Merge pull request #196 from 3b1b/eola2

Eola2

active_projects/eola2/determinant_puzzle.py

@@ -0,0 +1,286 @@
+from big_ol_pile_of_manim_imports import *
+
+
+class WorkOutNumerically(Scene):
+    CONFIG = {
+        "M1_COLOR": TEAL,
+        "M2_COLOR": PINK,
+    }
+
+    def construct(self):
+        self.add_question()
+        self.add_example()
+        self.compute_rhs()
+        self.compute_lhs()
+
+    def add_question(self):
+        equation = self.original_equation = TexMobject(
+            "\\det(", "M_1", "M_2", ")", "=",
+            "\\det(", "M_1", ")",
+            "\\det(", "M_2", ")",
+        )
+        equation.set_color_by_tex_to_color_map({
+            "M_1": self.M1_COLOR,
+            "M_2": self.M2_COLOR,
+        })
+        challenge = TextMobject("Explain in one sentence")
+        challenge.set_color(YELLOW)
+        group = VGroup(challenge, equation)
+        group.arrange_submobjects(DOWN)
+        group.to_edge(UP)
+
+        self.add(equation)
+        self.play(Write(challenge))
+        self.wait()
+
+    def add_example(self):
+        M1 = self.M1 = Matrix([[2, -1], [1, 1]])
+        M1.set_color(self.M1_COLOR)
+        self.M1_copy = M1.copy()
+        M2 = self.M2 = Matrix([[-1, 4], [1, 1]])
+        M2.set_color(self.M2_COLOR)
+        self.M2_copy = M2.copy()
+        eq_parts = TexMobject(
+            "\\det", "\\big(", "\\big)", "=",
+            "\\det", "\\big(", "\\big)",
+            "\\det", "\\big(", "\\big)",
+        )
+        for part in eq_parts.get_parts_by_tex("\\big"):
+            part.scale(2)
+            part.stretch(1.5, 1)
+        i1, i2, i3 = [
+            eq_parts.index_of_part(part) + 1
+            for part in eq_parts.get_parts_by_tex("\\big(")
+        ]
+        equation = self.equation_with_numbers = VGroup(*it.chain(
+            eq_parts[:i1], [M1, M2],
+            eq_parts[i1:i2], [self.M1_copy],
+            eq_parts[i2:i3], [self.M2_copy],
+            eq_parts[i3:],
+        ))
+        equation.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
+        eq_parts.get_part_by_tex("=").shift(0.2 * SMALL_BUFF * DOWN)
+        equation.scale_to_fit_width(FRAME_WIDTH - 2 * LARGE_BUFF)
+        equation.next_to(self.original_equation, DOWN, MED_LARGE_BUFF)
+
+        self.play(LaggedStart(FadeIn, equation))
+
+    def compute_rhs(self):
+        M1, M2 = self.M1_copy, self.M2_copy
+
+        line1 = VGroup(
+            TexMobject(
+                "\\big(", "2", "\\cdot", "2", "-",
+                "(-1)", "\\cdot", "1", "\\big)"
+            ),
+            TexMobject(
+                "\\big(", "-1", "\\cdot", "1", "-",
+                "4", "\\cdot", "1", "\\big)"
+            ),
+        )
+        line1.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
+        line1[0].set_color(self.M1_COLOR)
+        line1[1].set_color(self.M2_COLOR)
+        indices = [1, 3, 5, 7]
+
+        line2 = TexMobject("(3)", "(-5)")
+        line2.match_style(line1)
+        line3 = TexMobject("-15")
+        arrows = [TexMobject("\\downarrow") for x in range(2)]
+        lines = VGroup(line1, arrows[0], line2, arrows[1], line3)
+        lines.arrange_submobjects(DOWN, buff=MED_SMALL_BUFF)
+        lines.next_to(self.equation_with_numbers, DOWN, buff=MED_LARGE_BUFF)
+        lines.to_edge(RIGHT)
+
+        for matrix, det in zip([M1, M2], line1):
+            numbers = VGroup(*[det[i] for i in indices])
+            numbers_iter = iter(numbers)
+            non_numbers = VGroup(*filter(
+                lambda m: m not in numbers,
+                det
+            ))
+            matrix_numbers = VGroup(*[
+                matrix.mob_matrix[i][j].copy()
+                for i, j in (0, 0), (1, 1), (0, 1), (1, 0)
+            ])
+            self.play(
+                LaggedStart(FadeIn, non_numbers, run_time=1),
+                LaggedStart(
+                    ReplacementTransform,
+                    matrix_numbers,
+                    lambda m: (m, numbers_iter.next()),
+                    path_arc=TAU / 6
+                ),
+            )
+        self.play(LaggedStart(FadeIn, lines[1:], run_time=3))
+
+    def compute_lhs(self):
+        matrix = Matrix([[-3, 7], [0, 5]])
+        matrix.set_color(BLUE)
+        matrix.scale(0.8)
+        empty_det_tex = TexMobject("\\det", "\\big(", "\\big)")
+        empty_det_tex[1:].scale(1.5)
+        empty_det_tex[1:].match_height(matrix, stretch=True)
+        det_tex = VGroup(empty_det_tex[:2], matrix, *empty_det_tex[2:])
+        det_tex.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
+
+        group = VGroup(
+            det_tex,
+            TexMobject("\\downarrow"),
+            TexMobject("(-3)(5) - (7)(0)").scale(0.8),
+            TexMobject("\\downarrow"),
+            TexMobject("-15"),
+        )
+        group.arrange_submobjects(DOWN, buff=2 * SMALL_BUFF)
+        # group.scale_to_fit_height(0.4*FRAME_HEIGHT)
+        group.next_to(self.equation_with_numbers, DOWN)
+        group.shift(FRAME_WIDTH * LEFT / 4)
+
+        self.play(FadeIn(empty_det_tex))
+        self.play(*[
+            ReplacementTransform(M.copy(), matrix)
+            for M in self.M1, self.M2
+        ])
+        self.play(LaggedStart(FadeIn, group[1:]))
+        self.wait()
+
+
+class LetsGoInOneSentence(TeacherStudentsScene):
+    def construct(self):
+        self.teacher_says(
+            "Here we go, \\\\", "one sentence!"
+        )
+        self.change_all_student_modes("hooray")
+        self.teacher_says(
+            "Or three...", "",
+            target_mode="guilty"
+        )
+        self.change_all_student_modes("sassy")
+        self.wait(4)
+
+
+class SuccessiveLinearTransformations(LinearTransformationScene):
+    CONFIG = {
+        "matrix_2": [[3, -1], [0, 1]],
+        "matrix_1": [[2, 3], [-1. / 3, 2]],
+    }
+
+    def construct(self):
+        self.create_product_and_inverse()
+        self.scale_area_successively()
+        self.apply_transformations_successively()
+        self.scale_area_successively(
+            "\\det(M_2)", "\\det(M_1)", "\\det(M_1 M_2)",
+            reset=False
+        )
+        # self.show_det_as_scaling_factor()
+
+    def create_product_and_inverse(self):
+        self.matrix_product = np.dot(self.matrix_1, self.matrix_2)
+        self.matrix_product_inverse = np.linalg.inv(self.matrix_product)
+
+    def scale_area_successively(self, tex2="3", tex1="5", tex_prod="15", reset=True):
+        self.add_unit_square()
+        t1 = "$%s \\, \\cdot $" % tex1
+        t2 = "$%s \\, \\cdot $" % tex2
+        t3 = "Area"
+        areas = VGroup(
+            TextMobject("", "", t3),
+            TextMobject("", t2, t3),
+            TextMobject(t1, t2, t3),
+        )
+        areas.scale(0.8)
+        areas.move_to(self.square)
+        area = areas[0]
+        self.add_moving_mobject(area, areas[1])
+
+        self.play(
+            FadeIn(self.square),
+            Write(area),
+            Animation(self.basis_vectors)
+        )
+        self.apply_matrix(self.matrix_2)
+        self.wait()
+        self.add_moving_mobject(area, areas[2])
+        self.apply_matrix(self.matrix_1)
+        self.wait()
+
+        product = VGroup(area[:2])
+        brace = Brace(product, DOWN, buff=SMALL_BUFF)
+        brace_tex = brace.get_tex(tex_prod, buff=SMALL_BUFF)
+        brace_tex.scale(0.8, about_edge=UP)
+
+        self.play(
+            GrowFromCenter(brace),
+            Write(brace_tex)
+        )
+        self.wait()
+        if reset:
+            self.play(
+                FadeOut(VGroup(self.square, area, brace, brace_tex)),
+                Animation(self.plane),
+                Animation(self.basis_vectors)
+            )
+            self.transformable_mobjects.remove(self.square)
+            self.moving_mobjects = []
+            self.reset_plane()
+        self.wait()
+
+    def apply_transformations_successively(self):
+        M1, M2, all_space = expression = TexMobject(
+            "M_1", "M_2", "\\text{(All 2d space)}"
+        )
+        expression.set_color_by_tex_to_color_map({
+            "M_1": TEAL,
+            "M_2": PINK,
+        })
+        expression.shift(FRAME_WIDTH * LEFT / 4)
+        expression.to_edge(UP)
+        for part in expression:
+            part.add_background_rectangle()
+            part.background_rectangle.stretch(1.05, 0)
+        M1.save_state()
+        M1.move_to(ORIGIN)
+        M1.fade(1)
+
+        # Apply one after the other
+        self.play(
+            FocusOn(M2, run_time=1),
+            FadeIn(VGroup(M2, all_space))
+        )
+        self.add_foreground_mobjects(M2, all_space)
+        self.apply_matrix(self.matrix_2)
+        self.wait()
+        self.play(M1.restore)
+        self.add_foreground_mobjects(M1)
+        self.apply_matrix(self.matrix_1)
+        self.wait()
+
+        # Show full composition
+        rp, lp = parens = TexMobject("()")
+        matrices = VGroup(M1, M2)
+        matrices.generate_target()
+        parens.match_height(matrices)
+        lp.move_to(matrices, RIGHT)
+        matrices.target.next_to(lp, LEFT, SMALL_BUFF)
+        rp.next_to(matrices.target, LEFT, SMALL_BUFF)
+
+        self.reset_plane()
+        self.play(
+            MoveToTarget(matrices),
+            *map(GrowFromCenter, parens)
+        )
+        self.apply_matrix(self.matrix_product)
+        self.wait()
+        self.reset_plane()
+
+    def show_det_as_scaling_factor(self):
+        pass
+
+    ###
+
+    def reset_plane(self):
+        plane_and_bases = VGroup(self.plane, self.basis_vectors)
+        self.play(FadeOut(plane_and_bases))
+        self.apply_matrix(self.matrix_product_inverse, run_time=0)
+        self.play(FadeIn(plane_and_bases))

animation/creation.py

@@ -15,7 +15,8 @@ from utils.paths import counterclockwise_path
 from utils.rate_functions import double_smooth
 from utils.rate_functions import smooth
 
-#Drawing
+# Drawing
+
 
 class ShowPartial(Animation):
     def update_submobject(self, submobject, starting_submobject, alpha):
@@ -26,24 +27,29 @@ class ShowPartial(Animation):
     def get_bounds(self, alpha):
         raise Exception("Not Implemented")
 
+
 class ShowCreation(ShowPartial):
     CONFIG = {
-        "submobject_mode" : "one_at_a_time",
+        "submobject_mode": "one_at_a_time",
     }
+
     def get_bounds(self, alpha):
         return (0, alpha)
 
+
 class Uncreate(ShowCreation):
     CONFIG = {
-        "rate_func" : lambda t : smooth(1-t),
+        "rate_func": lambda t: smooth(1 - t),
-        "remover"   : True
+        "remover": True
     }
 
+
 class Write(ShowCreation):
     CONFIG = {
-        "rate_func" : None,
+        "rate_func": None,
-        "submobject_mode" : "lagged_start",
+        "submobject_mode": "lagged_start",
     }
+
     def __init__(self, mob_or_text, **kwargs):
         digest_config(self, kwargs)
         if isinstance(mob_or_text, str):
@@ -67,13 +73,15 @@ class Write(ShowCreation):
         else:
             self.run_time = 2
 
+
 class DrawBorderThenFill(Animation):
     CONFIG = {
-        "run_time" : 2,
+        "run_time": 2,
-        "stroke_width" : 2,
+        "stroke_width": 2,
-        "stroke_color" : None,
+        "stroke_color": None,
-        "rate_func" : double_smooth,
+        "rate_func": double_smooth,
     }
+
     def __init__(self, vmobject, **kwargs):
         if not isinstance(vmobject, VMobject):
             raise Exception("DrawBorderThenFill only works for VMobjects")
@@ -82,7 +90,7 @@ class DrawBorderThenFill(Animation):
 
     def update_submobject(self, submobject, starting_submobject, alpha):
         submobject.pointwise_become_partial(
-            starting_submobject, 0, min(2*alpha, 1)
+            starting_submobject, 0, min(2 * alpha, 1)
         )
         if alpha < 0.5:
             if self.stroke_color:
@@ -91,50 +99,55 @@ class DrawBorderThenFill(Animation):
                 color = starting_submobject.get_stroke_color()
             else:
                 color = starting_submobject.get_color()
-            submobject.set_stroke(color, width = self.stroke_width)
+            submobject.set_stroke(color, width=self.stroke_width)
-            submobject.set_fill(opacity = 0)
+            submobject.set_fill(opacity=0)
         else:
             if not self.reached_halfway_point_before:
                 self.reached_halfway_point_before = True
                 submobject.points = np.array(starting_submobject.points)
             width, opacity = [
-                interpolate(start, end, 2*alpha - 1)
+                interpolate(start, end, 2 * alpha - 1)
                 for start, end in [
                     (self.stroke_width, starting_submobject.get_stroke_width()),
                     (0, starting_submobject.get_fill_opacity())
                 ]
             ]
-            submobject.set_stroke(width = width)
+            submobject.set_stroke(width=width)
-            submobject.set_fill(opacity = opacity)
+            submobject.set_fill(opacity=opacity)
+
+# Fading
 
-#Fading
 
 class FadeOut(Transform):
     CONFIG = {
-        "remover" : True, 
+        "remover": True,
     }
+
     def __init__(self, mobject, **kwargs):
         target = mobject.copy()
         target.fade(1)
         Transform.__init__(self, mobject, target, **kwargs)
 
-    def clean_up(self, surrounding_scene = None):
+    def clean_up(self, surrounding_scene=None):
         Transform.clean_up(self, surrounding_scene)
         self.update(0)
 
+
 class FadeIn(Transform):
     def __init__(self, mobject, **kwargs):
         target = mobject.copy()
         Transform.__init__(self, mobject, target, **kwargs)
         self.starting_mobject.fade(1)
         if isinstance(self.starting_mobject, VMobject):
-            self.starting_mobject.set_stroke(width = 0)
+            self.starting_mobject.set_stroke(width=0)
-            self.starting_mobject.set_fill(opacity = 0)
+            self.starting_mobject.set_fill(opacity=0)
+
 
 class FadeInAndShiftFromDirection(Transform):
     CONFIG = {
-        "direction" : DOWN,
+        "direction": DOWN,
     }
+
     def __init__(self, mobject, **kwargs):
         digest_config(self, kwargs)
         target = mobject.copy()
@@ -142,19 +155,23 @@ class FadeInAndShiftFromDirection(Transform):
         mobject.fade(1)
         Transform.__init__(self, mobject, target, **kwargs)
 
+
 class FadeInFromDown(FadeInAndShiftFromDirection):
     """
     Essential a more convenient form of FadeInAndShiftFromDirection
     """
     CONFIG = {
-        "direction" : DOWN,
+        "direction": DOWN,
     }
 
-#Growing
+# Growing
+
+
 class GrowFromPoint(Transform):
     CONFIG = {
-        "point_color" : None,
+        "point_color": None,
     }
+
     def __init__(self, mobject, point, **kwargs):
         digest_config(self, kwargs)
         target = mobject.copy()
@@ -165,19 +182,23 @@ class GrowFromPoint(Transform):
         mobject.set_color(point_mob.get_color())
         Transform.__init__(self, mobject, target, **kwargs)
 
+
 class GrowFromCenter(GrowFromPoint):
     def __init__(self, mobject, **kwargs):
         GrowFromPoint.__init__(self, mobject, mobject.get_center(), **kwargs)
 
+
 class GrowArrow(GrowFromPoint):
     def __init__(self, arrow, **kwargs):
         GrowFromPoint.__init__(self, arrow, arrow.get_start(), **kwargs)
 
+
 class SpinInFromNothing(GrowFromCenter):
     CONFIG = {
-        "path_func" : counterclockwise_path()
+        "path_func": counterclockwise_path()
     }
 
+
 class ShrinkToCenter(Transform):
     def __init__(self, mobject, **kwargs):
         Transform.__init__(

extract_scene.py

@@ -1,7 +1,6 @@
 #!/usr/bin/env python2
 
 import sys
-# import getopt
 import argparse
 import imp
 import imp
@@ -11,8 +10,9 @@ import os
 import subprocess as sp
 import traceback
 
-from camera.camera import Camera
 from constants import *
+
+from camera.camera import Camera
 from scene.scene import Scene
 from utils.sounds import play_error_sound
 from utils.sounds import play_finish_sound

for_3b1b_videos/pi_creature_scene.py

@@ -25,17 +25,19 @@ from scene.scene import Scene
 from utils.rate_functions import squish_rate_func
 from utils.rate_functions import there_and_back
 
+
 class PiCreatureScene(Scene):
     CONFIG = {
-        "total_wait_time" : 0,
+        "total_wait_time": 0,
-        "seconds_to_blink" : 3,
+        "seconds_to_blink": 3,
-        "pi_creatures_start_on_screen" : True,
+        "pi_creatures_start_on_screen": True,
-        "default_pi_creature_kwargs" : {
+        "default_pi_creature_kwargs": {
-            "color" : GREY_BROWN,
+            "color": GREY_BROWN,
-            "flip_at_start" : True,
+            "flip_at_start": True,
         },
-        "default_pi_creature_start_corner" : DOWN+LEFT,
+        "default_pi_creature_start_corner": DOWN + LEFT,
     }
+
     def setup(self):
         self.pi_creatures = self.create_pi_creatures()
         self.pi_creature = self.get_primary_pi_creature()
@@ -66,7 +68,7 @@ class PiCreatureScene(Scene):
     def get_on_screen_pi_creatures(self):
         mobjects = self.get_mobjects()
         return VGroup(*filter(
-            lambda pi : pi in mobjects,
+            lambda pi: pi in mobjects,
             self.get_pi_creatures()
         ))
 
@@ -91,6 +93,7 @@ class PiCreatureScene(Scene):
         on_screen_mobjects = self.camera.extract_mobject_family_members(
             self.get_mobjects()
         )
+
         def has_bubble(pi):
             return hasattr(pi, "bubble") and \
                 pi.bubble is not None and \
@@ -102,7 +105,7 @@ class PiCreatureScene(Scene):
             old_bubble = pi_creature.bubble
             bubble = pi_creature.get_bubble(
                 *content,
-                bubble_class = bubble_class,
+                bubble_class=bubble_class,
                 **bubble_kwargs
             )
             anims += [
@@ -114,9 +117,9 @@ class PiCreatureScene(Scene):
             anims.append(PiCreatureBubbleIntroduction(
                 pi_creature,
                 *content,
-                bubble_class = bubble_class,
+                bubble_class=bubble_class,
-                bubble_kwargs = bubble_kwargs,
+                bubble_kwargs=bubble_kwargs,
-                target_mode = target_mode,
+                target_mode=target_mode,
                 **kwargs
             ))
         anims += [
@@ -130,22 +133,24 @@ class PiCreatureScene(Scene):
     def pi_creature_says(self, *args, **kwargs):
         self.introduce_bubble(
             *args,
-            bubble_class = SpeechBubble,
+            bubble_class=SpeechBubble,
             **kwargs
         )
 
     def pi_creature_thinks(self, *args, **kwargs):
         self.introduce_bubble(
             *args,
-            bubble_class = ThoughtBubble,
+            bubble_class=ThoughtBubble,
             **kwargs
         )
 
     def say(self, *content, **kwargs):
-        self.pi_creature_says(self.get_primary_pi_creature(), *content, **kwargs)
+        self.pi_creature_says(
+            self.get_primary_pi_creature(), *content, **kwargs)
 
     def think(self, *content, **kwargs):
-        self.pi_creature_thinks(self.get_primary_pi_creature(), *content, **kwargs)
+        self.pi_creature_thinks(
+            self.get_primary_pi_creature(), *content, **kwargs)
 
     def compile_play_args_to_animation_list(self, *args):
         """
@@ -157,13 +162,13 @@ class PiCreatureScene(Scene):
             return animations
 
         non_pi_creature_anims = filter(
-            lambda anim : anim.mobject not in self.get_pi_creatures(),
+            lambda anim: anim.mobject not in self.get_pi_creatures(),
             animations
         )
         if len(non_pi_creature_anims) == 0:
             return animations
         first_anim = non_pi_creature_anims[0]
-        #Look at ending state
+        # Look at ending state
         first_anim.update(1)
         point_of_interest = first_anim.mobject.get_center()
         first_anim.update(0)
@@ -174,7 +179,7 @@ class PiCreatureScene(Scene):
             if pi_creature in first_anim.mobject.submobject_family():
                 continue
             anims_with_pi_creature = filter(
-                lambda anim : pi_creature in anim.mobject.submobject_family(),
+                lambda anim: pi_creature in anim.mobject.submobject_family(),
                 animations
             )
             for anim in anims_with_pi_creature:
@@ -193,7 +198,7 @@ class PiCreatureScene(Scene):
     def blink(self):
         self.play(Blink(random.choice(self.get_on_screen_pi_creatures())))
 
-    def joint_blink(self, pi_creatures = None, shuffle = True, **kwargs):
+    def joint_blink(self, pi_creatures=None, shuffle=True, **kwargs):
         if pi_creatures is None:
             pi_creatures = self.get_on_screen_pi_creatures()
         creatures_list = list(pi_creatures)
@@ -202,25 +207,25 @@ class PiCreatureScene(Scene):
 
         def get_rate_func(pi):
             index = creatures_list.index(pi)
-            proportion = float(index)/len(creatures_list)
+            proportion = float(index) / len(creatures_list)
-            start_time = 0.8*proportion
+            start_time = 0.8 * proportion
             return squish_rate_func(
                 there_and_back,
                 start_time, start_time + 0.2
             )
 
         self.play(*[
-            Blink(pi, rate_func = get_rate_func(pi), **kwargs)
+            Blink(pi, rate_func=get_rate_func(pi), **kwargs)
             for pi in creatures_list
         ])
         return self
 
-    def wait(self, time = 1, blink = True):
+    def wait(self, time=1, blink=True):
         while time >= 1:
-            time_to_blink = self.total_wait_time%self.seconds_to_blink == 0
+            time_to_blink = self.total_wait_time % self.seconds_to_blink == 0
             if blink and self.any_pi_creatures_on_screen() and time_to_blink:
                 self.blink()
-                self.num_plays -= 1 #This shouldn't count as an animation
+                self.num_plays -= 1  # This shouldn't count as an animation
             else:
                 self.non_blink_wait()
             time -= 1
@@ -229,14 +234,14 @@ class PiCreatureScene(Scene):
             self.non_blink_wait(time)
         return self
 
-    def non_blink_wait(self, time = 1):
+    def non_blink_wait(self, time=1):
         Scene.wait(self, time)
         return self
 
     def change_mode(self, mode):
         self.play(self.get_primary_pi_creature().change_mode, mode)
 
-    def look_at(self, thing_to_look_at, pi_creatures = None):
+    def look_at(self, thing_to_look_at, pi_creatures=None):
         if pi_creatures is None:
             pi_creatures = self.get_pi_creatures()
         self.play(*it.chain(*[
@@ -244,30 +249,33 @@ class PiCreatureScene(Scene):
             for pi in pi_creatures
         ]))
 
+
 class TeacherStudentsScene(PiCreatureScene):
     CONFIG = {
-        "student_colors" : [BLUE_D, BLUE_E, BLUE_C],
+        "student_colors": [BLUE_D, BLUE_E, BLUE_C],
-        "student_scale_factor" : 0.8,
+        "student_scale_factor": 0.8,
-        "seconds_to_blink" : 2,
+        "seconds_to_blink": 2,
-        "screen_height" : 3,
+        "screen_height": 3,
     }
+
     def setup(self):
         PiCreatureScene.setup(self)
-        self.screen = ScreenRectangle(height = self.screen_height)
+        self.screen = ScreenRectangle(height=self.screen_height)
-        self.screen.to_corner(UP+LEFT)
+        self.screen.to_corner(UP + LEFT)
-        self.hold_up_spot = self.teacher.get_corner(UP+LEFT) + MED_LARGE_BUFF*UP
+        self.hold_up_spot = self.teacher.get_corner(
+            UP + LEFT) + MED_LARGE_BUFF * UP
 
     def create_pi_creatures(self):
         self.teacher = Mortimer()
         self.teacher.to_corner(DOWN + RIGHT)
-        self.teacher.look(DOWN+LEFT)
+        self.teacher.look(DOWN + LEFT)
         self.students = VGroup(*[
-            Randolph(color = c)
+            Randolph(color=c)
             for c in self.student_colors
         ])
         self.students.arrange_submobjects(RIGHT)
         self.students.scale(self.student_scale_factor)
-        self.students.to_corner(DOWN+LEFT)
+        self.students.to_corner(DOWN + LEFT)
         self.teacher.look_at(self.students[-1].eyes)
         for student in self.students:
             student.look_at(self.teacher.eyes)
@@ -307,7 +315,7 @@ class TeacherStudentsScene(PiCreatureScene):
         return self.pi_creature_thinks(student, *content, **kwargs)
 
     def change_all_student_modes(self, mode, **kwargs):
-        self.change_student_modes(*[mode]*len(self.students), **kwargs)
+        self.change_student_modes(*[mode] * len(self.students), **kwargs)
 
     def change_student_modes(self, *modes, **kwargs):
         added_anims = kwargs.pop("added_anims", [])
@@ -327,11 +335,11 @@ class TeacherStudentsScene(PiCreatureScene):
         submobject_mode = kwargs.get("submobject_mode", "lagged_start")
         return Transform(
             start, target,
-            submobject_mode = submobject_mode,
+            submobject_mode=submobject_mode,
-            run_time = 2
+            run_time=2
         )
 
-    def zoom_in_on_thought_bubble(self, bubble = None, radius = FRAME_Y_RADIUS+FRAME_X_RADIUS):
+    def zoom_in_on_thought_bubble(self, bubble=None, radius=FRAME_Y_RADIUS + FRAME_X_RADIUS):
         if bubble is None:
             for pi in self.get_pi_creatures():
                 if hasattr(pi, "bubble") and isinstance(pi.bubble, ThoughtBubble):
@@ -340,15 +348,16 @@ class TeacherStudentsScene(PiCreatureScene):
             if bubble is None:
                 raise Exception("No pi creatures have a thought bubble")
         vect = -bubble.get_bubble_center()
+
         def func(point):
-            centered = point+vect
+            centered = point + vect
-            return radius*centered/np.linalg.norm(centered)
+            return radius * centered / np.linalg.norm(centered)
         self.play(*[
             ApplyPointwiseFunction(func, mob)
             for mob in self.get_mobjects()
         ])
 
-    def teacher_holds_up(self, mobject, target_mode = "raise_right_hand", **kwargs):
+    def teacher_holds_up(self, mobject, target_mode="raise_right_hand", **kwargs):
         mobject.move_to(self.hold_up_spot, DOWN)
         mobject.shift_onto_screen()
         mobject_copy = mobject.copy()
@@ -358,5 +367,3 @@ class TeacherStudentsScene(PiCreatureScene):
             ReplacementTransform(mobject_copy, mobject),
             self.teacher.change, target_mode,
         )
-
-

mobject/matrix.py

@@ -12,12 +12,13 @@ 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)
+    prefix = "\\left[ \\begin{array}{%s}" % ("c" * n_cols)
     suffix = "\\end{array} \\right]"
     rows = [
         " & ".join(row)
@@ -25,36 +26,40 @@ def matrix_to_tex_string(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):
+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 = 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
+    if shift_dir[0] >= 0:  # Pointing right
-        shift_dir -= label.get_left() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*LEFT
+        shift_dir -= label.get_left() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER * LEFT
-    else: #Pointing left
+    else:  # Pointing left
-        shift_dir -= label.get_right() + DEFAULT_MOBJECT_TO_MOBJECT_BUFFER*RIGHT
+        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,
+        "v_buff": 0.5,
-        "h_buff" : 1,
+        "h_buff": 1,
-        "add_background_rectangles" : False
+        "add_background_rectangles": False
     }
+
     def __init__(self, matrix, **kwargs):
         """
         Matrix can either either include numbres, tex_strings,
@@ -89,9 +94,9 @@ class Matrix(VMobject):
                 if i == 0 and j == 0:
                     continue
                 elif i == 0:
-                    mob.next_to(matrix[i][j-1], RIGHT, self.h_buff)
+                    mob.next_to(matrix[i][j - 1], RIGHT, self.h_buff)
                 else:
-                    mob.next_to(matrix[i-1][j], DOWN, self.v_buff)
+                    mob.next_to(matrix[i - 1][j], DOWN, self.v_buff)
         return self
 
     def add_brackets(self):
@@ -107,7 +112,7 @@ class Matrix(VMobject):
 
     def set_color_columns(self, *colors):
         for i, color in enumerate(colors):
-            VGroup(*self.mob_matrix[:,i]).set_color(color)
+            VGroup(*self.mob_matrix[:, i]).set_color(color)
         return self
 
     def add_background_to_entries(self):
@@ -123,15 +128,3 @@ class Matrix(VMobject):
 
     def get_brackets(self):
         return self.brackets
-
-
-
-
-
-
-
-
-
-
-
-

requirements.txt

@@ -1,3 +1,4 @@
+argparse==1.4.0
 colour==0.1.2
 numpy==1.11.0
 Pillow==3.4.2

scene/vector_space_scene.py

@@ -36,25 +36,27 @@ X_COLOR = GREEN_C
 Y_COLOR = RED_C
 Z_COLOR = BLUE_D
 
+
 class VectorScene(Scene):
     CONFIG = {
-        "basis_vector_stroke_width" : 6
+        "basis_vector_stroke_width": 6
     }
-    def add_plane(self, animate = False, **kwargs):
+
+    def add_plane(self, animate=False, **kwargs):
         plane = NumberPlane(**kwargs)
         if animate:
-            self.play(ShowCreation(plane, submobject_mode = "lagged_start"))
+            self.play(ShowCreation(plane, submobject_mode="lagged_start"))
         self.add(plane)
         return plane
 
-    def add_axes(self, animate = False, color = WHITE, **kwargs):
+    def add_axes(self, animate=False, color=WHITE, **kwargs):
-        axes = Axes(color = color, tick_frequency = 1)
+        axes = Axes(color=color, tick_frequency=1)
         if animate:
-            self.play(ShowCreation(axes, submobject_mode = "one_at_a_time"))
+            self.play(ShowCreation(axes, submobject_mode="one_at_a_time"))
         self.add(axes)
         return axes
 
-    def lock_in_faded_grid(self, dimness = 0.7, axes_dimness = 0.5):
+    def lock_in_faded_grid(self, dimness=0.7, axes_dimness=0.5):
         plane = self.add_plane()
         axes = plane.get_axes()
         plane.fade(dimness)
@@ -63,9 +65,9 @@ class VectorScene(Scene):
         self.add(axes)
         self.freeze_background()
 
-    def add_vector(self, vector, color = YELLOW, animate = True, **kwargs):
+    def add_vector(self, vector, color=YELLOW, animate=True, **kwargs):
         if not isinstance(vector, Arrow):
-            vector = Vector(vector, color = color, **kwargs)
+            vector = Vector(vector, color=color, **kwargs)
         if animate:
             self.play(ShowCreation(vector))
         self.add(vector)
@@ -76,40 +78,41 @@ class VectorScene(Scene):
         self.play(Write(coords))
         return coords
 
-    def get_basis_vectors(self):
+    def get_basis_vectors(self, i_hat_color=X_COLOR, j_hat_color=Y_COLOR):
-        return [
+        return VGroup(*[
             Vector(
-                vect, color = color, 
+                vect,
-                stroke_width = self.basis_vector_stroke_width
+                color=color,
+                stroke_width=self.basis_vector_stroke_width
             )
             for vect, color in [
-                ([1, 0], X_COLOR), 
+                ([1, 0], i_hat_color),
-                ([0, 1], Y_COLOR)
+                ([0, 1], j_hat_color)
-            ]
             ]
+        ])
 
     def get_basis_vector_labels(self, **kwargs):
         i_hat, j_hat = self.get_basis_vectors()
         return VGroup(*[
             self.get_vector_label(
-                vect, label, color = color, 
+                vect, label, color=color,
-                label_scale_factor = 1,
+                label_scale_factor=1,
                 **kwargs
             )
-            for vect, label , color in [
+            for vect, label, color in [
                 (i_hat, "\\hat{\\imath}", X_COLOR),
                 (j_hat, "\\hat{\\jmath}", Y_COLOR),
             ]
         ])
 
     def get_vector_label(self, vector, label,
-                         direction = "left", 
+                         direction="left",
-                         rotate = False,
+                         rotate=False,
-                         color = None, 
+                         color=None,
-                         label_scale_factor = VECTOR_LABEL_SCALE_FACTOR):
+                         label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
         if not isinstance(label, TexMobject):
             if len(label) == 1:
-                label = "\\vec{\\textbf{%s}}"%label
+                label = "\\vec{\\textbf{%s}}" % label
             label = TexMobject(label)
             if color is None:
                 color = vector.get_color()
@@ -119,53 +122,53 @@ class VectorScene(Scene):
 
         angle = vector.get_angle()
         if not rotate:
-            label.rotate(-angle, about_point = ORIGIN)
+            label.rotate(-angle, about_point=ORIGIN)
         if direction is "left":
-            label.shift(-label.get_bottom() + 0.1*UP)
+            label.shift(-label.get_bottom() + 0.1 * UP)
         else:
-            label.shift(-label.get_top() + 0.1*DOWN)
+            label.shift(-label.get_top() + 0.1 * DOWN)
-        label.rotate(angle, about_point = ORIGIN)
+        label.rotate(angle, about_point=ORIGIN)
-        label.shift((vector.get_end() - vector.get_start())/2)
+        label.shift((vector.get_end() - vector.get_start()) / 2)
         return label
 
-    def label_vector(self, vector, label, animate = True, **kwargs):
+    def label_vector(self, vector, label, animate=True, **kwargs):
         label = self.get_vector_label(vector, label, **kwargs)
         if animate:
-            self.play(Write(label, run_time = 1))
+            self.play(Write(label, run_time=1))
         self.add(label)
         return label
 
     def position_x_coordinate(self, x_coord, x_line, vector):
-        x_coord.next_to(x_line, -np.sign(vector[1])*UP)
+        x_coord.next_to(x_line, -np.sign(vector[1]) * UP)
         x_coord.set_color(X_COLOR)
         return x_coord
 
     def position_y_coordinate(self, y_coord, y_line, vector):
-        y_coord.next_to(y_line, np.sign(vector[0])*RIGHT)
+        y_coord.next_to(y_line, np.sign(vector[0]) * RIGHT)
         y_coord.set_color(Y_COLOR)
         return y_coord
 
-    def coords_to_vector(self, vector, coords_start = 2*RIGHT+2*UP, clean_up = True):
+    def coords_to_vector(self, vector, coords_start=2 * RIGHT + 2 * UP, clean_up=True):
         starting_mobjects = list(self.mobjects)
         array = Matrix(vector)
         array.shift(coords_start)
         arrow = Vector(vector)
-        x_line = Line(ORIGIN, vector[0]*RIGHT)
+        x_line = Line(ORIGIN, vector[0] * RIGHT)
         y_line = Line(x_line.get_end(), arrow.get_end())
         x_line.set_color(X_COLOR)
         y_line.set_color(Y_COLOR)
         x_coord, y_coord = array.get_mob_matrix().flatten()
 
-        self.play(Write(array, run_time = 1))
+        self.play(Write(array, run_time=1))
         self.wait()
         self.play(ApplyFunction(
-            lambda x : self.position_x_coordinate(x, x_line, vector),
+            lambda x: self.position_x_coordinate(x, x_line, vector),
             x_coord
         ))
         self.play(ShowCreation(x_line))
         self.play(
             ApplyFunction(
-                lambda y : self.position_y_coordinate(y, y_line, vector),
+                lambda y: self.position_y_coordinate(y, y_line, vector),
                 y_coord
             ),
             FadeOut(array.get_brackets())
@@ -178,7 +181,7 @@ class VectorScene(Scene):
             self.clear()
             self.add(*starting_mobjects)
 
-    def vector_to_coords(self, vector, integer_labels = True, clean_up = True):
+    def vector_to_coords(self, vector, integer_labels=True, clean_up=True):
         starting_mobjects = list(self.mobjects)
         show_creation = False
         if isinstance(vector, Arrow):
@@ -187,8 +190,8 @@ class VectorScene(Scene):
         else:
             arrow = Vector(vector)
             show_creation = True
-        array = vector_coordinate_label(arrow, integer_labels = integer_labels)
+        array = vector_coordinate_label(arrow, integer_labels=integer_labels)
-        x_line = Line(ORIGIN, vector[0]*RIGHT)
+        x_line = Line(ORIGIN, vector[0] * RIGHT)
         y_line = Line(x_line.get_end(), arrow.get_end())
         x_line.set_color(X_COLOR)
         y_line.set_color(Y_COLOR)
@@ -206,18 +209,18 @@ class VectorScene(Scene):
         self.play(
             ShowCreation(x_line),
             Write(x_coord_start),
-            run_time = 1
+            run_time=1
         )
         self.play(
             ShowCreation(y_line),
             Write(y_coord_start),
-            run_time = 1
+            run_time=1
         )
         self.wait()
         self.play(
-            Transform(x_coord_start, x_coord, submobject_mode = "all_at_once"),
+            Transform(x_coord_start, x_coord, submobject_mode="all_at_once"),
-            Transform(y_coord_start, y_coord, submobject_mode = "all_at_once"),
+            Transform(y_coord_start, y_coord, submobject_mode="all_at_once"),
-            Write(brackets, run_time = 1),
+            Write(brackets, run_time=1),
         )
         self.wait()
 
@@ -236,49 +239,52 @@ class VectorScene(Scene):
         x_max = int(FRAME_X_RADIUS + abs(vector[0]))
         y_max = int(FRAME_Y_RADIUS + abs(vector[1]))
         dots = VMobject(*[
-            Dot(x*RIGHT + y*UP)
+            Dot(x * RIGHT + y * UP)
             for x in range(-x_max, x_max)
             for y in range(-y_max, y_max)
         ])
-        dots.set_fill(BLACK, opacity = 0)
+        dots.set_fill(BLACK, opacity=0)
-        dots_halfway = dots.copy().shift(vector/2).set_fill(WHITE, 1)
+        dots_halfway = dots.copy().shift(vector / 2).set_fill(WHITE, 1)
         dots_end = dots.copy().shift(vector)
 
         self.play(Transform(
-            dots, dots_halfway, rate_func = rush_into
+            dots, dots_halfway, rate_func=rush_into
         ))
         self.play(Transform(
-            dots, dots_end, rate_func = rush_from
+            dots, dots_end, rate_func=rush_from
         ))
         self.remove(dots)
 
+
 class LinearTransformationScene(VectorScene):
     CONFIG = {
-        "include_background_plane" : True,
+        "include_background_plane": True,
-        "include_foreground_plane" : True,
+        "include_foreground_plane": True,
-        "foreground_plane_kwargs" : {
+        "foreground_plane_kwargs": {
-            "x_radius" : FRAME_WIDTH,
+            "x_radius": FRAME_WIDTH,
-            "y_radius" : FRAME_HEIGHT,
+            "y_radius": FRAME_HEIGHT,
-            "secondary_line_ratio" : 0
+            "secondary_line_ratio": 0
         },
-        "background_plane_kwargs" : {
+        "background_plane_kwargs": {
-            "color" : GREY,
+            "color": GREY,
-            "secondary_color" : DARK_GREY,
+            "secondary_color": DARK_GREY,
-            "axes_color" : GREY,
+            "axes_color": GREY,
-            "stroke_width" : 2,
+            "stroke_width": 2,
         },
-        "show_coordinates" : False,
+        "show_coordinates": False,
-        "show_basis_vectors" : True,
+        "show_basis_vectors": True,
-        "i_hat_color" : X_COLOR,
+        "basis_vector_stroke_width": 6,
-        "j_hat_color" : Y_COLOR,
+        "i_hat_color": X_COLOR,
-        "leave_ghost_vectors" : False,
+        "j_hat_color": Y_COLOR,
-        "t_matrix" : [[3, 0], [1, 2]],
+        "leave_ghost_vectors": False,
+        "t_matrix": [[3, 0], [1, 2]],
     }
+
     def setup(self):
         if hasattr(self, "has_already_setup"):
             return
         self.has_already_setup = True
-        ##^This is to not break all the old Scenes
+        # ^This is to not break all the old Scenes
         self.background_mobjects = []
         self.foreground_mobjects = []
         self.transformable_mobjects = []
@@ -299,15 +305,12 @@ class LinearTransformationScene(VectorScene):
             self.plane = NumberPlane(**self.foreground_plane_kwargs)
             self.add_transformable_mobject(self.plane)
         if self.show_basis_vectors:
-            self.i_hat, self.j_hat = [
+            self.basis_vectors = self.get_basis_vectors(
-                self.add_vector(
+                i_hat_color=self.i_hat_color,
-                    coords, color, animate = False, stroke_width = 6
+                j_hat_color=self.j_hat_color,
             )
-                for coords, color in [
+            self.moving_vectors += list(self.basis_vectors)
-                    ((1, 0), self.i_hat_color),
+            self.i_hat, self.j_hat = self.basis_vectors
-                    ((0, 1), self.j_hat_color),
-                ]
-            ]
 
     def add_special_mobjects(self, mob_list, *mobs_to_add):
         for mobject in mobs_to_add:
@@ -324,13 +327,13 @@ class LinearTransformationScene(VectorScene):
     def add_transformable_mobject(self, *mobjects):
         self.add_special_mobjects(self.transformable_mobjects, *mobjects)
 
-    def add_moving_mobject(self, mobject, target_mobject = None):
+    def add_moving_mobject(self, mobject, target_mobject=None):
         mobject.target = target_mobject
         self.add_special_mobjects(self.moving_mobjects, mobject)
 
-    def add_unit_square(self, color = YELLOW, opacity = 0.3, animate = False):
+    def add_unit_square(self, color=YELLOW, opacity=0.3, animate=False):
-        square = Square(color = color, side_length = 1)
+        square = Square(color=color, side_length=1)
-        square.shift(-square.get_corner(DOWN+LEFT))
+        square.shift(-square.get_corner(DOWN + LEFT))
         if animate:
             added_anims = map(Animation, self.moving_vectors)
             self.play(ShowCreation(square), *added_anims)
@@ -342,9 +345,9 @@ class LinearTransformationScene(VectorScene):
         self.square = square
         return self
 
-    def add_vector(self, vector, color = YELLOW, **kwargs):
+    def add_vector(self, vector, color=YELLOW, **kwargs):
         vector = VectorScene.add_vector(
-            self, vector, color = color, **kwargs
+            self, vector, color=color, **kwargs
         )
         self.moving_vectors.append(vector)
         return vector
@@ -354,12 +357,12 @@ class LinearTransformationScene(VectorScene):
         self.add_foreground_mobject(coords)
         return coords
 
-    def add_transformable_label(self, vector, label, new_label = None, **kwargs):
+    def add_transformable_label(self, vector, label, new_label=None, **kwargs):
         label_mob = self.label_vector(vector, label, **kwargs)
         if new_label:
             label_mob.target_text = new_label
         else:
-            label_mob.target_text = "L(%s)"%label_mob.get_tex_string()
+            label_mob.target_text = "L(%s)" % label_mob.get_tex_string()
         label_mob.vector = vector
         label_mob.kwargs = kwargs
         if "animate" in label_mob.kwargs:
@@ -367,7 +370,7 @@ class LinearTransformationScene(VectorScene):
         self.transformable_labels.append(label_mob)
         return label_mob
 
-    def add_title(self, title, scale_factor = 1.5, animate = False):
+    def add_title(self, title, scale_factor=1.5, animate=False):
         if not isinstance(title, Mobject):
             title = TextMobject(title).scale(scale_factor)
         title.to_edge(UP)
@@ -378,7 +381,10 @@ class LinearTransformationScene(VectorScene):
         self.title = title
         return self
 
-    def get_matrix_transformation(self, transposed_matrix):
+    def get_matrix_transformation(self, matrix):
+        return self.get_transposed_matrix_transformation(np.array(matrix).T)
+
+    def get_transposed_matrix_transformation(self, transposed_matrix):
         transposed_matrix = np.array(transposed_matrix)
         if transposed_matrix.shape == (2, 2):
             new_matrix = np.identity(3)
@@ -393,7 +399,7 @@ class LinearTransformationScene(VectorScene):
         target = VMobject(*[mob.target for mob in pieces])
         if self.leave_ghost_vectors:
             self.add(start.copy().fade(0.7))
-        return Transform(start, target, submobject_mode = "all_at_once")
+        return Transform(start, target, submobject_mode="all_at_once")
 
     def get_moving_mobject_movement(self, func):
         for m in self.moving_mobjects:
@@ -405,7 +411,7 @@ class LinearTransformationScene(VectorScene):
 
     def get_vector_movement(self, func):
         for v in self.moving_vectors:
-            v.target = Vector(func(v.get_end()), color = v.get_color())
+            v.target = Vector(func(v.get_end()), color=v.get_color())
             norm = np.linalg.norm(v.target.get_end())
             if norm < 0.1:
                 v.target.get_tip().scale_in_place(norm)
@@ -418,12 +424,15 @@ class LinearTransformationScene(VectorScene):
             )
         return self.get_piece_movement(self.transformable_labels)
 
+    def apply_matrix(self, matrix, **kwargs):
+        self.apply_transposed_matrix(np.array(matrix).T, **kwargs)
+
     def apply_transposed_matrix(self, transposed_matrix, **kwargs):
-        func = self.get_matrix_transformation(transposed_matrix)
+        func = self.get_transposed_matrix_transformation(transposed_matrix)
         if "path_arc" not in kwargs:
             net_rotation = np.mean([
                 angle_of_vector(func(RIGHT)),
-                angle_of_vector(func(UP))-np.pi/2
+                angle_of_vector(func(UP)) - np.pi / 2
             ])
             kwargs["path_arc"] = net_rotation
         self.apply_function(func, **kwargs)
@@ -436,7 +445,7 @@ class LinearTransformationScene(VectorScene):
         self.plane.prepare_for_nonlinear_transform()
         self.apply_function(function, **kwargs)
 
-    def apply_function(self, function, added_anims = [], **kwargs):
+    def apply_function(self, function, added_anims=[], **kwargs):
         if "run_time" not in kwargs:
             kwargs["run_time"] = 3
         anims = [
@@ -451,14 +460,3 @@ class LinearTransformationScene(VectorScene):
             for f_mob in self.foreground_mobjects
         ] + added_anims
         self.play(*anims, **kwargs)
-
-
-
-
-
-
-
-
-
-
-