Merge pull request #5 from FOSSEE/master

Update fork. DONE

2 files changed, 478 insertions, 0 deletions

diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file_before_matrix.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file_before_matrix.py
new file mode 100755
index 0000000..96e456d
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file_before_matrix.py
@@ -0,0 +1,232 @@
+from manimlib.imports import *
+
+class Linear(GraphScene):
+
+    CONFIG = {
+    "x_min": -5,
+    "x_max": 5,
+    "y_min": -5,
+    "y_max": 5,
+    "graph_origin": ORIGIN,
+    "x_labeled_nums": list(range(-5, 6)),
+    "y_labeled_nums": list(range(-5, 6)),
+    "x_axis_width": 7,
+    "y_axis_height": 7,
+    }
+
+    def construct(self):
+        
+        XTD = self.x_axis_width/(self.x_max- self.x_min)
+        YTD = self.y_axis_height/(self.y_max- self.y_min)
+
+        self.setup_axes(animate = True)
+        heading = TextMobject(r"$T(x,y) = T(x+2y,x-y)$")
+        heading.move_to(UP*3+LEFT*4)
+        heading.scale(0.7)
+        self.play(Write(heading))
+        self.wait()
+
+        before = TextMobject("Before Linear Transformation")
+        before.set_color(ORANGE)
+        before.move_to(3*UP+4*RIGHT)
+        before.scale(0.75)
+        dot1 = Dot().shift(self.graph_origin+1*XTD*RIGHT+1*YTD*UP)
+        dot2 = Dot().shift(self.graph_origin+2*XTD*RIGHT+1*YTD*UP)
+        dot1.set_color(ORANGE)
+        dot2.set_color(ORANGE)
+        p1 = TextMobject(r"$P_1$")
+        p1.scale(0.75)
+        p1.set_color(ORANGE)
+        p1.move_to(self.graph_origin+1*XTD*RIGHT+1.5*YTD*UP)
+        p2 = TextMobject(r"$P_2$")
+        p2.set_color(ORANGE)
+        p2.scale(0.75)
+        p2.move_to(self.graph_origin+2*XTD*RIGHT+1.5*YTD*UP)
+
+        after = TextMobject("After applying Linear Transformation")
+        after.set_color(YELLOW)
+        after.move_to(3*UP+4.5*RIGHT)
+        after.scale(0.5)
+        dot3 = Dot().shift(self.graph_origin+3*XTD*RIGHT+0*YTD*UP)
+        dot4 = Dot().shift(self.graph_origin+4*XTD*RIGHT+1*YTD*UP)
+        dot3.set_color(YELLOW)
+        dot4.set_color(YELLOW)
+        p3 = TextMobject(r"$T(P_1)$")
+        p3.scale(0.7)
+        p3.set_color(YELLOW)
+        p3.move_to(self.graph_origin+3*XTD*RIGHT-1.1*YTD*UP)
+        p4 = TextMobject(r"$T(P_2)$")
+        p4.scale(0.7)
+        p4.set_color(YELLOW)
+        p4.move_to(self.graph_origin+4*XTD*RIGHT+1.5*YTD*UP)
+
+        self.play(Write(before), ShowCreation(dot1), ShowCreation(dot2),Write(p1), Write(p2))
+        self.wait(3)
+        self.play(Transform(before,after), Transform(dot1,dot3), Transform(dot2,dot4), Transform(p2,p4), Transform(p1,p3))
+        self.wait(3)
+
+
+class withgrid(LinearTransformationScene):
+    def construct(self):
+
+        heading = TextMobject(r"Now, Imagine this happening for all the vectors")
+        heading.scale(0.5)
+        heading.move_to(UP*2.5+LEFT*4)
+        self.play(Write(heading))
+        self.wait()
+
+        before = TextMobject("Before Linear Transformation")
+        before.set_color(ORANGE)
+        before.move_to(3.5*UP+4*RIGHT)
+        before.scale(0.75)
+        dot1 = Dot().shift(1*RIGHT+1*UP)
+        dot2 = Dot().shift(2*RIGHT+1*UP)
+        dot1.set_color(ORANGE)
+        dot2.set_color(ORANGE)
+        
+        dot1_c = Dot(radius = 0.05).shift(1*RIGHT+1*UP)
+        dot2_c = Dot(radius = 0.05).shift(2*RIGHT+1*UP)
+        dot1_c.set_color(YELLOW)
+        dot2_c.set_color(YELLOW)
+        self.add_transformable_mobject(dot1_c)
+        self.add_transformable_mobject(dot2_c)
+        
+        p1 = TextMobject(r"$P_1$")
+        p1.scale(0.75)
+        p1.set_color(ORANGE)
+        p1.move_to(1*RIGHT+1.5*UP)
+        p2 = TextMobject(r"$P_2$")
+        p2.scale(0.75)
+        p2.set_color(ORANGE)
+        p2.move_to(2*RIGHT+1.5*UP)
+
+        after = TextMobject("After applying Linear Transformation")
+        after.set_color(YELLOW)
+        after.move_to(3.5*UP+3.5*RIGHT)
+        after.scale(0.75)
+        dot3 = Dot().shift(3*RIGHT+0*UP)
+        dot4 = Dot().shift(4*RIGHT+1*UP)
+        dot3.set_color(YELLOW)
+        dot4.set_color(YELLOW)
+        p3 = TextMobject(r"$T(P_1)$")
+        p3.scale(0.75)
+        p3.set_color(YELLOW)
+        p3.move_to(3*RIGHT-0.6*UP)
+        p4 = TextMobject(r"$T(P_2)$")
+        p4.scale(0.75)
+        p4.set_color(YELLOW)
+        p4.move_to(4*RIGHT+1.5*UP)
+
+        self.play(Write(before), ShowCreation(dot1), ShowCreation(dot2),Write(p1), Write(p2))
+        self.wait(3)
+        matrix = [[1,2],[1,-1]]
+        dot1.set_color(GREY)
+        dot2.set_color(GREY)
+        self.play(FadeIn(dot1),FadeIn(dot2))
+        self.apply_matrix(matrix)
+        self.play(Transform(before,after), Transform(p2,p4), Transform(p1,p3))
+        self.play(Transform(before,after))
+        self.wait(3)
+
+        ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right]) = \left[\begin{array}{c} x+2y \\ x-y\end{array}\right]$")
+        ending.move_to(UP*2+LEFT*4)
+        self.play(Transform(heading,ending))
+        self.wait()
+
+from manimlib.imports import *
+class ThreeDExplanation(ThreeDScene):
+    
+    def construct(self):
+
+        text = TextMobject(r"$T(x,y) = (x+y,x-y,x+2y)$")
+        text.scale(0.75)
+        text.move_to(UP*2.5+LEFT*4)
+        self.add_fixed_in_frame_mobjects(text)
+        self.play(Write(text))
+        self.wait()
+
+        before = TextMobject("Before Linear Transformation")
+        self.add_fixed_in_frame_mobjects(before)
+        before.set_color(ORANGE)
+        before.move_to(3.5*UP+4*RIGHT)
+        before.scale(0.75)
+
+        p1 = TextMobject(r"$P_1$")
+        p2 = TextMobject(r"$P_2$")
+        p3 = TextMobject(r"$P_3$")
+        p1.scale(0.75)
+        p2.scale(0.75)
+        p3.scale(0.75)
+        dot1 = Dot().shift(1*RIGHT+1*UP)
+        dot2 = Dot().shift(2*RIGHT+1*UP)
+        dot3 = Dot().shift(1*RIGHT+1*DOWN)
+        dot1.set_color(ORANGE)
+        dot2.set_color(ORANGE)
+        dot3.set_color(ORANGE)
+        self.play(ShowCreation(before))
+        
+        p1.move_to(1*RIGHT+1*UP+[0,0,0.5])
+        p2.move_to(2*RIGHT+1*UP+[0,0,0.5])
+        p3.move_to(1*RIGHT-1*UP+[0,0,0.5])
+        
+        dot1_c = Dot(radius = 0.05).shift(1*RIGHT+1*UP)
+        dot2_c = Dot(radius = 0.05).shift(0*RIGHT+2*UP)
+        dot3_c = Dot(radius = 0.05).shift(1*RIGHT-1*UP)
+        dot1_c.set_color(YELLOW)
+        dot2_c.set_color(YELLOW)
+        dot3_c.set_color(YELLOW)
+        
+        axes = ThreeDAxes(x_min = -7,x_max=7,y_min=-4,y_max=4,z_min=-4,z_max=4)
+        self.play(ShowCreation(axes))
+        self.move_camera(distance = 100, phi=30*DEGREES,theta=45*DEGREES,run_time=3)
+        
+        self.begin_ambient_camera_rotation(rate=0.3)
+        self.wait(1)
+        self.stop_ambient_camera_rotation()
+
+        plane = NumberPlane()
+        self.add_fixed_orientation_mobjects(p1)
+        self.add_fixed_orientation_mobjects(p2)
+        self.add_fixed_orientation_mobjects(p3)
+        self.play(ShowCreation(dot1),ShowCreation(dot3),ShowCreation(dot2),ShowCreation(plane))
+        
+        self.play(FadeOut(before))
+        after = TextMobject("After applying Linear Transformation")
+        self.add_fixed_in_frame_mobjects(after)
+        after.set_color(YELLOW)
+        after.move_to(3.5*UP+3.5*RIGHT)
+        after.scale(0.75)
+      
+        self.play(FadeOut(p1),FadeOut(p2),FadeOut(p3))
+        matrix = [[1,1],[1,-1],[2,1]]
+        self.play(FadeOut(dot1),FadeOut(dot2),FadeOut(dot3),ApplyMethod(plane.apply_matrix,matrix),ApplyMethod(dot1_c.apply_matrix,matrix),ApplyMethod(dot3_c.apply_matrix,matrix),ApplyMethod(dot2_c.apply_matrix,matrix))
+        
+        p4 = TextMobject(r"$T(P_1)$")
+        p5 = TextMobject(r"$T(P_2)$")
+        p6 = TextMobject(r"$T(P_3)$")
+        p4.scale(0.75)
+        p5.scale(0.75)
+        p6.scale(0.75)
+        p4.move_to(2*RIGHT+0*UP+[0,0,3.5])
+        p5.move_to(2*RIGHT-2*UP+[0,0,2.5])
+        p6.move_to(0*RIGHT+2*UP+[0,0,1.5])
+        self.add_fixed_orientation_mobjects(p5)
+        self.add_fixed_orientation_mobjects(p4)
+        self.add_fixed_orientation_mobjects(p6)
+        
+        self.begin_ambient_camera_rotation(rate=0.3)
+        self.wait(3)
+        self.stop_ambient_camera_rotation()
+
+        ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right]) = \left[\begin{array}{c} x+y \\ x-y \\ x+2y \end{array}\right]$")
+        ending.scale(0.75)
+        ending.move_to(-UP*2+LEFT*4)
+        self.play(Transform(text,ending))
+        self.add_fixed_in_frame_mobjects(ending)
+
+        self.play(FadeOut(plane))
+        self.wait(3)
+
+        self.begin_ambient_camera_rotation(rate=0.5)
+        self.wait(5)
+        self.stop_ambient_camera_rotation()
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/square.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/square.py
new file mode 100644
index 0000000..e828de4
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/square.py
@@ -0,0 +1,246 @@
+from manimlib.imports import *
+
+class Linear(GraphScene):
+    CONFIG = {
+    "x_min": -5,
+    "x_max": 5,
+    "y_min": -5,
+    "y_max": 5,
+    "graph_origin": ORIGIN,
+    "x_labeled_nums": list(range(-5, 6)),
+    "y_labeled_nums": list(range(-5, 6)),
+    "x_axis_width": 7,
+    "y_axis_height": 7,
+    }
+    def construct(self):
+        
+        text = TextMobject("T(x,y) = T(x+y,y)")
+        text.scale(0.75)
+        text.set_color(PURPLE)
+        text.move_to(3*UP+5*LEFT)
+        self.play(Write(text))
+
+        XTD = self.x_axis_width/(self.x_max- self.x_min)
+        YTD = self.y_axis_height/(self.y_max- self.y_min)
+
+        self.setup_axes(animate = True)
+
+        text1 = TextMobject("Before Linear Transformation")
+        text1.scale(0.6)
+        text1.move_to(UP*3+3*RIGHT)
+
+        a = TextMobject("(1,1)")
+        b = TextMobject("(3,1)")
+        c = TextMobject("(3,2)")
+        d = TextMobject("(1,2)")
+        a.scale(0.5)
+        b.scale(0.5)
+        c.scale(0.5)
+        d.scale(0.5)
+        a.move_to(self.graph_origin+0.6*UP+0.6*RIGHT)
+        b.move_to(self.graph_origin+0.6*UP+3.4*RIGHT)
+        c.move_to(self.graph_origin+2.4*UP+3.4*RIGHT)
+        d.move_to(self.graph_origin+2.6*UP+0.6*RIGHT)
+
+        square = Polygon(self.graph_origin+UP+RIGHT,self.graph_origin+UP+3*RIGHT,self.graph_origin+2*UP+3*RIGHT,self.graph_origin+2*UP+RIGHT)
+        
+        self.play(Write(text1), Write(a), Write(b), Write(c), Write(d), ShowCreation(square))
+        self.wait(2)
+        self.play(FadeOut(text1), FadeOut(a), FadeOut(b), FadeOut(c), FadeOut(d), ApplyMethod(square.apply_matrix,[[1,1],[0,1]]))
+
+        a = TextMobject("(2,1)")
+        b = TextMobject("(4,1)")
+        c = TextMobject("(3,2)")
+        d = TextMobject("(5,2)")
+        a.scale(0.5)
+        b.scale(0.5)
+        c.scale(0.5)
+        d.scale(0.5)
+        a.move_to(self.graph_origin+0.6*UP+1.6*RIGHT)
+        b.move_to(self.graph_origin+0.6*UP+4.4*RIGHT)
+        d.move_to(self.graph_origin+2.4*UP+5.4*RIGHT)
+        c.move_to(self.graph_origin+2.4*UP+2.6*RIGHT)
+
+        text1 = TextMobject("After Linear Transformation")
+        text1.scale(0.6)
+        text1.move_to(UP*3+3*RIGHT)
+
+        self.play(Write(text1), Write(a), Write(b), Write(c), Write(d))
+        
+        self.wait(2)
+
+class grid(LinearTransformationScene):
+    def construct(self):
+
+        text = TextMobject("Now, consider all the vectors.")
+        text.scale(0.75)
+        text.set_color(PURPLE)
+        text.move_to(2.5*UP+3*LEFT)
+        self.play(Write(text))
+
+        text1 = TextMobject("Before Linear Transformation")
+        text1.scale(0.6)
+        text1.move_to(UP*3.5+3.5*RIGHT)
+
+        square = Polygon(UP+RIGHT,UP+3*RIGHT,2*UP+3*RIGHT,2*UP+RIGHT)
+        square.set_color(YELLOW)
+        
+        self.play(Write(text1), ShowCreation(square))
+        self.wait(2)
+        self.play(FadeOut(text1))
+        self.add_transformable_mobject(square)
+
+        text1 = TextMobject("After Linear Transformation")
+        text1.scale(0.6)
+        text1.move_to(UP*3.5+3.5*RIGHT)
+
+        matrix = [[1,1],[0,1]]
+
+        self.apply_matrix(matrix)
+        self.play(Write(text1))
+        
+        self.wait()
+
+class grid2(LinearTransformationScene):
+    CONFIG = {
+    "include_background_plane": True,
+    "include_foreground_plane": False,
+    "show_coordinates": True,
+    "show_basis_vectors": True,
+    "basis_vector_stroke_width": 3,
+    "i_hat_color": X_COLOR,
+    "j_hat_color": Y_COLOR,
+    "leave_ghost_vectors": True,
+    }
+
+    def construct(self):
+
+        text = TextMobject("Now, let us focus only on the standard basis")
+        text.scale(0.7)
+        text.set_color(PURPLE)
+        text.move_to(2.5*UP+3.5*LEFT)
+        self.play(Write(text))
+
+        text1 = TextMobject("Before Linear Transformation")
+        text1.scale(0.6)
+        text1.move_to(UP*3.5+3.5*RIGHT)
+
+        square = Polygon(UP+RIGHT,UP+3*RIGHT,2*UP+3*RIGHT,2*UP+RIGHT)
+        square.set_color(YELLOW)
+        
+        self.play(Write(text1), ShowCreation(square))
+        self.wait(2)
+        self.play(FadeOut(text1))
+        self.add_transformable_mobject(square)
+
+        text1 = TextMobject("After Linear Transformation")
+        text1.scale(0.6)
+        text1.move_to(UP*3.5+3.5*RIGHT)
+
+        matrix = [[1,1],[0,1]]
+
+        self.apply_matrix(matrix)
+        self.play(Write(text1))
+
+        self.play(FadeOut(square), FadeOut(text1))
+        
+        cor_x = TextMobject("(1,0)")
+        cor_y = TextMobject("(1,1)")
+        cor_x.scale(0.65)
+        cor_y.scale(0.65)
+        cor_y.move_to(1.25*RIGHT+1.5*UP)
+        cor_x.move_to(0.75*RIGHT-0.5*UP)
+        cor_x.set_color(GREEN)
+        cor_y.set_color(RED)
+        
+        x_cor = TextMobject(r"$\left[\begin{array}{c} 1\\0\end{array}\right]$")
+        x_cor.set_color(GREEN)
+        x_cor.scale(0.5)
+        y_cor = TextMobject(r"$\left[\begin{array}{c} 1\\1\end{array}\right]$")
+        x_cor.move_to(0.75*RIGHT-0.5*UP)
+        y_cor.move_to(1.25*RIGHT+1.5*UP)
+        y_cor.set_color(RED)
+        y_cor.scale(0.5)
+
+        text1 = TextMobject(r"$T(\left[\begin{array}{c} x\\y \end{array}\right]) = $",r"$\left[\begin{array}{c} x+y\\y \end{array}\right]$")
+        text1.scale(0.7)
+        text1.set_color(PURPLE)
+        text1.move_to(1.5*UP+3*LEFT)
+
+        text = TextMobject(r"$T(x,y) = (x+y,y)$")
+        text.scale(0.6)
+        text.set_color(PURPLE)
+        text.move_to(1.5*UP+3*LEFT)
+
+        self.play(FadeIn(text),FadeIn(cor_x), FadeIn(cor_y))
+        self.wait()
+
+        self.play(Transform(text,text1), Transform(cor_x,x_cor), Transform(cor_y,y_cor))
+
+        text3 = TextMobject(r"$\left[\begin{array}{c} x+y\\y \end{array}\right]$")
+        text3.scale(0.7)
+        text3.set_color(PURPLE)
+        text3.move_to(1.5*DOWN+5*LEFT)
+
+        equal = TextMobject("=")
+        equal.move_to(1.5*DOWN+3.5*LEFT)
+
+        text3 = TextMobject("[")
+        text4 = TextMobject(r"$\begin{array}{c} (1)x\\(0)x \end{array}$")
+        text5 = TextMobject(r"$\begin{array}{c} + \\ + \end{array}$")
+        text6 = TextMobject(r"$\begin{array}{c} (1)y\\(1)y \end{array}$")
+        text7 = TextMobject("]")
+        text3.scale(2)
+        text4.scale(0.7)
+        text5.scale(0.7)
+        text6.scale(0.7)
+        text7.scale(2)
+        text4.set_color(GREEN)
+        text5.set_color(PURPLE)
+        text6.set_color(RED)
+        text3.move_to(1.5*DOWN+3*LEFT)
+        text4.move_to(1.5*DOWN+2.5*LEFT)
+        text5.move_to(1.5*DOWN+2*LEFT)
+        text6.move_to(1.5*DOWN+1.5*LEFT)
+        text7.move_to(1.5*DOWN+1*LEFT)
+
+        text1[1].scale(1.2)
+        self.play(FadeOut(text1[0]), ApplyMethod(text1[1].move_to,1.5*DOWN+5*LEFT), FadeIn(text3), FadeIn(equal), FadeIn(text4), FadeIn(text5), FadeIn(text6), FadeIn(text7))
+
+        self.wait()
+        self.play(FadeOut(text1[1]))
+        
+        self.play(ApplyMethod(text3.move_to,1.5*DOWN+6*LEFT),
+        ApplyMethod(text4.move_to,1.5*DOWN+5.5*LEFT),
+        ApplyMethod(text5.move_to,1.5*DOWN+5*LEFT),
+        ApplyMethod(text6.move_to,1.5*DOWN+4.5*LEFT),
+        ApplyMethod(text7.move_to,1.5*DOWN+4*LEFT))
+        
+        text10 = TextMobject("[")
+        text11 = TextMobject(r"$\begin{array}{c} 1\\0 \end{array}$")
+        text13 = TextMobject(r"$\begin{array}{c} 1\\1 \end{array}$")
+        text14 = TextMobject("]")
+        text10.scale(2)
+        text11.scale(0.7)
+        text13.scale(0.7)
+        text14.scale(2)
+        text11.set_color(GREEN)
+        text13.set_color(RED)
+        text10.move_to(1.5*DOWN+3*LEFT)
+        text11.move_to(1.5*DOWN+2.75*LEFT)
+        text13.move_to(1.5*DOWN+2.25*LEFT)
+        text14.move_to(1.5*DOWN+2*LEFT)
+
+        self.play(FadeIn(text10), Transform(x_cor,text11), Transform(y_cor,text13), FadeIn(text14))
+
+        text15 = TextMobject(r"$\left[\begin{array}{c} x\\y \end{array}\right]$")
+        text15.scale(0.7)
+        text15.set_color(PURPLE)
+        text15.move_to(1.5*DOWN+1.5*LEFT)
+
+        self.play(FadeIn(text15))
+        self.play(FadeOut(text3), FadeOut(text4), FadeOut(text5), FadeOut(text7), FadeOut(text6))
+
+        text1[0].scale(1.2)
+        self.play(ApplyMethod(text1[0].move_to,1.5*DOWN+4.5*LEFT), FadeOut(equal))
+        self.wait(2)
\ No newline at end of file