Commit parts of assignment 3.

These were just "hanging around" in my repo.

assignment3/for_slides.py

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+import seaborn
+
+import matplotlib.pyplot as plt
+import numpy as np
+import scipy.spatial
+
+
+seaborn.set_palette('husl')
+
+COLORS = seaborn.husl_palette(6)
+YELLOW = COLORS[1]
+GREEN = COLORS[2]
+BLUE = COLORS[4]
+
+
+class Animation1(object):
+
+    def __init__(self, n, a, b, num_steps=10):
+        self.n = n
+        self.update_vec = np.array([a, b])
+        min_x = min(-1, -1 + a)  # a * 1.0 (max time)
+        max_x = max(1, 1 + a)
+        width_x = max_x - min_x
+        mid_x = 0.5 * (max_x + min_x)
+        min_y = min(-1, -1 + b)
+        max_y = max(1, 1 + b)
+        width_y = max_y - min_y
+        mid_y = 0.5 * (max_y + min_y)
+
+        self.fig = plt.figure()
+        self.ax = self.fig.gca()
+        self.ax.axis('scaled')
+        self.ax.set_xlim(mid_x - 0.55 * width_x,
+                         mid_x + 0.55 * width_x)
+        self.ax.set_ylim(mid_y - 0.55 * width_y,
+                         mid_y + 0.55 * width_y)
+        W, H = self.fig.get_size_inches()
+        self.fig.set_size_inches(2 * W, H)
+
+        self.curr_step = 0
+        self.num_steps = num_steps
+        self.dt = 1.0 / num_steps
+        self.path_collection = None
+
+    @property
+    def plot_frames(self):
+        return self.num_steps + 1
+
+    def init_func(self):
+        interval = np.linspace(-1, 1, self.n + 1)
+        X, Y = np.meshgrid(interval, interval)
+        X = X.flatten(order='F')
+        Y = Y.flatten(order='F')
+        self.path_collection = self.ax.scatter(X, Y, color=GREEN)
+        # For ``init_func`` with ``blit`` turned on, the initial
+        # frame should not have visible lines. See
+        # http://stackoverflow.com/q/21439489/1068170 for more info.
+        self.path_collection.set_visible(False)
+        return self.path_collection,
+
+    def update_plot(self, frame_number):
+        if self.curr_step != frame_number:
+            raise ValueError('Current step does not match '
+                             'frame number', self.curr_step,
+                             frame_number)
+
+        self.curr_step += 1
+        if frame_number == 0:
+            # ``init_func`` creates lines that are not visible, to
+            # address http://stackoverflow.com/q/21439489/1068170.
+            # So in the initial frame, we make them visible.
+            self.path_collection.set_visible(True)
+            return self.path_collection,
+
+        # Update the scatter offsets in-place.
+        offsets = self.path_collection.get_offsets()
+        offsets += self.dt * self.update_vec
+        return self.path_collection,
+
+    def inputs(self):
+        args = (
+            self.fig,
+            self.update_plot,
+        )
+        kwargs = {
+            'init_func': self.init_func,
+            'frames': self.plot_frames,
+            'interval': 20,
+            'blit': True,
+        }
+        return args, kwargs
+
+
+def example1():
+    animate_obj = Animation1(4, 1.0, 1.5, num_steps=30)
+    return animate_obj.inputs()
+
+
+class Animation2(object):
+
+    def __init__(self, n, num_steps=10):
+        self.n = n
+
+        self.fig = plt.figure()
+        self.ax = self.fig.gca()
+        self.ax.axis('scaled')
+        # Max-radius = sqrt(1 + 1) = sqrt(2)
+        self.ax.set_xlim(-1.55, 1.55)
+        self.ax.set_ylim(-1.55, 1.55)
+        W, H = self.fig.get_size_inches()
+        self.fig.set_size_inches(2 * W, H)
+
+        self.curr_step = 0
+        self.num_steps = num_steps
+        self.dt = 0.25 * np.pi / num_steps
+        c_dt = np.cos(self.dt)
+        s_dt = np.sin(self.dt)
+        self.update_mat = np.array([
+            [c_dt, -s_dt],
+            [s_dt, c_dt],
+        ])
+        self.path_collection = None
+
+    @property
+    def plot_frames(self):
+        return self.num_steps + 1
+
+    def init_func(self):
+        interval = np.linspace(-1, 1, self.n + 1)
+        X, Y = np.meshgrid(interval, interval)
+        X = X.flatten(order='F')
+        Y = Y.flatten(order='F')
+        self.path_collection = self.ax.scatter(X, Y, color=GREEN)
+        # For ``init_func`` with ``blit`` turned on, the initial
+        # frame should not have visible lines. See
+        # http://stackoverflow.com/q/21439489/1068170 for more info.
+        self.path_collection.set_visible(False)
+        return self.path_collection,
+
+    def update_plot(self, frame_number):
+        if self.curr_step != frame_number:
+            raise ValueError('Current step does not match '
+                             'frame number', self.curr_step,
+                             frame_number)
+
+        self.curr_step += 1
+        if frame_number == 0:
+            # ``init_func`` creates lines that are not visible, to
+            # address http://stackoverflow.com/q/21439489/1068170.
+            # So in the initial frame, we make them visible.
+            self.path_collection.set_visible(True)
+            return self.path_collection,
+
+        # Update the scatter offsets in-place.
+        offsets = self.path_collection.get_offsets()
+        new_offsets = offsets.dot(self.update_mat.T)
+        self.path_collection.set_offsets(new_offsets)
+        return self.path_collection,
+
+    def inputs(self):
+        args = (
+            self.fig,
+            self.update_plot,
+        )
+        kwargs = {
+            'init_func': self.init_func,
+            'frames': self.plot_frames,
+            'interval': 20,
+            'blit': True,
+        }
+        return args, kwargs
+
+
+def example2():
+    animate_obj = Animation2(4, num_steps=60)
+    return animate_obj.inputs()
+
+
+def example3():
+    npz_file = np.load('example3.npz')
+    N0 = npz_file['N0']
+    T0 = npz_file['T0']
+    N1 = npz_file['N1']
+    T1 = npz_file['T1']
+    plt.triplot(N0[:, 0], N0[:, 1], T0, color=GREEN)
+    plt.triplot(N1[:, 0], N1[:, 1], T1, linestyle='dashed',
+                color=YELLOW)
+    plt.axis('scaled')
+
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example4():
+    npz_file = np.load('example3.npz')
+    N0 = npz_file['N0']
+    T0 = npz_file['T0']
+    N1 = npz_file['N1']
+    T1 = npz_file['T1']
+    plt.triplot(N0[:, 0], N0[:, 1], T0, color=GREEN)
+    plt.triplot(N1[:, 0], N1[:, 1], T1, linestyle='dashed',
+                color=YELLOW)
+
+    for i, tri in enumerate(T1):
+        centroid = np.mean(N1[tri, :], axis=0)
+        plt.text(centroid[0], centroid[1], str(i))
+
+    plt.axis('scaled')
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example5():
+    npz_file = np.load('example5.npz')
+    N0 = npz_file['N0']
+    T0 = npz_file['T0']
+    N1 = npz_file['N1']
+    T1 = npz_file['T1']
+    D = {
+        1: npz_file['D1'],
+        6: npz_file['D6'],
+        7: npz_file['D7'],
+        28: npz_file['D28'],
+        29: npz_file['D29'],
+        32: npz_file['D32'],
+    }
+
+    t1 = N0[T0[1, :], :]
+    plt.plot(t1[[0, 1, 2, 0], 0], t1[[0, 1, 2, 0], 1],
+             color=GREEN, zorder=0)
+
+    for j in (1, 6, 7, 28, 29, 32):
+        tj = N1[T1[j, :], :]
+        line, = plt.plot(tj[[0, 1, 2, 0], 0], tj[[0, 1, 2, 0], 1],
+                         color=YELLOW, linestyle='dashed', zorder=0)
+        centroid = np.mean(tj, axis=0)
+        plt.text(centroid[0], centroid[1], str(j))
+
+    D_vals = np.vstack(D.values())
+    plt.scatter(D_vals[:, 0], D_vals[:, 1],
+                color='black', s=20, zorder=1)
+
+    plt.axis('scaled')
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example6():
+    npz_file = np.load('example5.npz')
+    N0 = npz_file['N0']
+    T0 = npz_file['T0']
+    N1 = npz_file['N1']
+    T1 = npz_file['T1']
+    D28 = npz_file['D28']
+
+    t1 = N0[T0[1, :], :]
+    plt.plot(t1[[0, 1, 2, 0], 0], t1[[0, 1, 2, 0], 1],
+             color=GREEN, zorder=0)
+    t28 = N1[T1[28, :], :]
+    line, = plt.plot(t28[[0, 1, 2, 0], 0], t28[[0, 1, 2, 0], 1],
+                     color=YELLOW, linestyle='dashed', zorder=0)
+    centroid = np.mean(t28, axis=0)
+    plt.text(centroid[0], centroid[1], '28')
+
+    delaunay_tri = scipy.spatial.Delaunay(D28)
+    tri_local = delaunay_tri.simplices
+    plt.triplot(D28[:, 0], D28[:, 1], tri_local, color=BLUE)
+
+    plt.axis('scaled')
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example6a():
+    npz_file = np.load('example5.npz')
+    N0 = npz_file['N0']
+    T0 = npz_file['T0']
+    N1 = npz_file['N1']
+    T1 = npz_file['T1']
+
+    t1 = N0[T0[1, :], :]
+    plt.plot(t1[[0, 1, 2, 0], 0], t1[[0, 1, 2, 0], 1],
+             color=GREEN, zorder=0)
+    for j in (1, 28):
+        tj = N1[T1[j, :], :]
+        line, = plt.plot(tj[[0, 1, 2, 0], 0], tj[[0, 1, 2, 0], 1],
+                         color=YELLOW, linestyle='dashed', zorder=0)
+        centroid = np.mean(tj, axis=0)
+        plt.text(centroid[0], centroid[1], str(j))
+
+    # NOTE: This is t28[2, :] and t1[2, :]
+    plt.scatter([-0.96172635972908305], [-0.43150147173950337],
+                color='black', zorder=1)
+
+    plt.axis('scaled')
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example7():
+    npz_file = np.load('example7.npz')
+    N = npz_file['N']
+    T = npz_file['T']
+
+    plt.triplot(N[:, 0], N[:, 1], T, color=GREEN)
+    plt.plot(N[:, 0], N[:, 1], 'o', color=YELLOW)
+    plt.title(r'$\Delta t = 0.1$', fontsize=20)
+
+    plt.axis('scaled')
+    plt.xlim(-1.1, 1.1)
+    plt.ylim(-1.1, 1.1)
+
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example8():
+    npz_file = np.load('example8.npz')
+    N = npz_file['N']
+    T = npz_file['T']
+
+    plt.triplot(N[:, 0], N[:, 1], T, color=GREEN)
+    plt.plot(N[:, 0], N[:, 1], 'o', color=YELLOW)
+    plt.title(r'$\Delta t = 0.2$', fontsize=20)
+
+    plt.axis('scaled')
+    plt.xlim(-1.1, 1.1)
+    plt.ylim(-1.1, 1.1)
+
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()
+
+
+def example9():
+    npz_file = np.load('example9.npz')
+    N = npz_file['N']
+    T = npz_file['T']
+    U = npz_file['U']
+
+    plt.tricontourf(N[:, 0], N[:, 1], T, U, 20, cmap='viridis')
+
+    plt.axis('scaled')
+    plt.colorbar()
+
+    fig = plt.gcf()
+    W, H = fig.get_size_inches()
+    fig.set_size_inches(1.5 * W, 1.5 * H)
+
+    plt.show()