2.5. Exercises for Lecture 2#

2.5.1. Exercise 2.1#

  • Create one-dimensional NumPy arrays using different generation techniques

2.5.2. Exercise 2.2#

  • Create a one-dimentional NumPy array containing a sequence of integer numbers from 1 to 100

  • Starting from this, create a one-dimensional NumPy array containing in each entry the sum of integer numbers from 1 until the index of that entry

2.5.3. Exercise 2.3#

  • Create a one-dimensional array containing the sequence of the first 50 even natural numbers

  • Create a one-dimensional array containing the sequence of the first 50 odd natural numbers

  • Create a one-dimensional array containing the element-wise sum of the previous two arrays

2.5.4. Exercise 2.4#

Inside a Python program, the current time may be obtained with the time library:

import time
time_snapshot = time.time ()
print (time_snapshot)

  • Compare the time performances of element-wise operations performed between two lists with respect to the same operation performed in compact form between two NumPy arrays

  • After which size the differences start being significant?

2.5.5. Exercise 2.5#

  • After finding how the numpy.sort function works, write a Python library containing a function that determines the median of an array.

  • Write a main program that tests the performance of the developed function.

2.5.6. Exercise 2.6#

  • Given an array of numbers, write a Python library containing a function which determines the the value below which lies the 25% of the values, and the one above which lies the 25% of the the values

  • Generalise the function to the case where the percentage of tails is set as input value

2.5.7. Exercise 2.7#

Write a Python library containing functions to perform the following operations for NumPy 1D arrays:

  • Calculate the mean of its elements

  • Calculate the variance of its elements

  • Calculate the standard deviation of its elements

  • Calculate the standard deviation from the mean of its elements

2.5.8. Exercise 2.8#

Write a program that draws the basic trigonometric functions over a meaningful domain, using NumPy universal functions

  • Show that the sin and cosin functions differ by a phase

  • Show that the terms A and B in the equation \(f(x) = \sin (x-A) + B\) represent horizontal and vertical translations of the functional form, respectively

  • Show that the terms C and D in the equation \(f(x) = D \cos (Cx)\) represent horizontal and vertical dilations of the functional form, respectivey

2.5.9. Exercise 2.9#

Write a program that draws the Mandelbrot set with matplotlib.