From 90cc46c2527f7798b5e9e442da56c1358322e2bf Mon Sep 17 00:00:00 2001 From: Archit Sangal Date: Tue, 7 Jul 2020 20:17:17 +0530 Subject: semi final round complete --- .../file1_introduction.py | 33 ++ .../file1_projections.py | 79 ----- .../file2_orthonormal.py | 333 --------------------- .../file2_projections.py | 79 +++++ .../file3_Non_Standard_Basis.py | 51 ---- .../file3_orthonormal.py | 333 +++++++++++++++++++++ .../file4_Non_Standard_Basis.py | 51 ++++ .../file_introduction.py | 33 -- 8 files changed, 496 insertions(+), 496 deletions(-) create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py delete mode 100755 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_projections.py delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_orthonormal.py create mode 100755 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file_introduction.py (limited to 'FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process') diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py new file mode 100644 index 0000000..ccd23c9 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py @@ -0,0 +1,33 @@ +from manimlib.imports import * + +class Orthonormal(Scene): + def construct(self): + Centre = DOWN + arrow_1 = Arrow(start = Centre+ORIGIN,end = Centre+1.414*(UP+RIGHT)) + arrow_2 = Arrow(start = Centre+ORIGIN,end = Centre+2*UP) + arrow_1.scale(1.35) + arrow_2.scale(1.35) + text = TextMobject("This is a set of linearly independent vectors") + text.scale(0.75) + text.move_to(3*UP+3*LEFT) + text.set_color(PURPLE_E) + arrow_1.set_color(PURPLE_E) + arrow_2.set_color(PURPLE_E) + self.play(Write(text)) + self.play(ShowCreation(arrow_1), ShowCreation(arrow_2)) + self.wait(2) + text1 = TextMobject("After we apply Gram-Schmidt Orthogonalization Process to set of linearly independent vectors") + text1.scale(0.6) + text1.move_to(3*UP+2*LEFT) + text1.set_color(GREEN) + arrow_a = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+RIGHT)) + arrow_a.set_color(GREEN) + arrow_a.scale(2) + self.play(Transform(text,text1)) + self.wait(2) + self.play(Transform(arrow_1,arrow_a)) + arrow_b = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+LEFT)) + arrow_b.set_color(GREEN) + arrow_b.scale(2) + self.play(Transform(arrow_2,arrow_b)) + self.wait(2) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_projections.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_projections.py deleted file mode 100755 index dd4b8d4..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_projections.py +++ /dev/null @@ -1,79 +0,0 @@ -from manimlib.imports import * - -class Projections(GraphScene): - CONFIG = { - "x_min": -6, - "x_max": 6, - "y_min": -4, - "y_max": 4, - "graph_origin" : ORIGIN , - } - def construct(self): - - self.setup_axes(animate=True) - - XTD = self.x_axis_width/(self.x_max-self.x_min) - YTD = self.y_axis_height/(self.y_max-self.y_min) - - arrow_a = Arrow(start = ORIGIN, end = 4*XTD*RIGHT) - arrow_a.scale(1.2) - arrow_a.set_color(DARK_BLUE) - arrow_b = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT) - arrow_b.scale(1.3) - arrow_b.set_color(DARK_BLUE) - self.play(ShowCreation(arrow_a), ShowCreation(arrow_b)) - - text = TextMobject(r"Consider 2 linearly independent vectors $a$ and $b$") - text.set_color(DARK_BLUE) - text.scale(0.6) - text.move_to(3*YTD*UP+5*XTD*LEFT) - text_a = TextMobject("a") - text_a.move_to(0.4*YTD*DOWN+3*XTD*RIGHT) - text_a.set_color(DARK_BLUE) - text_b = TextMobject("b") - text_b.move_to(1.5*YTD*UP+RIGHT*XTD) - text_b.set_color(DARK_BLUE) - - self.play(Write(text),Write(text_a), Write(text_b)) - self.wait() - - arrow_b_copy = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT) - arrow_b_copy.scale(1.25) - - arrow_p = Arrow(start = ORIGIN, end = 2*XTD*RIGHT) - arrow_p.scale(1.5) - arrow_p.set_color(GOLD_E) - - text_p = TextMobject("p") - text_p.move_to(0.25*DOWN+RIGHT) - text_p.set_color(GOLD_E) - - self.play(FadeOut(text), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b)) - text = TextMobject(r"$p$ is the projection of $b$ on $a$") - text.set_color(GOLD_E) - text.move_to(3*UP+4*LEFT) - text.scale(0.8) - self.play(Write(text),Write(text_p)) - self.wait() - - self.play(FadeIn(text_a), FadeIn(text_b)) - - arrow_o = Arrow(start = 2*XTD*RIGHT, end = 2*YTD*UP+2*XTD*RIGHT) - arrow_o.scale(1.5) - arrow_o.set_color(GREEN_E) - - text_o = TextMobject("b-p") - text_o.move_to(UP*YTD+2.7*XTD*RIGHT) - text_o.set_color(GREEN_E) - - self.play(ShowCreation(arrow_o)) - self.play(FadeOut(text),Write(text_o)) - - text = TextMobject(r"Observe, ($b-p$) is orthogonal to $a$") - text.set_color(GREEN_E) - text.move_to(2*DOWN+4*LEFT) - text.scale(0.8) - self.play(Write(text)) - self.wait(2) - - self.play(FadeOut(self.axes), FadeOut(arrow_a), FadeOut(arrow_b), FadeOut(arrow_b_copy), FadeOut(arrow_o), FadeOut(text_a), FadeOut(text_b), FadeOut(text_o), FadeOut(text_p), FadeOut(text)) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_orthonormal.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_orthonormal.py deleted file mode 100644 index af51fc6..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_orthonormal.py +++ /dev/null @@ -1,333 +0,0 @@ -from manimlib.imports import * - -class Algo(ThreeDScene): - def construct(self): - - axes = ThreeDAxes(x_min = -5,x_max=5,y_min=-3,y_max=3,z_min=-4,z_max=4) - self.play(ShowCreation(axes)) - - text = TextMobject(r"This is the vector $\beta_1(=\left[\begin{array}{c} 4\\0\\0 \end{array}\right])$") - text.set_color(GREEN) - text.scale(0.6) - text.move_to(3*UP+5*LEFT) - self.play(Write(text)) - - arrow_a = Arrow(start = ORIGIN, end = 4*RIGHT) - arrow_a.set_color(GREEN) - arrow_a.scale(1.15) - self.play(ShowCreation(arrow_a)) - - text_a = TextMobject(r"$\beta_1$") - text_a.move_to(0.4*DOWN+3*RIGHT) - text_a.set_color(GREEN) - text_a.scale(0.75) - self.play(Write(text_a)) - self.wait() - self.play(FadeOut(text)) - - text = TextMobject(r"Normalize $\beta_1$ to get $\alpha_1$") - text.set_color(DARK_BLUE) - text.scale(0.75) - text.move_to(3*UP+5*LEFT) - self.play(Write(text)) - - alpha_1 = Arrow(start = ORIGIN,end = RIGHT) - alpha_1.scale(1.9) - alpha_1.set_color(DARK_BLUE) - text_alpha_1 = TextMobject(r"$\alpha_1$") - text_alpha_1.move_to(0.4*DOWN+RIGHT) - text_alpha_1.set_color(DARK_BLUE) - text_alpha_1.scale(0.75) - self.play(Transform(text_a,text_alpha_1), Transform(arrow_a,alpha_1)) - self.wait() - self.play(FadeOut(text)) - - text = TextMobject(r"Consider another vector $\beta_2(=\left[\begin{array}{c} 2\\2\\0 \end{array}\right])$") - text1 = TextMobject(r"which is linearly independent to $\beta_1$") - text.set_color(GREEN) - text1.set_color(GREEN) - text.scale(0.6) - text1.scale(0.6) - text.move_to(3*UP+4*LEFT) - text1.move_to(2*UP+4*LEFT) - self.play(Write(text)) - self.play(Write(text1)) - - arrow_b = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT) - arrow_b.scale(1.2) - arrow_b.set_color(GREEN) - text_b = TextMobject(r"$\beta_2$") - text_b.move_to(1.5*UP+RIGHT) - text_b.set_color(GREEN) - text_b.scale(0.75) - - self.play(ShowCreation(arrow_b), Write(text_b)) - self.wait() - - arrow_b_copy = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT) - arrow_b_copy.scale(1.2) - - arrow_p = Arrow(start = ORIGIN, end = 2*RIGHT) - arrow_p.scale(1.35) - arrow_p.set_color(GOLD_E) - - text_p = TextMobject("p") - text_p.move_to(0.25*DOWN+RIGHT) - text_p.set_color(GOLD_E) - - self.play(FadeOut(text), FadeOut(text1), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b)) - text = TextMobject(r"$p$ is the projection of $\beta_2$ on $\alpha_1$") - text.set_color(GOLD_E) - text.move_to(3*UP+4*LEFT) - text.scale(0.8) - self.play(Write(text),Write(text_p)) - self.wait() - - self.play(FadeIn(text_b)) - - arrow_o = Arrow(start = 2*RIGHT, end = 2*UP+2*RIGHT) - arrow_o.scale(1.35) - arrow_o.set_color(PURPLE_E) - - text_o = TextMobject(r"$\beta_2-p$") - text_o.move_to(UP+2.7*RIGHT) - text_o.scale(0.75) - text_o.set_color(PURPLE_E) - - self.play(ShowCreation(arrow_o)) - self.play(FadeOut(text),Write(text_o)) - - text = TextMobject(r"$\beta_2-p$ is orthogonal to p") - text1 = TextMobject(r"(and hence orthogonal to $\alpha_1$ also)") - text.set_color(PURPLE_E) - text1.set_color(PURPLE_E) - text.scale(0.7) - text1.scale(0.7) - text.move_to(3*UP+4*LEFT) - text1.move_to(2.5*UP+4*LEFT) - self.play(Write(text)) - self.play(Write(text1)) - self.wait(2) - - self.play(FadeOut(text_p), FadeIn(arrow_a), FadeOut(text), FadeOut(text1), FadeOut(arrow_b_copy), FadeOut(arrow_p), FadeOut(text_b), FadeOut(arrow_b)) - self.play(ApplyMethod(arrow_o.move_to,UP), ApplyMethod(text_o.move_to,RIGHT+UP)) - - text = TextMobject(r"Now, Normalize $\beta_2-p$") - text.set_color(DARK_BLUE) - text.scale(0.6) - text.move_to(3*UP+4*LEFT) - self.play(Write(text)) - - alpha_2 = Arrow(start = ORIGIN,end = UP) - alpha_2.scale(1.9) - alpha_2.set_color(DARK_BLUE) - text_alpha_2 = TextMobject(r"$\alpha_2$") - text_alpha_2.move_to(0.4*LEFT+UP) - text_alpha_2.set_color(DARK_BLUE) - text_alpha_2.scale(0.75) - self.play(Transform(text_o,text_alpha_2), Transform(arrow_o,alpha_2), FadeIn(text_a)) - self.wait() - self.play(FadeOut(text),FadeOut(text_a),FadeOut(text_o)) - - self.add(axes) - ############################################################################# - axis = TextMobject(r"$\alpha_1$",r"$\alpha_2$",r"$\alpha_3$",r"$\beta_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$") - axis.scale(0.5) - axis[0].move_to(0.5*RIGHT+[0,0,-0.5]) - axis[1].move_to(0.5*UP+[0,0,-0.5]) - axis[2].move_to(np.array([0,0,0.5])) - axis[3].move_to(np.array([1,1,1.5])) - self.add_fixed_orientation_mobjects(axis[0]) - self.add_fixed_orientation_mobjects(axis[1]) - ############################################################################# - - text = TextMobject(r"These are the same two orthonormal vectors $\alpha_{1}$ and $\alpha_{2}$") - text.scale(0.6) - text.set_color(DARK_BLUE) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*(DOWN+RIGHT)) - self.play(Write(text)) - - self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3) - self.begin_ambient_camera_rotation(rate=0.3) - - line1 = Line(start = ORIGIN,end = 1*RIGHT) - line1.set_color(DARK_BLUE) - tip1 = Polygon(RIGHT,0.8*RIGHT-0.2*DOWN,0.8*RIGHT-0.2*UP) - tip1.set_opacity(1) - tip1.set_fill(DARK_BLUE) - tip1.set_color(DARK_BLUE) - - arrow2 = Line(start = ORIGIN,end = 1*UP) - arrow2.set_color(DARK_BLUE) - tip2 = Polygon(UP,0.8*UP-0.2*RIGHT,0.8*UP-0.2*LEFT) - tip2.set_opacity(1) - tip2.set_fill(DARK_BLUE) - tip2.set_color(DARK_BLUE) - arrow2.set_color(DARK_BLUE) - - self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), FadeOut(arrow_a), FadeOut(arrow_o)) - self.wait() - - a_line = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2]) - a_line.set_color(GOLD_E) - a_tip = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8]) - a_tip.set_opacity(1) - a_tip.set_fill(GOLD_E) - a_tip.set_color(GOLD_E) - - a_line_c1 = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2]) - a_line_c1.set_color(GOLD_E) - a_tip_c1 = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8]) - a_tip_c1.set_opacity(1) - a_tip_c1.set_fill(GOLD_E) - a_tip_c1.set_color(GOLD_E) - - self.play(FadeOut(text), ShowCreation(a_line), ShowCreation(a_tip), ShowCreation(a_line_c1), ShowCreation(a_tip_c1)) - - text = TextMobject(r"Now, we have a vector $\beta_3(=\left[\begin{array}{c} 2\\2\\2 \end{array}\right])$") - text.set_color(GOLD_E) - text.scale(0.7) - self.add_fixed_in_frame_mobjects(text) - self.add_fixed_orientation_mobjects(axis[3]) - text.move_to(3*(DOWN+RIGHT)) - self.play(Write(text)) - self.wait() - self.play(FadeOut(text)) - - p_line1 = Line(start = ORIGIN,end = 2*RIGHT) - p_line1.set_color(GOLD_E) - p_tip1 = Polygon(RIGHT,0.8*RIGHT+0.2*DOWN,0.8*RIGHT+0.2*UP) - p_tip1.move_to(2*RIGHT) - p_tip1.set_opacity(1) - p_tip1.set_fill(GOLD_E) - p_tip1.set_color(GOLD_E) - - self.play(Transform(a_line_c1,p_line1),Transform(a_tip_c1,p_tip1)) - - text = TextMobject(r"Take projection of $\beta_3$ on $\alpha_1$") - text.scale(0.6) - text.set_color(GOLD_E) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*(DOWN+RIGHT)) - self.play(Write(text)) - self.wait() - self.play(FadeOut(text)) - - o_line1 = Line(start = 2*RIGHT,end = 2*UP+2*RIGHT+[0,0,2]) - o_line1.set_color(GREEN_E) - o_tip1 = Polygon(2*UP+2*RIGHT+[0,0,2],1.8*UP+2*RIGHT+[0,0,1.8]+0.2*RIGHT,1.8*UP+2*RIGHT+[0,0,1.8]-0.2*RIGHT) - o_tip1.set_opacity(1) - o_tip1.set_fill(GREEN_E) - o_tip1.set_color(GREEN_E) - - a_line1 = Line(start = ORIGIN,end = 2*UP+[0,0,2]) - a_line1.set_color(GREEN_E) - a_tip1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT) - a_tip1.set_opacity(1) - a_tip1.set_fill(GREEN_E) - a_tip1.set_color(GREEN_E) - - a_line1_c1 = Line(start = ORIGIN,end = 2*UP+[0,0,2]) - a_line1_c1.set_color(GREEN_E) - a_tip1_c1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT) - a_tip1_c1.set_opacity(1) - a_tip1_c1.set_fill(GREEN_E) - a_tip1_c1.set_color(GREEN_E) - - text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$)") - text.set_color(GREEN_E) - text.scale(0.6) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*(DOWN+RIGHT)) - self.play(Write(text)) - self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) - self.wait(2) - self.play(FadeOut(a_line_c1), FadeOut(a_tip_c1), - FadeOut(a_line), FadeOut(a_tip), FadeOut(axis[3]), - Transform(o_line1,a_line1), Transform(o_tip1,a_tip1)) - - self.wait() - self.play(FadeOut(text)) - - p_arrow2 = Line(start = ORIGIN,end = 2*UP) - p_arrow2.set_color(GOLD_E) - p_tip2 = Polygon(2*UP,1.8*UP+0.2*RIGHT,1.8*UP+0.2*LEFT) - p_tip2.set_opacity(1) - p_tip2.set_fill(GOLD_E) - p_tip2.set_color(GOLD_E) - p_arrow2.set_color(GOLD_E) - - last_a = Line(start = 2*UP,end = [0,2,2]) - last_a.set_color(PURPLE_E) - last_a_tip = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT) - last_a_tip.move_to([0,2,2]) - last_a_tip.set_opacity(1) - last_a_tip.set_fill(PURPLE_E) - last_a_tip.set_color(PURPLE_E) - - self.wait() - text = TextMobject(r"Take projection on $\alpha_2$") - text.scale(0.6) - text.set_color(GOLD_E) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*(DOWN+RIGHT)) - self.play(Write(text)) - self.play(Transform(a_line1_c1,p_arrow2),Transform(a_tip1_c1,p_tip2)) - self.wait() - self.play(FadeOut(text)) - - text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$)") - text.set_color(PURPLE_E) - text.scale(0.6) - self.add_fixed_in_frame_mobjects(text) - text.move_to(3*DOWN+3.5*RIGHT) - self.play(Write(text)) - self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) - self.wait(2) - self.play(ShowCreation(last_a_tip), ShowCreation(last_a)) - self.wait() - self.play(FadeOut(text)) - - larrow3 = Line(start = ORIGIN,end = [0,0,2]) - larrow3.set_color(PURPLE_E) - ltip3 = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT) - ltip3.set_opacity(1) - ltip3.set_fill(PURPLE_E) - ltip3.set_color(PURPLE_E) - self.wait() - self.play(FadeOut(o_line1), FadeOut(o_tip1), FadeOut(a_line1_c1), FadeOut(a_tip1_c1), Transform(last_a,larrow3), Transform(last_a_tip,ltip3)) - - text = TextMobject(r"Normalize, the vector") - text1 = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$") - text.set_color(PURPLE_E) - text1.set_color(PURPLE_E) - text.scale(0.6) - text1.scale(0.6) - self.add_fixed_in_frame_mobjects(text) - self.add_fixed_in_frame_mobjects(text1) - text.move_to(3*DOWN+3*RIGHT) - text1.move_to(3.5*DOWN+3*RIGHT) - self.play(Write(text)) - self.play(Write(text1)) - - arrow3 = Line(start = ORIGIN,end = [0,0,1]) - arrow3.set_color(DARK_BLUE) - tip3 = Polygon([0,0,1],[0,0,0.8]-0.2*RIGHT,[0,0,0.8]-0.2*LEFT) - tip3.set_opacity(1) - tip3.set_fill(DARK_BLUE) - tip3.set_color(DARK_BLUE) - self.play(Transform(last_a,arrow3), Transform(last_a_tip,tip3)) - self.add_fixed_orientation_mobjects(axis[2]) - - self.wait() - self.play(FadeOut(text),FadeOut(text1)) - - text = TextMobject(r"These are the three orthonormal vectors $\alpha_1, \alpha_2, \alpha_3$") - text.set_color(DARK_BLUE) - self.add_fixed_in_frame_mobjects(text) - text.scale(0.6) - text.move_to(3*DOWN+3.5*RIGHT) - self.play(Write(text)) - - self.wait(3) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py new file mode 100755 index 0000000..dd4b8d4 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py @@ -0,0 +1,79 @@ +from manimlib.imports import * + +class Projections(GraphScene): + CONFIG = { + "x_min": -6, + "x_max": 6, + "y_min": -4, + "y_max": 4, + "graph_origin" : ORIGIN , + } + def construct(self): + + self.setup_axes(animate=True) + + XTD = self.x_axis_width/(self.x_max-self.x_min) + YTD = self.y_axis_height/(self.y_max-self.y_min) + + arrow_a = Arrow(start = ORIGIN, end = 4*XTD*RIGHT) + arrow_a.scale(1.2) + arrow_a.set_color(DARK_BLUE) + arrow_b = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT) + arrow_b.scale(1.3) + arrow_b.set_color(DARK_BLUE) + self.play(ShowCreation(arrow_a), ShowCreation(arrow_b)) + + text = TextMobject(r"Consider 2 linearly independent vectors $a$ and $b$") + text.set_color(DARK_BLUE) + text.scale(0.6) + text.move_to(3*YTD*UP+5*XTD*LEFT) + text_a = TextMobject("a") + text_a.move_to(0.4*YTD*DOWN+3*XTD*RIGHT) + text_a.set_color(DARK_BLUE) + text_b = TextMobject("b") + text_b.move_to(1.5*YTD*UP+RIGHT*XTD) + text_b.set_color(DARK_BLUE) + + self.play(Write(text),Write(text_a), Write(text_b)) + self.wait() + + arrow_b_copy = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT) + arrow_b_copy.scale(1.25) + + arrow_p = Arrow(start = ORIGIN, end = 2*XTD*RIGHT) + arrow_p.scale(1.5) + arrow_p.set_color(GOLD_E) + + text_p = TextMobject("p") + text_p.move_to(0.25*DOWN+RIGHT) + text_p.set_color(GOLD_E) + + self.play(FadeOut(text), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b)) + text = TextMobject(r"$p$ is the projection of $b$ on $a$") + text.set_color(GOLD_E) + text.move_to(3*UP+4*LEFT) + text.scale(0.8) + self.play(Write(text),Write(text_p)) + self.wait() + + self.play(FadeIn(text_a), FadeIn(text_b)) + + arrow_o = Arrow(start = 2*XTD*RIGHT, end = 2*YTD*UP+2*XTD*RIGHT) + arrow_o.scale(1.5) + arrow_o.set_color(GREEN_E) + + text_o = TextMobject("b-p") + text_o.move_to(UP*YTD+2.7*XTD*RIGHT) + text_o.set_color(GREEN_E) + + self.play(ShowCreation(arrow_o)) + self.play(FadeOut(text),Write(text_o)) + + text = TextMobject(r"Observe, ($b-p$) is orthogonal to $a$") + text.set_color(GREEN_E) + text.move_to(2*DOWN+4*LEFT) + text.scale(0.8) + self.play(Write(text)) + self.wait(2) + + self.play(FadeOut(self.axes), FadeOut(arrow_a), FadeOut(arrow_b), FadeOut(arrow_b_copy), FadeOut(arrow_o), FadeOut(text_a), FadeOut(text_b), FadeOut(text_o), FadeOut(text_p), FadeOut(text)) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py deleted file mode 100644 index 6410a2c..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_Non_Standard_Basis.py +++ /dev/null @@ -1,51 +0,0 @@ -from manimlib.imports import * - -class NSB(ThreeDScene): - def construct(self): - - axes = ThreeDAxes(x_min = -4,x_max=4,y_min=-4,y_max=4,z_min=-4,z_max=4) - self.play(ShowCreation(axes)) - self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3) - self.begin_ambient_camera_rotation(rate=0.5) - - matrix = [[0.577,0.577,0.577],[-0.577,0.577,0.577],[0.577,-0.577,0.577]] - - line1 = Line(start = ORIGIN,end = 1*RIGHT) - line1.set_color(DARK_BLUE) - tip1 = Polygon(RIGHT,0.9*RIGHT-0.1*DOWN,0.9*RIGHT-0.1*UP) - tip1.set_opacity(1) - tip1.set_fill(DARK_BLUE) - tip1.set_color(DARK_BLUE) - - arrow2 = Line(start = ORIGIN,end = 1*UP) - arrow2.set_color(DARK_BLUE) - tip2 = Polygon(UP,0.9*UP-0.1*RIGHT,0.9*UP-0.1*LEFT) - tip2.set_opacity(1) - tip2.set_fill(DARK_BLUE) - tip2.set_color(DARK_BLUE) - arrow2.set_color(DARK_BLUE) - - arrow3 = Line(start = ORIGIN,end = [0,0,1]) - arrow3.set_color(DARK_BLUE) - tip3 = Polygon([0,0,1],[0,0,0.9]-0.1*RIGHT,[0,0,0.9]-0.1*LEFT) - tip3.set_opacity(1) - tip3.set_fill(DARK_BLUE) - tip3.set_color(DARK_BLUE) - - line1.apply_matrix(matrix) - tip1.apply_matrix(matrix) - arrow2.apply_matrix(matrix) - tip2.apply_matrix(matrix) - arrow3.apply_matrix(matrix) - tip3.apply_matrix(matrix) - - self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3)) - - text = TextMobject(r"This is also a set of Orthonormal Vectors") - text.set_color(DARK_BLUE) - self.add_fixed_in_frame_mobjects(text) - text.scale(0.6) - text.move_to(3*DOWN+3.5*RIGHT) - self.play(Write(text)) - - self.wait(7) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py new file mode 100644 index 0000000..af51fc6 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py @@ -0,0 +1,333 @@ +from manimlib.imports import * + +class Algo(ThreeDScene): + def construct(self): + + axes = ThreeDAxes(x_min = -5,x_max=5,y_min=-3,y_max=3,z_min=-4,z_max=4) + self.play(ShowCreation(axes)) + + text = TextMobject(r"This is the vector $\beta_1(=\left[\begin{array}{c} 4\\0\\0 \end{array}\right])$") + text.set_color(GREEN) + text.scale(0.6) + text.move_to(3*UP+5*LEFT) + self.play(Write(text)) + + arrow_a = Arrow(start = ORIGIN, end = 4*RIGHT) + arrow_a.set_color(GREEN) + arrow_a.scale(1.15) + self.play(ShowCreation(arrow_a)) + + text_a = TextMobject(r"$\beta_1$") + text_a.move_to(0.4*DOWN+3*RIGHT) + text_a.set_color(GREEN) + text_a.scale(0.75) + self.play(Write(text_a)) + self.wait() + self.play(FadeOut(text)) + + text = TextMobject(r"Normalize $\beta_1$ to get $\alpha_1$") + text.set_color(DARK_BLUE) + text.scale(0.75) + text.move_to(3*UP+5*LEFT) + self.play(Write(text)) + + alpha_1 = Arrow(start = ORIGIN,end = RIGHT) + alpha_1.scale(1.9) + alpha_1.set_color(DARK_BLUE) + text_alpha_1 = TextMobject(r"$\alpha_1$") + text_alpha_1.move_to(0.4*DOWN+RIGHT) + text_alpha_1.set_color(DARK_BLUE) + text_alpha_1.scale(0.75) + self.play(Transform(text_a,text_alpha_1), Transform(arrow_a,alpha_1)) + self.wait() + self.play(FadeOut(text)) + + text = TextMobject(r"Consider another vector $\beta_2(=\left[\begin{array}{c} 2\\2\\0 \end{array}\right])$") + text1 = TextMobject(r"which is linearly independent to $\beta_1$") + text.set_color(GREEN) + text1.set_color(GREEN) + text.scale(0.6) + text1.scale(0.6) + text.move_to(3*UP+4*LEFT) + text1.move_to(2*UP+4*LEFT) + self.play(Write(text)) + self.play(Write(text1)) + + arrow_b = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT) + arrow_b.scale(1.2) + arrow_b.set_color(GREEN) + text_b = TextMobject(r"$\beta_2$") + text_b.move_to(1.5*UP+RIGHT) + text_b.set_color(GREEN) + text_b.scale(0.75) + + self.play(ShowCreation(arrow_b), Write(text_b)) + self.wait() + + arrow_b_copy = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT) + arrow_b_copy.scale(1.2) + + arrow_p = Arrow(start = ORIGIN, end = 2*RIGHT) + arrow_p.scale(1.35) + arrow_p.set_color(GOLD_E) + + text_p = TextMobject("p") + text_p.move_to(0.25*DOWN+RIGHT) + text_p.set_color(GOLD_E) + + self.play(FadeOut(text), FadeOut(text1), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b)) + text = TextMobject(r"$p$ is the projection of $\beta_2$ on $\alpha_1$") + text.set_color(GOLD_E) + text.move_to(3*UP+4*LEFT) + text.scale(0.8) + self.play(Write(text),Write(text_p)) + self.wait() + + self.play(FadeIn(text_b)) + + arrow_o = Arrow(start = 2*RIGHT, end = 2*UP+2*RIGHT) + arrow_o.scale(1.35) + arrow_o.set_color(PURPLE_E) + + text_o = TextMobject(r"$\beta_2-p$") + text_o.move_to(UP+2.7*RIGHT) + text_o.scale(0.75) + text_o.set_color(PURPLE_E) + + self.play(ShowCreation(arrow_o)) + self.play(FadeOut(text),Write(text_o)) + + text = TextMobject(r"$\beta_2-p$ is orthogonal to p") + text1 = TextMobject(r"(and hence orthogonal to $\alpha_1$ also)") + text.set_color(PURPLE_E) + text1.set_color(PURPLE_E) + text.scale(0.7) + text1.scale(0.7) + text.move_to(3*UP+4*LEFT) + text1.move_to(2.5*UP+4*LEFT) + self.play(Write(text)) + self.play(Write(text1)) + self.wait(2) + + self.play(FadeOut(text_p), FadeIn(arrow_a), FadeOut(text), FadeOut(text1), FadeOut(arrow_b_copy), FadeOut(arrow_p), FadeOut(text_b), FadeOut(arrow_b)) + self.play(ApplyMethod(arrow_o.move_to,UP), ApplyMethod(text_o.move_to,RIGHT+UP)) + + text = TextMobject(r"Now, Normalize $\beta_2-p$") + text.set_color(DARK_BLUE) + text.scale(0.6) + text.move_to(3*UP+4*LEFT) + self.play(Write(text)) + + alpha_2 = Arrow(start = ORIGIN,end = UP) + alpha_2.scale(1.9) + alpha_2.set_color(DARK_BLUE) + text_alpha_2 = TextMobject(r"$\alpha_2$") + text_alpha_2.move_to(0.4*LEFT+UP) + text_alpha_2.set_color(DARK_BLUE) + text_alpha_2.scale(0.75) + self.play(Transform(text_o,text_alpha_2), Transform(arrow_o,alpha_2), FadeIn(text_a)) + self.wait() + self.play(FadeOut(text),FadeOut(text_a),FadeOut(text_o)) + + self.add(axes) + ############################################################################# + axis = TextMobject(r"$\alpha_1$",r"$\alpha_2$",r"$\alpha_3$",r"$\beta_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$") + axis.scale(0.5) + axis[0].move_to(0.5*RIGHT+[0,0,-0.5]) + axis[1].move_to(0.5*UP+[0,0,-0.5]) + axis[2].move_to(np.array([0,0,0.5])) + axis[3].move_to(np.array([1,1,1.5])) + self.add_fixed_orientation_mobjects(axis[0]) + self.add_fixed_orientation_mobjects(axis[1]) + ############################################################################# + + text = TextMobject(r"These are the same two orthonormal vectors $\alpha_{1}$ and $\alpha_{2}$") + text.scale(0.6) + text.set_color(DARK_BLUE) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + + self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3) + self.begin_ambient_camera_rotation(rate=0.3) + + line1 = Line(start = ORIGIN,end = 1*RIGHT) + line1.set_color(DARK_BLUE) + tip1 = Polygon(RIGHT,0.8*RIGHT-0.2*DOWN,0.8*RIGHT-0.2*UP) + tip1.set_opacity(1) + tip1.set_fill(DARK_BLUE) + tip1.set_color(DARK_BLUE) + + arrow2 = Line(start = ORIGIN,end = 1*UP) + arrow2.set_color(DARK_BLUE) + tip2 = Polygon(UP,0.8*UP-0.2*RIGHT,0.8*UP-0.2*LEFT) + tip2.set_opacity(1) + tip2.set_fill(DARK_BLUE) + tip2.set_color(DARK_BLUE) + arrow2.set_color(DARK_BLUE) + + self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), FadeOut(arrow_a), FadeOut(arrow_o)) + self.wait() + + a_line = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2]) + a_line.set_color(GOLD_E) + a_tip = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8]) + a_tip.set_opacity(1) + a_tip.set_fill(GOLD_E) + a_tip.set_color(GOLD_E) + + a_line_c1 = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2]) + a_line_c1.set_color(GOLD_E) + a_tip_c1 = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8]) + a_tip_c1.set_opacity(1) + a_tip_c1.set_fill(GOLD_E) + a_tip_c1.set_color(GOLD_E) + + self.play(FadeOut(text), ShowCreation(a_line), ShowCreation(a_tip), ShowCreation(a_line_c1), ShowCreation(a_tip_c1)) + + text = TextMobject(r"Now, we have a vector $\beta_3(=\left[\begin{array}{c} 2\\2\\2 \end{array}\right])$") + text.set_color(GOLD_E) + text.scale(0.7) + self.add_fixed_in_frame_mobjects(text) + self.add_fixed_orientation_mobjects(axis[3]) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.wait() + self.play(FadeOut(text)) + + p_line1 = Line(start = ORIGIN,end = 2*RIGHT) + p_line1.set_color(GOLD_E) + p_tip1 = Polygon(RIGHT,0.8*RIGHT+0.2*DOWN,0.8*RIGHT+0.2*UP) + p_tip1.move_to(2*RIGHT) + p_tip1.set_opacity(1) + p_tip1.set_fill(GOLD_E) + p_tip1.set_color(GOLD_E) + + self.play(Transform(a_line_c1,p_line1),Transform(a_tip_c1,p_tip1)) + + text = TextMobject(r"Take projection of $\beta_3$ on $\alpha_1$") + text.scale(0.6) + text.set_color(GOLD_E) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.wait() + self.play(FadeOut(text)) + + o_line1 = Line(start = 2*RIGHT,end = 2*UP+2*RIGHT+[0,0,2]) + o_line1.set_color(GREEN_E) + o_tip1 = Polygon(2*UP+2*RIGHT+[0,0,2],1.8*UP+2*RIGHT+[0,0,1.8]+0.2*RIGHT,1.8*UP+2*RIGHT+[0,0,1.8]-0.2*RIGHT) + o_tip1.set_opacity(1) + o_tip1.set_fill(GREEN_E) + o_tip1.set_color(GREEN_E) + + a_line1 = Line(start = ORIGIN,end = 2*UP+[0,0,2]) + a_line1.set_color(GREEN_E) + a_tip1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT) + a_tip1.set_opacity(1) + a_tip1.set_fill(GREEN_E) + a_tip1.set_color(GREEN_E) + + a_line1_c1 = Line(start = ORIGIN,end = 2*UP+[0,0,2]) + a_line1_c1.set_color(GREEN_E) + a_tip1_c1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT) + a_tip1_c1.set_opacity(1) + a_tip1_c1.set_fill(GREEN_E) + a_tip1_c1.set_color(GREEN_E) + + text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$)") + text.set_color(GREEN_E) + text.scale(0.6) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) + self.wait(2) + self.play(FadeOut(a_line_c1), FadeOut(a_tip_c1), + FadeOut(a_line), FadeOut(a_tip), FadeOut(axis[3]), + Transform(o_line1,a_line1), Transform(o_tip1,a_tip1)) + + self.wait() + self.play(FadeOut(text)) + + p_arrow2 = Line(start = ORIGIN,end = 2*UP) + p_arrow2.set_color(GOLD_E) + p_tip2 = Polygon(2*UP,1.8*UP+0.2*RIGHT,1.8*UP+0.2*LEFT) + p_tip2.set_opacity(1) + p_tip2.set_fill(GOLD_E) + p_tip2.set_color(GOLD_E) + p_arrow2.set_color(GOLD_E) + + last_a = Line(start = 2*UP,end = [0,2,2]) + last_a.set_color(PURPLE_E) + last_a_tip = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT) + last_a_tip.move_to([0,2,2]) + last_a_tip.set_opacity(1) + last_a_tip.set_fill(PURPLE_E) + last_a_tip.set_color(PURPLE_E) + + self.wait() + text = TextMobject(r"Take projection on $\alpha_2$") + text.scale(0.6) + text.set_color(GOLD_E) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*(DOWN+RIGHT)) + self.play(Write(text)) + self.play(Transform(a_line1_c1,p_arrow2),Transform(a_tip1_c1,p_tip2)) + self.wait() + self.play(FadeOut(text)) + + text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$)") + text.set_color(PURPLE_E) + text.scale(0.6) + self.add_fixed_in_frame_mobjects(text) + text.move_to(3*DOWN+3.5*RIGHT) + self.play(Write(text)) + self.play(ShowCreation(o_line1), ShowCreation(o_tip1)) + self.wait(2) + self.play(ShowCreation(last_a_tip), ShowCreation(last_a)) + self.wait() + self.play(FadeOut(text)) + + larrow3 = Line(start = ORIGIN,end = [0,0,2]) + larrow3.set_color(PURPLE_E) + ltip3 = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT) + ltip3.set_opacity(1) + ltip3.set_fill(PURPLE_E) + ltip3.set_color(PURPLE_E) + self.wait() + self.play(FadeOut(o_line1), FadeOut(o_tip1), FadeOut(a_line1_c1), FadeOut(a_tip1_c1), Transform(last_a,larrow3), Transform(last_a_tip,ltip3)) + + text = TextMobject(r"Normalize, the vector") + text1 = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$") + text.set_color(PURPLE_E) + text1.set_color(PURPLE_E) + text.scale(0.6) + text1.scale(0.6) + self.add_fixed_in_frame_mobjects(text) + self.add_fixed_in_frame_mobjects(text1) + text.move_to(3*DOWN+3*RIGHT) + text1.move_to(3.5*DOWN+3*RIGHT) + self.play(Write(text)) + self.play(Write(text1)) + + arrow3 = Line(start = ORIGIN,end = [0,0,1]) + arrow3.set_color(DARK_BLUE) + tip3 = Polygon([0,0,1],[0,0,0.8]-0.2*RIGHT,[0,0,0.8]-0.2*LEFT) + tip3.set_opacity(1) + tip3.set_fill(DARK_BLUE) + tip3.set_color(DARK_BLUE) + self.play(Transform(last_a,arrow3), Transform(last_a_tip,tip3)) + self.add_fixed_orientation_mobjects(axis[2]) + + self.wait() + self.play(FadeOut(text),FadeOut(text1)) + + text = TextMobject(r"These are the three orthonormal vectors $\alpha_1, \alpha_2, \alpha_3$") + text.set_color(DARK_BLUE) + self.add_fixed_in_frame_mobjects(text) + text.scale(0.6) + text.move_to(3*DOWN+3.5*RIGHT) + self.play(Write(text)) + + self.wait(3) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py new file mode 100644 index 0000000..6410a2c --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py @@ -0,0 +1,51 @@ +from manimlib.imports import * + +class NSB(ThreeDScene): + def construct(self): + + axes = ThreeDAxes(x_min = -4,x_max=4,y_min=-4,y_max=4,z_min=-4,z_max=4) + self.play(ShowCreation(axes)) + self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3) + self.begin_ambient_camera_rotation(rate=0.5) + + matrix = [[0.577,0.577,0.577],[-0.577,0.577,0.577],[0.577,-0.577,0.577]] + + line1 = Line(start = ORIGIN,end = 1*RIGHT) + line1.set_color(DARK_BLUE) + tip1 = Polygon(RIGHT,0.9*RIGHT-0.1*DOWN,0.9*RIGHT-0.1*UP) + tip1.set_opacity(1) + tip1.set_fill(DARK_BLUE) + tip1.set_color(DARK_BLUE) + + arrow2 = Line(start = ORIGIN,end = 1*UP) + arrow2.set_color(DARK_BLUE) + tip2 = Polygon(UP,0.9*UP-0.1*RIGHT,0.9*UP-0.1*LEFT) + tip2.set_opacity(1) + tip2.set_fill(DARK_BLUE) + tip2.set_color(DARK_BLUE) + arrow2.set_color(DARK_BLUE) + + arrow3 = Line(start = ORIGIN,end = [0,0,1]) + arrow3.set_color(DARK_BLUE) + tip3 = Polygon([0,0,1],[0,0,0.9]-0.1*RIGHT,[0,0,0.9]-0.1*LEFT) + tip3.set_opacity(1) + tip3.set_fill(DARK_BLUE) + tip3.set_color(DARK_BLUE) + + line1.apply_matrix(matrix) + tip1.apply_matrix(matrix) + arrow2.apply_matrix(matrix) + tip2.apply_matrix(matrix) + arrow3.apply_matrix(matrix) + tip3.apply_matrix(matrix) + + self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3)) + + text = TextMobject(r"This is also a set of Orthonormal Vectors") + text.set_color(DARK_BLUE) + self.add_fixed_in_frame_mobjects(text) + text.scale(0.6) + text.move_to(3*DOWN+3.5*RIGHT) + self.play(Write(text)) + + self.wait(7) \ No newline at end of file diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file_introduction.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file_introduction.py deleted file mode 100644 index ccd23c9..0000000 --- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file_introduction.py +++ /dev/null @@ -1,33 +0,0 @@ -from manimlib.imports import * - -class Orthonormal(Scene): - def construct(self): - Centre = DOWN - arrow_1 = Arrow(start = Centre+ORIGIN,end = Centre+1.414*(UP+RIGHT)) - arrow_2 = Arrow(start = Centre+ORIGIN,end = Centre+2*UP) - arrow_1.scale(1.35) - arrow_2.scale(1.35) - text = TextMobject("This is a set of linearly independent vectors") - text.scale(0.75) - text.move_to(3*UP+3*LEFT) - text.set_color(PURPLE_E) - arrow_1.set_color(PURPLE_E) - arrow_2.set_color(PURPLE_E) - self.play(Write(text)) - self.play(ShowCreation(arrow_1), ShowCreation(arrow_2)) - self.wait(2) - text1 = TextMobject("After we apply Gram-Schmidt Orthogonalization Process to set of linearly independent vectors") - text1.scale(0.6) - text1.move_to(3*UP+2*LEFT) - text1.set_color(GREEN) - arrow_a = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+RIGHT)) - arrow_a.set_color(GREEN) - arrow_a.scale(2) - self.play(Transform(text,text1)) - self.wait(2) - self.play(Transform(arrow_1,arrow_a)) - arrow_b = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+LEFT)) - arrow_b.set_color(GREEN) - arrow_b.scale(2) - self.play(Transform(arrow_2,arrow_b)) - self.wait(2) \ No newline at end of file -- cgit