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End of Cramers

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This commit is contained in:
Grant Sanderson 2018-04-29 18:03:17 -07:00
parent 8491e4b860
commit 870cfbad0c
1 changed files with 63 additions and 14 deletions
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77
active_projects/eola2/cramer.py
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@ -71,6 +71,13 @@ class LinearSystem(VGroup):
# Scenes
class CramerOpeningQuote(OpeningQuote):
CONFIG = {
"quote": ["Computers are useless. They \\\\ can only give you answers."],
"author": "Pablo Picasso",
}
class LeaveItToComputers(TeacherStudentsScene):
CONFIG = {
"random_seed": 1,
@ -83,26 +90,30 @@ class LeaveItToComputers(TeacherStudentsScene):
system.target.scale(0.5)
system.target.to_corner(UL)
colors = [X_COLOR, Y_COLOR, Z_COLOR]
cramer_groups = VGroup()
for i in range(3):
numer_matrix = get_cramer_matrix(
system.matrix_mobject, system.output_vect_mob,
index=i
)
VGroup(*numer_matrix.mob_matrix[:, i]).set_color(colors[i])
VGroup(*numer_matrix.mob_matrix[:, i]).set_stroke(colors[i], 1)
numer = VGroup(
get_det_text(numer_matrix, initial_scale_factor=4),
get_det_text(numer_matrix, initial_scale_factor=3),
numer_matrix
)
numer.to_corner(UP)
denom_matrix_mobject = system.matrix_mobject.copy()
denom_matrix_mobject = system.matrix_mobject.deepcopy()
denom = VGroup(
get_det_text(denom_matrix_mobject, initial_scale_factor=4),
get_det_text(denom_matrix_mobject, initial_scale_factor=3),
denom_matrix_mobject,
)
rhs = VGroup(numer, Line(LEFT, RIGHT).match_width(numer), denom)
rhs.arrange_submobjects(DOWN)
rhs.scale_to_fit_height(2.25)
rhs.move_to(self.hold_up_spot, DOWN)
rhs.to_edge(RIGHT, buff=LARGE_BUFF)
equals = TexMobject("=").next_to(rhs, LEFT)
variable = system.input_vect_mob.elements[i].copy()
variable.next_to(equals, LEFT)
@ -149,6 +160,7 @@ class LeaveItToComputers(TeacherStudentsScene):
denom_mover.target = numer.deepcopy()
column1 = VGroup(*denom_mover.target[1].mob_matrix[:, 0])
column1.set_fill(opacity=0)
column1.set_stroke(width=0)
self.play(MoveToTarget(denom_mover))
self.look_at(system)
self.play(
@ -210,7 +222,7 @@ class PrerequisiteKnowledge(TeacherStudentsScene):
images = Group(*[
ImageMobject("eola%d_thumbnail" % d)
for d in [5, 6, 7]
for d in [5, 7, 6]
])
images.arrange_submobjects(RIGHT, buff=LARGE_BUFF)
images.next_to(h_line, DOWN, MED_LARGE_BUFF)
@ -235,22 +247,42 @@ class PrerequisiteKnowledge(TeacherStudentsScene):
class NotTheMostComputationallyEfficient(Scene):
CONFIG = {
"words": "Not the most \\\\ computationally \\\\ efficient",
"words": "Not the most \\\\ computationally efficient",
"word_height": 4,
"opacity": 0.7,
}
def construct(self):
big_rect = FullScreenFadeRectangle(opacity=0.5)
big_rect = FullScreenFadeRectangle(opacity=self.opacity)
self.add(big_rect)
words = TextMobject(self.words)
words.set_color(RED)
words.set_stroke(WHITE, 1)
words.scale_to_fit_height(self.word_height)
words.scale_to_fit_width(FRAME_WIDTH - 2 * MED_LARGE_BUFF)
self.play(Write(words))
self.wait()
class WhyLearnIt(TeacherStudentsScene):
def construct(self):
self.student_says(
"What?!? Then why \\\\ learn it?",
bubble_kwargs={"direction": LEFT},
student_index=2,
target_mode="angry",
)
self.change_all_student_modes("angry")
self.wait()
self.play(
self.teacher.change, "raise_right_hand",
self.get_student_changes("erm", "happy" "pondering"),
RemovePiCreatureBubble(self.students[2], target_mode="pondering"),
)
self.look_at(self.screen)
self.wait(10)
class SetupSimpleSystemOfEquations(LinearTransformationScene):
CONFIG = {
"matrix": [[3, 2], [-1, 2]],
@ -1265,10 +1297,18 @@ class SolvingASystemWithOrthonormalMatrix(LinearTransformationScene):
TexMobject("="),
moving_output_vect_label.generate_target(),
TexMobject("\\cdot"),
moving_column_mob.generate_target()
moving_column_mob.generate_target(use_deepcopy=True)
)
equation.movers = VGroup(
moving_var, moving_output_vect_label, moving_column_mob)
moving_var, moving_output_vect_label, moving_column_mob
)
for element in moving_column_mob.target.submobject_family():
if not isinstance(element, TexMobject):
continue
tex_string = element.get_tex_string()
if "sin" in tex_string or "cos" in tex_string:
element.set_stroke(width=1)
element.scale(1.25)
equation.to_write = equation[1::2]
equation[2].match_height(equation[4])
equation.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
@ -1276,15 +1316,23 @@ class SolvingASystemWithOrthonormalMatrix(LinearTransformationScene):
equation.add_to_back(equation.background_rectangle)
equations.add(equation)
equations.arrange_submobjects(DOWN, buff=MED_LARGE_BUFF)
equations.to_corner(UR)
equations.scale(1.25)
equations.to_corner(UR, buff=MED_SMALL_BUFF)
equations_rect = BackgroundRectangle(equations, buff=MED_LARGE_BUFF)
equations_rect.set_fill(opacity=0.9)
for i, equation in enumerate(equations):
self.play(
anims = [
FadeIn(equation.background_rectangle),
Write(equation.to_write),
LaggedStart(MoveToTarget, equation.movers,
path_arc=60 * DEGREES),
)
LaggedStart(
MoveToTarget, equation.movers,
path_arc=60 * DEGREES
)
]
if i == 0:
anims.insert(0, FadeIn(equations_rect))
self.play(*anims)
self.wait()
def get_column_animations(self, matrix_mobject, column_mobs):
@ -1991,6 +2039,7 @@ class WriteCramersRule(Scene):
def construct(self):
words = TextMobject("``Cramer's Rule''")
words.scale_to_fit_width(FRAME_WIDTH - LARGE_BUFF)
words.add_background_rectangle()
self.play(Write(words))
self.wait()