Basic Python Programming Help Needed Involving Arrays And Random Locations

Consider a 100X100 array. Generate an array of several thousand random locations within such an array, e.g. (3,75) and (56, 34). Calculate how often one of your random locations

Solution 1:

You can skip actually generating the array and go directly to the frequency calculation:

First of all, it should be noted that since both the x and y coordinates are completely random:

We have the rule:

P(A or B) = P(A) + P(B) - P(A and B)

So we can say that

P(X or Y within 15) = P(X within 15) + P(Y within 15) - P(X and Y within 15)

Since it's implied that X and Y are uniformly random from 0 to 99 (or from 1 to 100), we can assume that

P(X within 15) = P(Y within 15)

So the whole thing becomes

P(X or Y within 15) = 2P(X within 15) - P(X within 15)^2

Now, we just need to calculate P(X within 15). Observe that X can only take integer values, so the function f(x) = |X - 49.5| - 35 will be greater than zero for x = 0..14 and x = 85..99. (We're indexing from zero, but it's the equivalent to going from 1...100).

So, the code:

from random import randrange

N = 3000
P_x_within_15 = sum(abs(randrange(100) - 49.5) - 35 > 0 for _ in range(N)) / float(N)

print "Frequency of X or Y within 15 pixels of edge:",
print 2 * P_x_within_15 - P_x_within_15 ** 2

As you may have noticed, we skipped actually creating an array, and just added up the boolean (True/False with True = 1, False = 0) results of the random numbers as they were generated.

EDIT - Actually creating an array

To create an array of random coordinates for a 100 x 100 matrix:

Using numpy the code would be:

from random import randrange
N = 3000
coords_array = array([randrange(100) for _ in range(2 * N)]).reshape(N, 2)

Using pure python, it would be:

from random import randrange
N = 3000
coords_list = [(randrange(100), randrange(100)) for _ in range(N)]

A couple things to note here:

1. In python, indices are sequenced from zero. randrange(100) will give you a number between 0 and 99, inclusive.

2. N is simply the number of coordinates we wish to generate

3. Terminology point: In python, the data structures represented by square brackets are lists, not arrays (even though they are equivalent to arrays in other programming languages). In your code above array1 is a python list, not an array (which is a different data structure). Counterpoint: numpy however, extensively uses arrays. In your code, when you do array(array1), you are, in fact, creating a numpy array.

4. The stuff between the square brackets is called a list comprehension. It is semantically equivalent to:

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coords_list = []
for _ in range(N):
    coords_list.append((randrange(100), randrange(100)))

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