manim/topics/matrix.py

import numpy as np

from animation.creation import ShowCreation
from animation.creation import Write
from animation.transform import ApplyFunction
from animation.transform import ApplyMethod
from animation.transform import ApplyPointwiseFunction
from animation.creation import FadeOut
from animation.transform import Transform
from mobject.mobject import Mobject
from mobject.svg.tex_mobject import TexMobject
from mobject.svg.tex_mobject import TextMobject
from mobject.types.vectorized_mobject import VGroup
from mobject.types.vectorized_mobject import VMobject
from scene.scene import Scene
from mobject.geometry import Arrow
from mobject.shape_matchers import BackgroundRectangle
from mobject.geometry import Circle
from mobject.geometry import Dot
from mobject.geometry import Line
from mobject.geometry import Vector
from topics.number_line import Axes
from topics.number_line import NumberPlane

from constants import *

VECTOR_LABEL_SCALE_FACTOR = 0.8

def matrix_to_tex_string(matrix):
    matrix = np.array(matrix).astype("string")
    if matrix.ndim == 1:
        matrix = matrix.reshape((matrix.size, 1))
    n_rows, n_cols = matrix.shape
    prefix = "\\left[ \\begin{array}{%s}"%("c"*n_cols)
    suffix = "\\end{array} \\right]"
    rows = [
        " & ".join(row)
        for row in matrix
    ]
    return prefix + " \\\\ ".join(rows) + suffix

def matrix_to_mobject(matrix):
    return TexMobject(matrix_to_tex_string(matrix))

def vector_coordinate_label(vector_mob, integer_labels = True, 
                            n_dim = 2, color = WHITE):
    vect = np.array(vector_mob.get_end())
    if integer_labels:
        vect = np.round(vect).astype(int)
    vect = vect[:n_dim]
    vect = vect.reshape((n_dim, 1))
    label = Matrix(vect, add_background_rectangles = True)
    label.scale(VECTOR_LABEL_SCALE_FACTOR)

    shift_dir = np.array(vector_mob.get_end())
    if shift_dir[0] >= 0: #Pointing right
        shift_dir -= label.get_left() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*LEFT
    else: #Pointing left
        shift_dir -= label.get_right() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*RIGHT
    label.shift(shift_dir)
    label.set_color(color)
    label.rect = BackgroundRectangle(label)
    label.add_to_back(label.rect)
    return label

class Matrix(VMobject):
    CONFIG = {
        "v_buff" : 0.5,
        "h_buff" : 1,
        "add_background_rectangles" : False
    }
    def __init__(self, matrix, **kwargs):
        """
        Matrix can either either include numbres, tex_strings, 
        or mobjects
        """
        VMobject.__init__(self, **kwargs)
        matrix = np.array(matrix)
        if matrix.ndim == 1:
            matrix = matrix.reshape((matrix.size, 1))
        if not isinstance(matrix[0][0], Mobject):
            matrix = matrix.astype("string")
            matrix = self.string_matrix_to_mob_matrix(matrix)
        self.organize_mob_matrix(matrix)
        self.add(*matrix.flatten())
        self.add_brackets()
        self.center()
        self.mob_matrix = matrix
        if self.add_background_rectangles:
            for mob in matrix.flatten():
                mob.add_background_rectangle()

    def string_matrix_to_mob_matrix(self, matrix):
        return np.array([
            map(TexMobject, row)
            for row in matrix
        ]).reshape(matrix.shape)

    def organize_mob_matrix(self, matrix):
        for i, row in enumerate(matrix):
            for j, elem in enumerate(row):
                mob = matrix[i][j]
                if i == 0 and j == 0:
                    continue
                elif i == 0:
                    mob.next_to(matrix[i][j-1], RIGHT, self.h_buff)
                else:
                    mob.next_to(matrix[i-1][j], DOWN, self.v_buff)
        return self

    def add_brackets(self):
        bracket_pair = TexMobject("\\big[ \\big]")
        bracket_pair.scale(2)
        bracket_pair.stretch_to_fit_height(self.get_height() + 0.5)
        l_bracket, r_bracket = bracket_pair.split()
        l_bracket.next_to(self, LEFT)
        r_bracket.next_to(self, RIGHT)
        self.add(l_bracket, r_bracket)
        self.brackets = VMobject(l_bracket, r_bracket)
        return self

    def set_color_columns(self, *colors):
        for i, color in enumerate(colors):
            VMobject(*self.mob_matrix[:,i]).set_color(color)
        return self

    def add_background_to_entries(self):
        for mob in self.get_entries():
            mob.add_background_rectangle()
        return self

    def get_mob_matrix(self):
        return self.mob_matrix

    def get_entries(self):
        return VMobject(*self.get_mob_matrix().flatten())

    def get_brackets(self):
        return self.brackets

class NumericalMatrixMultiplication(Scene):
    CONFIG = {
        "left_matrix" : [[1, 2], [3, 4]],
        "right_matrix" : [[5, 6], [7, 8]],
        "use_parens" : True,
    }
    def construct(self):
        left_string_matrix, right_string_matrix = [
            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()