Finished a prototype Euler Integration scene

electric_field_simulation/euler.py

@@ -46,11 +46,6 @@ def __init__(self, color = BLUE_E, sign = "-", **kwargs):
         super(Electron, self).__init__(color = color, sign = sign, **kwargs)
 
 class ChangingElectricField(Scene):
-    CONFIG = {
-        "vector_field_config": {},
-        "num_particles": 6,
-        "anim_time": 5
-    }
     def __init__(self, vector_field_config = {}, num_particles = 6, anim_time = 5, **kwargs):
         super(ChangingElectricField, self).__init__(**kwargs)
         self.vector_field_config = vector_field_config

matrix_exp/euler_integration.py

@@ -5,4 +5,52 @@
 # Table of contents:
 # 1 - motivation: 4 moving parts to the DE, complexity
 # 2 - 1D case
-# 3 - 2D case
+# 3 - 2D case
+
+class Euler_Integration_2D(Scene):
+    def __init__(self, derivative, init_val, dt, n_step, **kwargs):
+        super(Euler_Integration_2D, self).__init__(**kwargs)
+        self.derivative = derivative
+        self.init_val = init_val
+        self.dt = dt
+        self.n_step = n_step
+
+    def construct(self):
+        vec_field = VectorField(self.derivative)
+        self.add(vec_field)
+
+        x_n = self.init_val
+
+        x_pt = Dot()
+        x_pt.move_to(x_n)
+        x_pt_label = MathTex("x_" + str(0)).next_to(x_pt, direction = DOWN)
+        self.play(FadeIn(x_pt), FadeIn(x_pt_label))
+        self.wait(2)
+
+        for n in range(self.n_step):
+
+            Dx = numpy.append(self.derivative(x_n), 0.0)
+            Dx_vec = Vector(Dx).put_start_and_end_on(x_n, x_n + Dx)
+            Dx_vec_label_pre = MathTex("\\frac{dx}{dt}").next_to(Dx_vec, direction = DOWN)
+            Dx_vec_label_post = MathTex("\\frac{1}{" + str(int(1 / self.dt)) + "}\\frac{dx}{dt}").next_to(Dx_vec, direction = DOWN)
+            self.play(FadeIn(Dx_vec), FadeIn(Dx_vec_label_pre))
+            self.wait(2)
+            self.play(Dx_vec.animate.scale(self.dt, about_point = Dx_vec.get_start()), ReplacementTransform(Dx_vec_label_pre, Dx_vec_label_post))
+            #self.play(Dx_vec.animate.put_start_and_end_on(x_n, x_n + self.dt * Dx))
+
+            x_pt = Dot()
+            x_pt.move_to(x_n + self.dt * Dx)
+            x_pt_label = MathTex("x_" + str(n + 1)).next_to(x_pt, direction = DOWN)
+            self.play(FadeIn(x_pt))
+            self.wait(2)
+
+            self.play(FadeOut(Dx_vec), FadeOut(Dx_vec_label_post), FadeIn(x_pt_label))
+
+            x_n = x_n + self.dt * Dx
+
+class Linear_2D_Int(Euler_Integration_2D):
+    def __init__(self):
+        A = numpy.array([[0.0, -1.0], [1.0, 0.0]])
+        Ax = lambda p: numpy.matmul(A, p[0:2])
+        x0 = numpy.array([1.5, 2.0, 0.0])
+        super(Linear_2D_Int, self).__init__(Ax, x0, 0.5, 2)

matrix_exp/matrix_exponential.py

@@ -11,6 +11,32 @@
 # draw Ax & then show rescale animation by t or t/2
 # Show sum as a new point
 
+class Euler_Integration_2D(Scene):
+    def __init__(self, derivative, init_val, dt, n_step, **kwargs):
+        super(Euler_Integration_2D, self).__init__(**kwargs)
+        self.derivative = derivative
+        self.init_val = init_val
+        self.dt = dt
+        self.n_step = n_step
+
+    def construct(self):
+        vec_field = VectorField(self.derivative)
+        x_n = self.init_val
+        for n in range(self.n_step):
+
+            x_pt = Dot(point = x_n)
+            x_pt_label = MathTex("x_" + str(n)).next_to(x_pt, direction = DOWN)
+            self.play(FadeIn(x_pt), FadeIn(x_pt_label))
+            self.wait(2)
+
+            Dx = vec_field.get_vector(x_n)
+            Dx_vec = Vector(Dx).put_start_and_end_on(x_n, x_n + Dx)
+            Dx_vec_label = MathTex("\\frac{dx}{dt}").next_to(Dx_vec, direction = DOWN)
+            self.play(FadeIn(Dx_vec), FadeIn(Dx_vec_label))
+            self.wait(2)
+            self.play(Dx_vec.animate.scale(self.dt))
+
+
 
 # Second thing to do: Write animation for the algebraic expression
 # Highlight elements of the line as we go: