Training

Create a file training8.py with the following functions:

1. Write a function f1(x) which accepts an number x as input and computes and returns

   

2. Write a function f2(x) which accepts the number x as input and computes and returns

   

   where log refers to the natural logarithm (the Python function name is math.log).

3. A function positive_places(f,xs) that takes as arguments some function f and a list of numbers xs and returns a list of those-and-only-those elements x of xs for which f(x) is strictly greater than zero. This task was given already as a training exercise in lab 6 where we also provide some input and output examples.

   In this lab, we ask that you write the same function without usage of a for or while loop to practice list comprehension or the use of filter.

Submit training8.py with subject line training8.

Assessed part

Create a file lab8.py with the following functionality. As you will need to use f1 and f2 in the exercises below, you may want to copy your file training8.py to the new name lab8.py and then add more functions to lab8.py.

1. Write a function create_plot_data(f, xmin, xmax, n) which returns a tuple (xs, ys) where xs and ys are two sequences, each containing n numbers:

   

   The function is expected to work for any n >= 2.

   Examples (here the tuple of returned sequences is a tuple of lists):

   In [ ]: def f(x):
   ...:     return x * 10
   ...:
   
   In [ ]: create_plot_data(f, -1, 1, 2)
   Out[ ]: ([-1.0, 1.0], [-10.0, 10.0])
   
   In [ ]: create_plot_data(f, 0, 2, 5)
   Out[ ]: ([0.0, 0.5, 1.0, 1.5, 2.0], [0.0, 5.0, 10.0, 15.0, 20.0])
   
   
   In [ ]: def f(x):
   ...:     return 0
   ...:
   
   In [ ]: create_plot_data(f, 0, 1.5, 4)
   Out[ ]: ([0.0, 0.5, 1.0, 1.5], [0, 0, 0, 0])
   

2. Using pylab or matplotlib, write a function myplot() that computes f1(x) [by calling the function f1 of course, or -- even better -- calling create_plot_data] and plots f1(x) using 1001 points for x ranging from -2 to +2. The function should return None.

   Then extend this function myplot to also plot f2(x) in the same graph.

   To plot two or more curves on the same figure, just use the plot() command twice.

   Label x-axis and provide a legend showing the function name (i.e. f1 and f2) for the two curves.

3. Extend the function myplot() so that it saves a png file of the graph (with name plot.png) and a pdf file of the graph (with name plot.pdf) through pylab/matplotlib commands.

   (Note: Generally, it is better to use pdf files rather than png files as pdf files are based on vector graphics and produce higher print quality, and can be zoomed without appearing pixelated. On the other hand, png files are good choice, for example, to include in webpages.)

4. Use the pylab-navigation bar (at the bottom of the figure) to zoom into the image. For x > 0, what is the value x of the functions where f1(x) = f2(x)?

   (If you are using the the IPython console and by default your plots appear inline, i.e. in the IPYthon console, then you cannot zoom into the figure. If so, you should use the command %matplotlib qt in the console. After you have done this, the next plot figure should appear in its own pop-up window, and allow you to zoom in and out in the figure.

   To switch back to figures showing in the IPython console, use %matplotlib inline).

   Using this graphical information, write a function find_cross() which uses scipy.optimize.brentq to find the value x (approximately) for which f1(x) = cos(2 * pi * x) * exp(-x * x) and f2(x) = log(x + 2.1) have the same value. We are only interested in the solution where x > 0.

   Your function find_cross() should return the approximation of the root that scipy.optimize.brentq returns (the default tolerance settings are okay).

5. Write a function reverse_dic(d) that takes a dictionary d as the input argument and returns a dictionary r. If the dictionary d has a key k and an associated value v, then the dictionary r should have a key v and a value k. (This is only expected to work for dictionaries that have a unique set of values although you do not need to check for this.)

Submit lab8.py using lab8 as the subject line.

Last updated: 2016-10-30 at 12:17