[projects] add random-walk project

projects/project_random_walk/Makefile

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+latex:
+	pdflatex *.tex > /dev/null
+	pdflatex *.tex > /dev/null
+
+clean:
+	rm -rf *.log *.aux *.zip *.out auto
+	rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+	zip `basename *.tex .tex`.zip *.pdf *.dat *.mat

projects/project_random_walk/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()

projects/project_random_walk/random_walk.tex

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+\documentclass[addpoints,11pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+\section*{Random walk with memory.}
+
+Some animals perform a random walk when searching for food. In some
+cases this random walk is not completely random. In fact, sometimes
+there is some memory involved. Whenever there is a positive gradient
+in food gain between successive steps the animal will continue in the
+very same direction as before. When the next step leads to a decrease
+in food gain the animal switches back to a random walk.
+
+
+\begin{questions}
+  \question{} The accompanying dataset (random\_world.mat) contains a
+  single variable stored. This is the world (10000\,m$^2$ area with
+  10\,cm spatial resolution) in which there are randomly distributed
+  food sources (Gaussian blotches of food).
+  
+  \begin{parts}
+    \part{} Create a plot of the world.\\[0.5ex]
+    \part{} Create a model animal that performs a pure random walk. The
+    agent can walk in eight different directions (the cardinal and
+    diagonal directions) with a stepsize of 10\,cm
+    (approximately). Let the agent start at a random location in the
+    world and count how much food it eats in 10000 steps (eaten food
+    disappears from the world, of course). If the agent bumps into the
+    borders of the world choose a different direction.\\[0.5ex]
+    \part{} Plot a typical example walk. (You can also make an animation
+    with MATLAB)\\[0.5ex]
+    \part{} Same as above, but create a model animal that has some memory,
+    i.e. the direction is kept constant as long as there is a positive
+    gradient in the food gain. Otherwise a random walk is performed\\[0.5ex]
+    \part{} Plot a typical example walk also for this agent.\\[0.5ex]
+    \part{} Compare the performance of the two agents. Create appropriate
+    plots and apply statistical methods.
+  \end{parts}
+\end{questions}
+
+\end{document}