Problem 1

A function object is a value you can assign to a variable or pass as an argument. For example, do_twice is a function that takes a function object as an argument and calls it twice:

def do_twice(f):
    f()
    f()

Here's an example that uses do_twice to call a function named print_spam twice.

def print_spam():
    print 'spam'

do_twice(print_spam)

1. Type this example into a Jupyter notebook and test it.
2. Modify do_twice so that it takes two arguments, a function object and a value, and calls the function twice, passing the value as an argument to the function.
3. Write a more general version of print_spam, called print_twice, that takes a string as a parameter and prints it twice.
4. Use the modified version of do_twice to call print_twice twice, passing 'spam' as an argument.
5. Define a new function called do_four that takes a function object and a value and calls the function four times, passing the value as a parameter. There should be only two statements in the body of this function, not four.

Problem 2

In a Jupyter notebook use NumPy to solve the following:

1. Create a uniform subdivision of the interval -1.3 to 2.5 with 64 subdivisions.
2. Generate an array of length \(3n\) filled with the cyclic pattern 1, 2, 3.
3. Create an array of the first 10 odd integers.
4. Create a 10 x 10 arrays of zeros and then "frame" it with a border of ones.
5. Create an 8 x 8 array with a checkerboard pattern of zeros and ones using a slicing + striding approach.
6. Try using the dot function on a vector-vector, matrix-vector and matrix-matrix example. (This may seem simple but it's good to see how the results differ in each case.)
7. Create a function which creates an n×n array with (i,j)-entry equal to i+j.
8. Evaluate cos and sin on the interval [0, 1] and then stack the results into a tall array with rows being the (cos(x), sin(x)) entries.
9. Create a random 3x5 array using the np.random.rand(3, 5) function and compute: the sum of all the entries, the sum of the rows and the sum of the columns. (Just like sorted had an optional key= argument, many Numpy functions have an optional axis= argument!)
10. Create a random 5x5 array using the function np.random.rand(5, 5). We want to sort the rows according to the second column. Try combining array slicing + argsort + indexing to do this.

Refer to the NumPy documentation and SciPy Lecture Notes for help.

Problem 3

In a Jupyter notebook use NumPy and Matplotlib to create a plot of the Batman equation. The outline should be should be yellow and the enclosed space should be filled with black. Remove the grid and axes (i.e. plain white background) and insert your first name into the inside the symbol as large as it can be without touching the edges of the symbol. Color your name yellow too.

Refer to the Matplotlib documentation and gallery for help.