Description
Material covered
• Numpy
Notes
You must save all your code as a script. The program should be written using
vectorization.
Grading
Total marks is 2.
If you have completed exercise 1, you can work on challenge and super challenge
questions. Challenge and super challenge questions are optional. You will either receive
0, 1 or 2 mark for completion of the mandatory exercise.
Note – You do not have to successfully complete challenge and super challenge questions
to get the full marks.
You will receive 2 marks for correct solution to Exercise 1. No submission or empty
submission will be a direct 0. Use only what have been taught in class or described in this
lab.
Exercises
Exercise 1: Random walk
Fair use
This problem is adapted from Exercise 37 of Langtangen’s “A Primer on Scientific
Programming with Python”.
Simulating gas particles in a closed space is something you can do with a Monte Carlo
type simulation – simulate a period of time (using a loop) and “move” particles around
(change values for (x, y) coordinates) for each unit of time. This kind of simulation is
called a “random walk”.
Download the file randomwalk.py. This implements a Monte Carlo simulation for a
random 2-dimensional walk. It uses numpy arrays, but it does not use them
idiomatically.
Your task for this exercise is to change this program to use numpy arrays idiomatically.
That is, the block
for i in range(np):
direction = random.randint(1, 4)
if direction == NORTH:
ypositions[i] += 1
elif direction == SOUTH:
ypositions[i] -= 1
elif direction == EAST:
xpositions[i] += 1
elif direction == WEST:
xpositions[i] -= 1
should be rewritten to use numpy arrays of random integers.
Challenge: multidimensional arrays
Rewrite the code so that (x, y) coordinates are represented with a 2-dimensional numpy
array. Here’s how you can start:
coords = np.zeros(shape=(np, 2))
# xpositions = numpy.zeros(np)
# ypositions = numpy.zeros(np)
Remember that you can index entire columns of a 2-dimensional array by using the
notation [:,n] to get the n
th column.
Super challenge: no loops
Rewrite the code so that it has no loops. You’ll need to think in 3 dimensions to
accomplish this.
Answer some question first:
1. Can you simulate time without loops?
2. Each unit of time depends on the unit of time before it. Can different matrices in a
3-dimensional numpy array depend on each other?
If you can answer “yes” to both of these questions, then proceed!
