Day 8 exercises

Solutions at Day 8 exercise solutions.

Simple arrays

5 minutes.

Create this array:

2  7 12  0
3  9  3  4
4  0  1  3

What is the array shape?

What is the array ndim?

How about the len of the array?

Can you get the ndim and len from the shape?

Creating arrays using functions

10 minutes.

1. Create a 1D array from 2 through 5 inclusive.

2. Make an array with 10 elements between 2 and 5 inclusive.

3. Make an all-ones array shape (4, 4).

4. Make an identity array shape (6, 6).

5. Make this array with a single Python / numpy command:

   1  0  0
   0  2  0
   0  0  3
   

Look at the docstring for np.random.randn. Make a shape (3, 5) array with random numbers from a mean=0, variance = 1 normal distribution.

Simple visualizations

7 minutes.

1. Make an array x with 100 evenly spaced values between 0 and 2 * pi;
2. Make an array y which contains the cosine of the corresponding value in x - so y[i] = cos(x[i]) (hint: np.lookfor('cosine')).
3. Plot x against y;
4. Make a 10 by 20 array of mean 0 variance 1 normal random numbers;
5. Display this array as an image;
6. Investigate plt.cm. See if you can work out how to make the displayed image be grayscale instead of color.

Indexing and slicing, array creation

10 minutes.

1. Create the following array, call this a (you did this before):

   2  7 12  0
   3  9  3  4
   4  0  1  3
   

2. Get the 2nd row of a ([ 3 9 3 4]);

3. Get the 3rd column of a ([12 3 1]);

4. Create the following arrays (with correct data types):

   [[1, 1, 1, 1],
    [1, 1, 1, 1],
    [1, 1, 1, 2],
    [1, 6, 1, 1]]
   
   [[0., 0., 0., 0., 0.],
    [2., 0., 0., 0., 0.],
    [0., 3., 0., 0., 0.],
    [0., 0., 4., 0., 0.],
    [0., 0., 0., 5., 0.],
    [0., 0., 0., 0., 6.]]
   

   Par on course: 3 statements for each

   Hint: Individual array elements can be accessed similarly to a list, e.g. a[1] or a[1, 2].

   Hint: Examine the docstring for diag.

5. Skim through the documentation for np.tile, and use this function to construct the array:

   [[4, 3, 4, 3, 4, 3],
    [2, 1, 2, 1, 2, 1],
    [4, 3, 4, 3, 4, 3],
    [2, 1, 2, 1, 2, 1]]
   

Fancy indexing using boolean arrays

5 minutes.

1. Create the following array a (same as before):

   2  7 12  0
   3  9  3  4
   4  0  1  3
   

2. Use > to make a mask that is true where the elements are greater than 5, like this:

   False True  True  False
   False True  False False
   False False False False
   

3. Return all the elements in a that are greater than 5.

4. Set all the elements greater than 5 to be equal to 5, to get this:

   2  5  5  0
   3  5  3  4
   4  0  1  3
   

Elementwise operations

10 minutes.

Remember our array a:

2  7 12  0
3  9  3  4
4  0  1  3

1. Use array slicing to get a new array composed of the even columns (0, 2) of a. Now get array that contains the odd columns (1, 3) of a. Add these two arrays.

2. Generate this array:

   [2**0, 2**1, 2**2, 2**3, 2**4]
   

3. Generate an array length 10 such that this is true of the elements (where x[i] is the element of x at index i):

   x[i] = 2 ** (3 * i) - i
   

Summary functions

Remember our array a:

2  7 12  0
3  9  3  4
4  0  1  3

What are the:

• sum of all the values?
• sum of the columns?
• sum of the rows?
• mean?
• min?
• max?