Exercise

Exercise

  • How do you import numpy?

  • Name three different options to create a numpy array.

  • How do you get the shape of an array?

  • How do you get the data type of an array?

  • What types can the elements of an numpy array have? Name four different ones.

  • What type will have the arrays created from the following lists?

    l1 = [1, 2, 3]
l2 = [1., 2, 3]
l3 = [1., 2, 3 + 0j]

  • What is the fundamental difference between a slice of a numpy array and a list?

  • What is the meaning of ... in an index tuple?

  • Over which axis are multi-dimensional arrays iterated?

  • Which shape does the following array has:

    a = np.arange(3 * 4 * 10).reshape(2, -1, 5)

  • Test the performance difference between numpy and pure Python. Compute the square of 1000 numbers using both a list and a numpy array. You can measure the time for the computation by adding the cell magic %%timeit as the first line of the cell. Use one cell for each case. Note that %%timeit runs a lot of repetitions to get a more robust estimate of the run time.

  • Create an evenly spaced 1D array ranging from -π to π in steps of 0.1. Now create an array covering the same range but having exactly 100 elements. Note that there is a numpy constant (np.pi) for π.

  • Compute the mean, variance and standard deviation of one of the arrays created above.

  • Write a function that computes the angle in radians between two n-dimensional vectors. Use as many numpy functions as possible. The cosine of the angle between two vectors is given by

\[ cos(\alpha) = \frac{\vec{a}\cdot\vec{b}}{|\vec{a}||\vec{b}|}\]

  • Extend the function above to take two multi-dimensional arrays as input. Interpret, by default, the data along the last axis as the vectors. However, also try to give the possibility to use another axis.

  • How can you deal with missing data in numpy?

  • How do you mask and unmask data?

  • Draw ten random numbers which are uniformly distributed between zero and one.

  • Repeat intermediate level exercise 4 of the basic exercises but without using Turtle. First code a single canon ball shot. Then try to do all possible combinations of initial speed and angle within a single loop. Exploit numpys broadcasting capabilities!

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