob_matrix(matrix)
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self.add(*matrix.flatten())
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self.add_brackets()
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self.center()
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self.mob_matrix = matrix
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if self.add_background_rectangles:
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for mob in matrix.flatten():
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mob.add_background_rectangle()
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def string_matrix_to_mob_matrix(self, matrix):
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return np.array([
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map(TexMobject, row)
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for row in matrix
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]).reshape(matrix.shape)
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def organize_mob_matrix(self, matrix):
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for i, row in enumerate(matrix):
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for j, elem in enumerate(row):
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mob = matrix[i][j]
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if i == 0 and j == 0:
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continue
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elif i == 0:
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mob.next_to(matrix[i][j-1], RIGHT, self.h_buff)
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else:
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mob.next_to(matrix[i-1][j], DOWN, self.v_buff)
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return self
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def add_brackets(self):
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bracket_pair = TexMobject("\\big[ \\big]")
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bracket_pair.scale(2)
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bracket_pair.stretch_to_fit_height(self.get_height() + 0.5)
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l_bracket, r_bracket = bracket_pair.split()
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l_bracket.next_to(self, LEFT)
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r_bracket.next_to(self, RIGHT)
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self.add(l_bracket, r_bracket)
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self.brackets = VMobject(l_bracket, r_bracket)
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return self
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def set_color_columns(self, *colors):
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for i, color in enumerate(colors):
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VMobject(*self.mob_matrix[:,i]).set_color(color)
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return self
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def add_background_to_entries(self):
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for mob in self.get_entries():
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mob.add_background_rectangle()
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return self
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def get_mob_matrix(self):
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return self.mob_matrix
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def get_entries(self):
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return VMobject(*self.get_mob_matrix().flatten())
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def get_brackets(self):
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return self.brackets
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class NumericalMatrixMultiplication(Scene):
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CONFIG = {
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"left_matrix" : [[1, 2], [3, 4]],
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"right_matrix" : [[5, 6], [7, 8]],
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"use_parens" : True,
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}
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def construct(self):
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left_string_matrix, right_string_matrix = [
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np.array(matrix).astype("string")
|
||||
for matrix in self.left_matrix, self.right_matrix
|
||||
]
|
||||
if right_string_matrix.shape[0] != left_string_matrix.shape[1]:
|
||||
raise Exception("Incompatible shapes for matrix multiplication")
|
||||
|
||||
left = Matrix(left_string_matrix)
|
||||
right = Matrix(right_string_matrix)
|
||||
result = self.get_result_matrix(
|
||||
left_string_matrix, right_string_matrix
|
||||
)
|
||||
|
||||
self.organize_matrices(left, right, result)
|
||||
self.animate_product(left, right, result)
|
||||
|
||||
|
||||
def get_result_matrix(self, left, right):
|
||||
(m, k), n = left.shape, right.shape[1]
|
||||
mob_matrix = np.array([VMobject()]).repeat(m*n).reshape((m, n))
|
||||
for a in range(m):
|
||||
for b in range(n):
|
||||
template = "(%s)(%s)" if self.use_parens else "%s%s"
|
||||
parts = [
|
||||
prefix + template%(left[a][c], right[c][b])
|
||||
for c in range(k)
|
||||
for prefix in ["" if c == 0 else "+"]
|
||||
]
|
||||
mob_matrix[a][b] = TexMobject(parts, next_to_buff = 0.1)
|
||||
return Matrix(mob_matrix)
|
||||
|
||||
def add_lines(self, left, right):
|
||||
line_kwargs = {
|
||||
"color" : BLUE,
|
||||
"stroke_width" : 2,
|
||||
}
|
||||
left_rows = [
|
||||
VMobject(*row) for row in left.get_mob_matrix()
|
||||
]
|
||||
h_lines = VMobject()
|
||||
for row in left_rows[:-1]:
|
||||
h_line = Line(row.get_left(), row.get_right(), **line_kwargs)
|
||||
h_line.next_to(row, DOWN, buff = left.v_buff/2.)
|
||||
h_lines.add(h_line)
|
||||
|
||||
right_cols = [
|
||||
VMobject(*col) for col in np.transpose(right.get_mob_matrix())
|
||||
]
|
||||
v_lines = VMobject()
|
||||
for col in right_cols[:-1]:
|
||||
v_line = Line(col.get_top(), col.get_bottom(), **line_kwargs)
|
||||
v_line.next_to(col, RIGHT, buff = right.h_buff/2.)
|
||||
v_lines.add(v_line)
|
||||
|
||||
self.play(ShowCreation(h_lines))
|
||||
self.play(ShowCreation(v_lines))
|
||||
self.wait()
|
||||
self.show_frame()
|
||||
|
||||
def organize_matrices(self, left, right, result):
|
||||
equals = TexMobject("=")
|
||||
everything = VMobject(left, right, equals, result)
|
||||
everything.arrange_submobjects()
|
||||
everything.scale_to_fit_width(FRAME_WIDTH-1)
|
||||
self.add(everything)
|
||||
|
||||
|
||||
def animate_product(self, left, right, result):
|
||||
l_matrix = left.get_mob_matrix()
|
||||
r_matrix = right.get_mob_matrix()
|
||||
result_matrix = result.get_mob_matrix()
|
||||
circle = Circle(
|
||||
radius = l_matrix[0][0].get_height(),
|
||||
color = GREEN
|
||||
)
|
||||
circles = VMobject(*[
|
||||
entry.get_point_mobject()
|
||||
for entry in l_matrix[0][0], r_matrix[0][0]
|
||||
])
|
||||
(m, k), n = l_matrix.shape, r_matrix.shape[1]
|
||||
for mob in result_matrix.flatten():
|
||||
mob.set_color(BLACK)
|
||||
lagging_anims = []
|
||||
for a in range(m):
|
||||
for b in range(n):
|
||||
for c in range(k):
|
||||
l_matrix[a][c].set_color(YELLOW)
|
||||
r_matrix[c][b].set_color(YELLOW)
|
||||
for c in range(k):
|
||||
start_parts = VMobject(
|
||||
l_matrix[a][c].copy(),
|
||||
r_matrix[c][b].copy()
|
||||
)
|
||||
result_entry = result_matrix[a][b].split()[c]
|
||||
|
||||
new_circles = VMobject(*[
|
||||
circle.copy().shift(part.get_center())
|
||||
for part in start_parts.split()
|
||||
])
|
||||
self.play(Transform(circles, new_circles))
|
||||
self.play(
|
||||
Transform(
|
||||
start_parts,
|
||||
result_entry.copy().set_color(YELLOW),
|
||||
path_arc = -np.pi/2,
|
||||
submobject_mode = "all_at_once",
|
||||
),
|
||||
*lagging_anims
|
||||
)
|
||||
result_entry.set_color(YELLOW)
|
||||
self.remove(start_parts)
|
||||
lagging_anims = [
|
||||
ApplyMethod(result_entry.set_color, WHITE)
|
||||
]
|
||||
|
||||
for c in range(k):
|
||||
l_matrix[a][c].set_color(WHITE)
|
||||
r_matrix[c][b].set_color(WHITE)
|
||||
self.play(FadeOut(circles), *lagging_anims)
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -25,9 +25,9 @@ from mobject.coordinate_systems import Axes
|
|||
from mobject.coordinate_systems import NumberPlane
|
||||
|
||||
from constants import *
|
||||
from topics.matrix import Matrix
|
||||
from topics.matrix import VECTOR_LABEL_SCALE_FACTOR
|
||||
from topics.matrix import vector_coordinate_label
|
||||
from mobject.matrix import Matrix
|
||||
from mobject.matrix import VECTOR_LABEL_SCALE_FACTOR
|
||||
from mobject.matrix import vector_coordinate_label
|
||||
from utils.rate_functions import rush_from
|
||||
from utils.rate_functions import rush_into
|
||||
from utils.space_ops import angle_of_vector
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue