[project] solution for random walk (py)

projects/project_random_walk/solution/random_walk.py

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+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.mlab as mlab
+import scipy.io as scio
+from IPython import embed
+
+
+def create_food_blotch(size_x=51, size_y=51, noise=0.01, threshold=0.008):
+    x = np.arange(-np.round(size_x/2), np.round(size_x/2)+1)
+    y = np.arange(-np.round(size_y/2), np.round(size_y/2)+1)
+    X, Y = np.meshgrid(x, y)
+    Z = mlab.bivariate_normal(X, Y, sigmax=10, sigmay=10)
+    food = (np.random.rand(size_x, size_y) * noise) + Z
+    return food
+
+
+def create_world(width=100, height=100, d=0.1, food_sources=100, noise=0.01):
+    my_world = np.zeros((int(width/d), int(height/d)))
+    print("placing food sources ...")
+    for i in range(food_sources):
+        x = np.random.randint(0, width/d)
+        y = np.random.randint(0, height/d)
+        food = create_food_blotch(noise=noise)
+        if (x + food.shape[1]) > my_world.shape[1]:
+            x -= food.shape[1]
+        if (y + food.shape[0]) > my_world.shape[0]:
+            y -= food.shape[0]
+        my_world[y:y+food.shape[0], x:x+food.shape[1]] += food
+    return my_world
+
+
+def get_step():
+    options = [-1, 1]
+    step = np.asarray([options[np.random.randint(0, 2)], options[np.random.randint(0, 2)]])
+    return step
+
+
+def is_valid_step(pos, step, max_x, max_y):
+    new_pos = pos + step
+    if (new_pos[0] < max_y) & (new_pos[1] < max_x) & (new_pos[0] >= 0) & (new_pos[1] >= 0):
+        return True
+    return False
+
+
+def do_valid_step(pos, max_x, max_y):
+    valid = False
+    while not valid:
+        step = get_step()
+        valid = is_valid_step(pos, step, max_x, max_y)
+    new_pos = pos + step
+    return new_pos, step
+
+
+def random_walk(world, steps=10000):
+    x_positions = np.zeros(steps)
+    y_positions = np.zeros(steps)
+    start_x = np.random.randint(0, world.shape[1])
+    start_y = np.random.randint(0, world.shape[0])
+    eaten_food = 0
+    new_pos = np.asarray([start_y, start_x])
+    for i in range(steps):
+        new_pos, step = do_valid_step(new_pos, world.shape[1], world.shape[0])
+        x_positions[i] = new_pos[1]
+        y_positions[i] = new_pos[0]
+        eaten_food += world[new_pos[0], new_pos[1]]
+        world[new_pos[0], new_pos[1]] = 0.0
+    return x_positions, y_positions, eaten_food
+
+
+def not_so_random_walk(world, steps=10000):
+    x_positions = np.zeros(steps)
+    y_positions = np.zeros(steps)
+    start_x = np.random.randint(0, world.shape[1])
+    start_y = np.random.randint(0, world.shape[0])
+    previous_food = 0.0
+    current_food = 0.0
+    eaten_food = 0
+    pos = np.asarray([start_y, start_x])
+    step = None
+    for i in range(steps):
+        gradient = current_food - previous_food
+        if (gradient <= 0) or ((step is not None) and \
+                               (not is_valid_step(pos, step, world.shape[1], world.shape[0]))):
+            pos, step = do_valid_step(pos, world.shape[1], world.shape[0])
+        else:
+            pos += step
+        x_positions[i] = pos[1]
+        y_positions[i] = pos[0]
+        previous_food = current_food
+        current_food = world[pos[0], pos[1]]
+        eaten_food += current_food
+        world[pos[0], pos[1]] -= current_food
+    return x_positions, y_positions, eaten_food
+
+
+if __name__ == '__main__':
+    print("create world... ")
+    world = create_world(noise=0.0, food_sources=50)
+    trials = 10
+    gain_random = np.zeros(trials)
+    gain_nsr = np.zeros(trials)
+    print("run")
+    for i in range(trials):
+        x, y, gain_random[i] = random_walk(world.copy(), 100000)
+        x2, y2, gain_nsr[i] = not_so_random_walk(world.copy(), 100000)
+
+    print("random walk yields: %.2f +- %.2f food per 100000 steps" % (np.mean(gain_random),
+                                                                      np.std(gain_random)))
+    print("not so random walk yields: %.2f +- %.2f food per 100000 steps" % (np.mean(gain_nsr),
+                                                                             np.std(gain_nsr)))
+
+    scio.savemat('random_world.mat', {'world': world})
+    plt.imshow(world)
+    plt.scatter(x[::2], y[::2], s=0.5, color='red')
+    plt.scatter(x2[::2], y2[::2], s=0.5, color='green')
+    plt.show()