Merge pull request #72 from simranchhattani/master

Final changes

8 files changed, 251 insertions, 82 deletions

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py
new file mode 100644
index 0000000..6d2edc8
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py
@@ -0,0 +1,174 @@
+from manimlib.imports import *

+

+

+VECTORS = [[1, 2],

+           [-4, 2],

+           [-3, -3],

+           [3,-2],

+           [3,3],

+           [-2,1],

+           [-1,-3]]

+

+class Scene1(LinearTransformationScene):

+    

+    CONFIG = {

+        "include_background_plane": True,

+        "include_foreground_plane": False,

+        "show_coordinates": False,

+        "show_basis_vectors": True,

+        "basis_vector_stroke_width": 3,

+        

+    }

+    def construct(self):

+        self.setup()

+        ihat, jhat = self.get_basis_vectors()

+        labels = self.get_basis_vector_labels()

+        self.add(ihat, jhat)

+        self.add(*labels)

+        

+        self.show_vector_as_basis_sum()

+        self.wait(2)

+

+    def show_vector_as_basis_sum(self):

+        text1 = TextMobject(r"Vector Space $\mathbb{R}^2$}").scale(0.8).shift(3*UP)

+        text1.add_background_rectangle()

+        self.play(ShowCreation(text1))

+        text2 = TextMobject(r"$\mathbb{R}^2$",color=BLUE_E).scale(0.8).shift(6.5*LEFT+3.5*UP)

+        text3 = TextMobject(r"\text{Basis Vectors:}",r"\text{$\hat{i}$}",r"\text{,}",r"\text{$\hat{j}$}").scale(0.7).shift(2*UP+2.5*RIGHT)

+        text3[1].set_color(GREEN_C)

+        text3[3].set_color(RED_C)

+

+        self.wait(2)

+        self.play(Transform(text1,text2))

+        self.wait(1)

+        self.play(ShowCreation(text3))

+        self.wait(1.7)

+        self.play(FadeOut(text3))

+

+        for i in range(len(VECTORS)):

+            v = self.add_vector(VECTORS[i], stroke_width = 3,color=YELLOW_D)

+

+            linei = Line(start = ORIGIN, end = VECTORS[i][0]*RIGHT)

+            linei.set_color(GREEN_C)

+            linej = Line(start = linei.get_end(),

+                         end = linei.get_end() + VECTORS[i][1]*UP)

+            linej.set_color(RED_C)

+            self.play(ShowCreation(linei))

+            self.play(ShowCreation(linej))

+            vlabel = self.get_vector_label(v, str(VECTORS[i][0]) +

+                                           r"\imath" + "+" +

+                                           str(VECTORS[i][1]) +

+                                           r"\jmath", at_tip = True)

+            self.play(ShowCreation(vlabel))

+            

+            self.play(FadeOut(linei),FadeOut(linej))

+            self.wait(1)

+            dot = Dot(v.get_end(), fill_color = v.get_stroke_color())

+            self.play(ShowCreation(dot),FadeOut(v),FadeOut(vlabel))

+            self.wait(0.3)

+

+class Scene2(LinearTransformationScene):

+    CONFIG = {

+        "num_vectors" : 16,

+        "start_color" : GREY,

+        "end_color" : YELLOW_D,

+        "include_background_plane": True,

+        "include_foreground_plane": False,

+    }

+

+    def get_vectors(self):

+        return [

+            Vector([x, y], stroke_width = 3.5)

+            for x in np.arange(-int(FRAME_X_RADIUS), int(FRAME_X_RADIUS)+0.5, 0.5)

+            for y in np.arange(-int(FRAME_Y_RADIUS), int(FRAME_Y_RADIUS)+0.5, 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)

+        axes.set_color(WHITE)

+        axes.fade(axes_dimness)

+        self.add(axes)

+

+    def construct(self):

+        self.lock_in_faded_grid()

+

+        vectors = self.get_vectors()

+        colors = Color(self.start_color).range_to(

+            self.end_color, len(vectors)

+        )

+        for vect, color in zip(vectors, colors):

+            vect.set_color(color)

+

+        vector_group = VGroup(*vectors)

+        self.play(

+            ShowCreation(

+                vector_group,

+                run_time = 3

+            )

+        )

+

+        self.wait(1)

+

+        vectors.sort(key=lambda v: v.get_length())

+        def v_to_dot(vector):

+            return Dot(vector.get_end(), fill_color = vector.get_stroke_color())

+        self.wait()

+        rate_functions = [

+            squish_rate_func(smooth, float(x)/(len(vectors)+2), 1)

+            for x in range(len(vectors))

+        ]

+        self.play(*[

+            Transform(v, v_to_dot(v), rate_func = rf, run_time = 3)

+            for v, rf in zip(vectors, rate_functions)

+        ])

+        self.wait(2)

+        self.play_final_animation(vectors, rate_functions)

+        self.wait(2)

+

+        text1 = TextMobject(" Basis is the minimum information required to ").shift(3.1*UP).scale(0.8)

+        text2 = TextMobject("generate the whole space.").scale(0.8).shift(2.6*UP)

+        

+        text1.add_background_rectangle()

+        text2.add_background_rectangle()

+        

+        

+

+        self.play(ShowCreation(text1),ShowCreation(text2))

+        

+        self.play(ShowCreation(self.get_basis_vectors()))

+        self.wait(3)

+

+    def play_final_animation(self, vectors, rate_functions):

+

+        h_line = Line(

+            FRAME_X_RADIUS*RIGHT, FRAME_X_RADIUS*LEFT,

+            stroke_width = 0.5,

+            color = BLUE_E

+        )

+        v_line = Line(

+            FRAME_Y_RADIUS*UP, FRAME_Y_RADIUS*DOWN,

+            stroke_width = 0.5,

+            color = BLUE_E

+        )

+        line_pairs = [

+            VGroup(h_line.copy().shift(y), v_line.copy().shift(x))

+            for v in vectors

+            for x, y, z in [v.get_center()]

+        ]

+        plane = NumberPlane()

+        

+        self.play(

+            ShowCreation(plane),

+            *[

+                Transform(v, p, rate_func = rf)

+                for v, p, rf in zip(vectors, line_pairs, rate_functions)

+            ]

+        )

+        self.remove(*vectors)

+

+        

+        

+

+    
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py
new file mode 100644
index 0000000..ec82daa
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py
@@ -0,0 +1,52 @@
+from manimlib.imports import *

+class ThreeDSpace(ThreeDScene):

+

+

+    def construct(self):

+        axes = ThreeDAxes()

+        self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)

+        self.begin_ambient_camera_rotation(rate=0.09)

+        

+       

+        

+        

+        cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)

+        cube.set_fill(TEAL)

+        

+        cube.set_opacity(0.4) 

+        

+        

+        plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])

+        plane1.set_opacity(0.65)

+        plane1.set_fill(PURPLE)

+        plane1.set_color(PURPLE)

+        

+        

+        plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])

+        plane2.set_opacity(0.7)

+        plane2.set_fill(RED)

+        plane2.set_color(RED)

+        line = Line(color=YELLOW,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)

+

+        vgroup = VGroup(plane1,plane2,line,cube)

+        vgroup.shift([-1,-1,-1])

+        

+        dot = Dot(color=BLACK).shift([0.5,0.5,0.5]).scale(1)

+        text = TextMobject(r"\text{The}",r"\text{line}",r"\text{representing the intersection of the two planes is a Subspace.}",opacity = 0.6).scale(0.7).shift(3*UP)

+        text[1].set_color(YELLOW)

+        self.add_fixed_in_frame_mobjects(text)

+        self.play(ShowCreation(text))

+        

+        

+        self.play(ShowCreation(cube))

+        self.play(ShowCreation(plane1))

+        self.play(ShowCreation(plane2))

+

+        self.play(ShowCreation(line),ShowCreation(dot))

+        

+

+        self.wait(15)

+

+        

+

+  
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
deleted file mode 100644
index ada173e..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
+++ /dev/null
@@ -1,82 +0,0 @@
-from manimlib.imports import *

-class Subspace_Example(Scene):

-    def construct(self):

-        sq = Square(side = 2, color=BLACK).shift(2*LEFT)

-        sq.set_fill(color=RED,opacity=350)

-        line1=Line(color=BLACK).shift(2*LEFT)

-        line1.rotate(np.pi/2)

-        line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)

-        line2.scale(0.5)

-        line3=Line(color=BLACK).shift(+1.5*LEFT)

-        line3.scale(0.5)

-        a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)

-        a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)

-        a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)

-        a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)

-        big_rect=Rectangle().scale(3).shift(0.5*DOWN)

-        big_rect.set_fill(color=GREY,opacity=350)

-        vec_space=TextMobject("$Vector Space$").scale(0.77).shift(4.5*RIGHT+3.5*UP)

-        sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.77).shift(3.8*RIGHT+2*UP)

-        self.play(ShowCreation(vec_space))

-        self.play(ShowCreation(big_rect),ShowCreation(sub))

-        self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))

-        rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)

-        rec.rotate(np.pi/2)

-        rec.set_fill(color=BLUE,opacity=350)

-        line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)

-        line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)

-        line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)

-        b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)

-        b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)

-        b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)

-        b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)

-        self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))

-        self.wait(1)

-        text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)

-        text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)

-        self.play(ShowCreation(text1),ShowCreation(text2))

-        self.wait(3)

-        self.play(FadeOut(text1),FadeOut(text2))

-        rec.shift(3*LEFT+2.01*DOWN)

-        line4.shift(3*LEFT+2*DOWN)

-        line5.shift(3*LEFT+2*DOWN)

-        line6.shift(3*LEFT+2*DOWN)

-        b1.shift(3.1*LEFT+2.1*DOWN)

-        b2.shift(3.1*LEFT+2.1*DOWN)

-        b3.shift(2.9*LEFT+2*DOWN)

-        b4.shift(2.9*LEFT+2.3*DOWN)

-        self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))

-        self.wait(2)

-        

-        text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)

-        text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)

-        text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)

-        self.play(ShowCreation(text3),ShowCreation(text4))

-        self.wait(3)

-        rec.set_fill(color=GREY,opacity=350)

-        self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))

-        sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)

-        sq1.set_fill(color=RED,opacity=350)

-        sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)

-        sq2.set_fill(color=RED,opacity=350)

-        rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)

-        rec1.set_fill(color=RED,opacity=350)

-        rec2=Rectangle(height=1.5,width=1,color=BLACK)

-        rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)

-        self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))

-        a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)

-        b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)

-        c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)

-        d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)

-        self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))

-        self.wait(2.3)

-        text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)

-        text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)

-        text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)

-        self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))

-        self.wait(3)

-

-        

-

-

-

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py
new file mode 100644
index 0000000..115a722
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py
@@ -0,0 +1,25 @@
+from manimlib.imports import *

+class ThreeDSpace(ThreeDScene):

+

+

+    def construct(self):

+        axes = ThreeDAxes()

+        self.add(axes)

+        self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)

+        self.begin_ambient_camera_rotation(rate=0.09)

+        plane1 = Polygon([-1.5,1.5,-1.5],[1.5,1.5,-1.5],[1.5,-1.5,1.5],[-1.5,-1.5,1.5])

+        plane1.set_opacity(0.65)

+        plane1.set_fill(GREEN)

+        plane1.set_color(GREEN)

+        

+        

+        plane2 = Polygon([-1.5,1.5,1.5],[1.5,1.5,1.5],[1.5,-1.5,-1.5],[-1.5,-1.5,-1.5])

+        plane2.set_opacity(0.7)

+        plane2.set_fill(MAROON_A)

+        plane2.set_color(MAROON_A)

+        line = Line(color=YELLOW,set_opacity=100,start=[1.5,1.2,1.2],end=[-1.5,1.2,1.2])

+        

+        

+        self.play(ShowCreation(plane1),ShowCreation(plane2),ShowCreation(line))

+        self.wait(10)

+

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4
new file mode 100644
index 0000000..d384f80
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4
new file mode 100644
index 0000000..d43bfbe
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
deleted file mode 100644
index 32b02be..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
+++ /dev/null
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4
new file mode 100644
index 0000000..390f4cf
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4