mirror of
https://github.com/3b1b/manim.git
synced 2025-09-01 00:48:45 +00:00
Up to definition of eigenvectors
This commit is contained in:
Grant Sanderson
parent
0df8b73a87
commit
2de817010d
3 changed files with 242 additions and 13 deletions
|
|
@ -19,6 +19,7 @@ from mobject.vectorized_mobject import *
|
|||
|
||||
from eola.matrix import *
|
||||
from eola.two_d_space import *
|
||||
from eola.chapter1 import plane_wave_homotopy
|
||||
|
||||
class OpeningQuote(Scene):
|
||||
def construct(self):
|
||||
|
|
@ -103,7 +104,7 @@ class StudentsFindThisConfusing(TeacherStudentsScene):
|
|||
self.random_blink(3)
|
||||
|
||||
class ShowComments(Scene):
|
||||
pass
|
||||
pass #TODO
|
||||
|
||||
class EigenThingsArentAllThatBad(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
|
|
@ -111,7 +112,10 @@ class EigenThingsArentAllThatBad(TeacherStudentsScene):
|
|||
"Eigen-things aren't \\\\ actually so bad",
|
||||
pi_creature_target_mode = "hooray"
|
||||
)
|
||||
self.random_blink(5)
|
||||
self.change_student_modes(
|
||||
"pondering", "pondering", "erm"
|
||||
)
|
||||
self.random_blink(4)
|
||||
|
||||
class ManyPrerequisites(Scene):
|
||||
def construct(self):
|
||||
|
|
@ -256,14 +260,10 @@ class VectorRemainsOnSpan(ExampleTranformationScene):
|
|||
|
||||
class IHatAsEigenVector(ExampleTranformationScene):
|
||||
def construct(self):
|
||||
# self.highlight_first_column()
|
||||
def homotopy(x, y, z, t):
|
||||
pass
|
||||
x_axis = self.plane.axes[0]
|
||||
self.play(
|
||||
x_axis.highlight, GREEN_E,
|
||||
Homotopy(plane_wave_homotopy, x_axis, run_time = 3)
|
||||
)
|
||||
self.highlight_first_column()
|
||||
self.highlight_x_axis()
|
||||
self.apply_transposed_matrix(self.t_matrix, path_arc = 0)
|
||||
self.label_i_hat_landing_spot()
|
||||
|
||||
def highlight_first_column(self):
|
||||
faders = VGroup(self.plane, self.i_hat, self.j_hat)
|
||||
|
|
@ -276,14 +276,214 @@ class IHatAsEigenVector(ExampleTranformationScene):
|
|||
self.play(faders.restore, Animation(self.matrix))
|
||||
self.dither()
|
||||
|
||||
def highlight_x_axis(self):
|
||||
x_axis = self.plane.axes[0]
|
||||
targets = [
|
||||
self.i_hat.copy().scale(val)
|
||||
for val in -SPACE_WIDTH, SPACE_WIDTH, 1
|
||||
]
|
||||
lines = [
|
||||
Line(v1.get_end(), v2.get_end(), color = YELLOW)
|
||||
for v1, v2 in adjascent_pairs([self.i_hat]+targets)
|
||||
]
|
||||
for target, line in zip(targets, lines):
|
||||
self.play(
|
||||
ShowCreation(line),
|
||||
Transform(self.i_hat, target),
|
||||
)
|
||||
self.dither()
|
||||
self.remove(*lines)
|
||||
x_axis.highlight(YELLOW)
|
||||
|
||||
def label_i_hat_landing_spot(self):
|
||||
array = Matrix(self.t_matrix[0])
|
||||
array.highlight(X_COLOR)
|
||||
array.rect = BackgroundRectangle(array)
|
||||
array.add_to_back(array.rect)
|
||||
brace = Brace(self.i_hat, buff = 0)
|
||||
brace.put_at_tip(array)
|
||||
|
||||
self.play(GrowFromCenter(brace))
|
||||
matrix = self.matrix.copy()
|
||||
self.play(
|
||||
Transform(matrix.rect, array.rect),
|
||||
Transform(matrix.get_brackets(), array.get_brackets()),
|
||||
Transform(
|
||||
VGroup(*matrix.get_mob_matrix()[:,0]),
|
||||
array.get_entries()
|
||||
),
|
||||
)
|
||||
self.dither()
|
||||
|
||||
class AllXAxisVectorsAreEigenvectors(ExampleTranformationScene):
|
||||
def construct(self):
|
||||
vectors = VGroup(*[
|
||||
self.add_vector(u*x*RIGHT, animate = False)
|
||||
for x in reversed(range(1, int(SPACE_WIDTH)+1))
|
||||
for u in -1, 1
|
||||
])
|
||||
vectors.gradient_highlight(YELLOW, X_COLOR)
|
||||
self.play(ShowCreation(vectors))
|
||||
self.dither()
|
||||
self.apply_transposed_matrix(self.t_matrix, path_arc = 0)
|
||||
self.dither()
|
||||
|
||||
class SneakierEigenVector(ExampleTranformationScene):
|
||||
def construct(self):
|
||||
pass
|
||||
coords = [-1, 1]
|
||||
vector = Vector(coords)
|
||||
array = Matrix(coords)
|
||||
array.scale(0.7)
|
||||
array.highlight(vector.get_color())
|
||||
array.add_to_back(BackgroundRectangle(array))
|
||||
array.target = array.copy()
|
||||
array.next_to(vector.get_end(), LEFT)
|
||||
array.target.next_to(2*vector.get_end(), LEFT)
|
||||
two_times = TexMobject("2 \\cdot")
|
||||
two_times.add_background_rectangle()
|
||||
two_times.next_to(array.target, LEFT)
|
||||
span_line = Line(-4*vector.get_end(), 4*vector.get_end())
|
||||
span_line.highlight(MAROON_B)
|
||||
|
||||
self.matrix.shift(-2*self.matrix.get_center()[0]*RIGHT)
|
||||
|
||||
self.add_vector(vector)
|
||||
self.play(Write(array))
|
||||
self.play(
|
||||
ShowCreation(span_line),
|
||||
Animation(vector),
|
||||
Animation(array),
|
||||
)
|
||||
self.dither()
|
||||
self.apply_transposed_matrix(
|
||||
self.t_matrix,
|
||||
added_anims = [
|
||||
MoveToTarget(array),
|
||||
Transform(VectorizedPoint(array.get_left()), two_times)
|
||||
],
|
||||
path_arc = 0,
|
||||
)
|
||||
self.dither()
|
||||
|
||||
class FullSneakyEigenspace(ExampleTranformationScene):
|
||||
def construct(self):
|
||||
self.matrix.shift(-2*self.matrix.get_center()[0]*RIGHT)
|
||||
vectors = VGroup(*[
|
||||
self.add_vector(u*x*(LEFT+UP), animate = False)
|
||||
for x in reversed(np.arange(0.5, 5, 0.5))
|
||||
for u in -1, 1
|
||||
])
|
||||
vectors.gradient_highlight(MAROON_B, YELLOW)
|
||||
words = TextMobject("Stretch by 2")
|
||||
words.add_background_rectangle()
|
||||
words.next_to(ORIGIN, DOWN+LEFT, buff = MED_BUFF)
|
||||
words.shift(MED_BUFF*LEFT)
|
||||
words.rotate(vectors[0].get_angle())
|
||||
words.start = words.copy()
|
||||
words.start.scale(0.5)
|
||||
words.start.set_fill(opacity = 0)
|
||||
|
||||
self.play(ShowCreation(vectors))
|
||||
self.dither()
|
||||
self.apply_transposed_matrix(
|
||||
self.t_matrix,
|
||||
added_anims = [Transform(words.start, words)],
|
||||
path_arc = 0
|
||||
)
|
||||
self.dither()
|
||||
|
||||
class NameEigenvectorsAndEigenvalues(ExampleTranformationScene):
|
||||
CONFIG = {
|
||||
"show_basis_vectors" : False
|
||||
}
|
||||
def construct(self):
|
||||
pass
|
||||
self.remove(self.matrix)
|
||||
self.foreground_mobjects.remove(self.matrix)
|
||||
x_vectors = VGroup(*[
|
||||
self.add_vector(u*x*RIGHT, animate = False)
|
||||
for x in range(int(SPACE_WIDTH)+1, 0, -1)
|
||||
for u in -1, 1
|
||||
])
|
||||
x_vectors.gradient_highlight(YELLOW, X_COLOR)
|
||||
self.remove(x_vectors)
|
||||
sneak_vectors = VGroup(*[
|
||||
self.add_vector(u*x*(LEFT+UP), animate = False)
|
||||
for x in np.arange(int(SPACE_HEIGHT), 0, -0.5)
|
||||
for u in -1, 1
|
||||
])
|
||||
sneak_vectors.gradient_highlight(MAROON_B, YELLOW)
|
||||
self.remove(sneak_vectors)
|
||||
|
||||
x_words = TextMobject("Stretched by 3")
|
||||
sneak_words = TextMobject("Stretched by 2")
|
||||
for words in x_words, sneak_words:
|
||||
words.add_background_rectangle()
|
||||
words.next_to(x_vectors, DOWN)
|
||||
words.next_to(words.get_center(), LEFT, buff = 1.5)
|
||||
eigen_word = TextMobject("Eigenvectors")
|
||||
eigen_word.add_background_rectangle()
|
||||
eigen_word.replace(words)
|
||||
words.target = eigen_word
|
||||
eigen_val_words = TextMobject(
|
||||
"with eigenvalue ",
|
||||
"%s"%words.get_tex_string()[-1]
|
||||
)
|
||||
eigen_val_words.add_background_rectangle()
|
||||
eigen_val_words.next_to(words, DOWN, aligned_edge = RIGHT)
|
||||
words.eigen_val_words = eigen_val_words
|
||||
x_words.eigen_val_words.highlight(X_COLOR)
|
||||
sneak_words.eigen_val_words.highlight(YELLOW)
|
||||
|
||||
VGroup(
|
||||
sneak_words,
|
||||
sneak_words.target,
|
||||
sneak_words.eigen_val_words,
|
||||
).rotate(sneak_vectors[0].get_angle())
|
||||
|
||||
non_eigen = Vector([1, 1], color = PINK)
|
||||
non_eigen_span = Line(
|
||||
-SPACE_HEIGHT*non_eigen.get_end(),
|
||||
SPACE_HEIGHT*non_eigen.get_end(),
|
||||
color = RED
|
||||
)
|
||||
non_eigen_words = TextMobject("""
|
||||
Knocked off
|
||||
its own span
|
||||
""")
|
||||
non_eigen_words.add_background_rectangle()
|
||||
non_eigen_words.scale(0.7)
|
||||
non_eigen_words.next_to(non_eigen.get_end(), RIGHT)
|
||||
non_eigen_span.fade()
|
||||
|
||||
for vectors in x_vectors, sneak_vectors:
|
||||
self.play(ShowCreation(vectors, run_time = 1))
|
||||
self.dither()
|
||||
for words in x_words, sneak_words:
|
||||
self.play(Write(words, run_time = 1.5))
|
||||
self.add_foreground_mobject(words)
|
||||
self.dither()
|
||||
self.play(ShowCreation(non_eigen))
|
||||
self.play(
|
||||
ShowCreation(non_eigen_span),
|
||||
Write(non_eigen_words),
|
||||
Animation(non_eigen)
|
||||
)
|
||||
self.add_vector(non_eigen, animate = False)
|
||||
self.dither()
|
||||
self.apply_transposed_matrix(
|
||||
self.t_matrix,
|
||||
added_anims = [FadeOut(non_eigen_words)],
|
||||
path_arc = 0,
|
||||
)
|
||||
self.dither(2)
|
||||
self.play(*map(FadeOut, [non_eigen, non_eigen_span]))
|
||||
self.play(*map(MoveToTarget, [x_words, sneak_words]))
|
||||
self.dither()
|
||||
for words in x_words, sneak_words:
|
||||
self.play(Write(words.eigen_val_words), run_time = 2)
|
||||
self.dither()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -19,6 +19,7 @@ from mobject.vectorized_mobject import *
|
|||
|
||||
from eola.matrix import *
|
||||
from eola.two_d_space import *
|
||||
from eola.chapter9 import Jennifer, You
|
||||
|
||||
class Chapter0(LinearTransformationScene):
|
||||
CONFIG = {
|
||||
|
|
@ -84,6 +85,34 @@ class Chapter5(LinearTransformationScene):
|
|||
self.square.set_stroke(width = 0)
|
||||
self.apply_transposed_matrix(self.t_matrix, run_time = 0)
|
||||
|
||||
class Chapter9(Scene):
|
||||
def construct(self):
|
||||
you = You()
|
||||
jenny = Jennifer()
|
||||
you.change_mode("erm")
|
||||
jenny.change_mode("speaking")
|
||||
you.shift(LEFT)
|
||||
jenny.shift(2*RIGHT)
|
||||
|
||||
vector = Vector([3, 2])
|
||||
vector.center().shift(2*DOWN)
|
||||
vector.set_stroke(width = 8)
|
||||
vector.tip.scale_in_place(2)
|
||||
|
||||
you.coords = Matrix([3, 2])
|
||||
jenny.coords = Matrix(["5/3", "1/3"])
|
||||
for pi in jenny, you:
|
||||
pi.bubble = pi.get_bubble("speech", width = 3, height = 3)
|
||||
if pi is you:
|
||||
pi.bubble.shift(MED_BUFF*RIGHT)
|
||||
else:
|
||||
pi.coords.scale(0.8)
|
||||
pi.bubble.shift(MED_BUFF*LEFT)
|
||||
pi.bubble.add_content(pi.coords)
|
||||
pi.add(pi.bubble, pi.coords)
|
||||
pi.look_at(vector)
|
||||
|
||||
self.add(you, jenny, vector)
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -6,7 +6,7 @@ from geometry import Line
|
|||
from helpers import *
|
||||
|
||||
|
||||
class Stars(Mobject):
|
||||
class Stars(Mobject1D):
|
||||
CONFIG = {
|
||||
"stroke_width" : 1,
|
||||
"radius" : SPACE_WIDTH,
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue