1. Recitation 7 Programming for Engineers in Python

2. Plan Plotting Debugging The Code 2

3. Plotting - Example 3

4. Plotting 4 To install matplotlib package, just click matplotlib downloadmatplotlib download Simple example import matplotlib.pyplot as plt # shorten the module’s name plt.plot([1,2,3,4]) plt.ylabel(‘some numbers') plt.show(False) # False is required when calling ‘show’ from the shell A list represents a vector! A single input list = y values x vector - from 0

5. Plotting 5 Create square numbers plt.plot([1,4,9,16]) Choose correct x values – two lists! plt.plot([1,2,3,4], [1,4,9,16], ‘ro’) Fix ranges of axes plt.axis([0, 6, 0, 20]) Order: [xmin, xmax, ymin, ymax]

6. Line Styles 6 The entire description

7. Plot Continuous Values 7 Show cos(x) of x values 0-5, with 0.1 step size. How is this range created? >>> range(0, 5, 0.1) TypeError: range() integer step argument expected, got float. Use numpy! import numpy as np x = np.arange(0, 5, 0.1)

8. Numpy Arrays - Creation 8 >>> A= np.array([[1, 2, 4, 8], [16, 32, 64, 128]]) # 2x4 matrix array([[1, 2, 4, 8], [16, 32, 64, 128]]) >>> B= np.arange(8).reshape(2, 4) # reshaped into 2x4 matrix array([[0, 1, 2, 3], [4, 5, 6, 7]]) >>> np.zeros((2, 4)) # create a 2x4 matrix of zeros array([[0., 0., 0., 0.], [0., 0., 0., 0.]])

9. Numpy Arrays 9 >>> np.ones((2, 4)) # create a 2x4 matrix of ones array([[1., 1., 1., 1.], [1., 1., 1., 1.]]) >>> A– B # elementwise subtraction array([[1, 1, 2, 5], [12, 27, 58, 121]]) >>> B**2 array([[0, 1, 4, 9], [16, 25, 36, 49])

10. Numpy Arrays - Arithmatics 10 >>> A*B # elementwise product array([[ 0, 2, 8, 24], [ 64, 160, 384, 896]]) >>> np.dot(A, np.transpose(B)) # dot product, dims must agree array([[ 34, 94], [ 544, 1504]]) >>> B.cumsum(axis=1) # cumulative sum along each row array([[ 0, 1, 3, 6], [ 4, 9, 15, 22]])

11. Plot Continuous Values 11 Left plt.plot(x, np.cos(2*np.pi*x), 'r--') Right x1 = np.arange(0, 10, 0.1) x2 = np.arange(0, 10) plt.plot(x1, np.exp(x1), 'b-', x2, np.exp(x2), 'ro')

12. Explaining the Data 12 How can I know what a plot refers to? plt.xlabel(‘radians’) plt.ylabel(‘cosine’) plt.title(‘Cosine Function’)

13. Subplots 13

14. Subplots 14  subplot(numRows, numCols, plotNum) >>> subplot(3, 2, 4) Lose the commas if rows and cols < 10 plt.subplot(211) plt.plot(x, np.cos(2*np.pi*x), 'r--') plt.subplot(212) x1 = np.arange(0, 10, 0.1) x2= np.arange(0, 10) plt.plot(x1, np.exp(x), 'b-', x2, np.exp(x2), 'ro') Plot 1Plot 2 Plot 3Plot 4 Plot 5Plot 6

15. Show Histograms 15 # create data mu = 100 sigma = 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data plt.hist(x, 50, normed = 1, facecolor='g') # arrange plot plt.xlabel('Smarts') plt.ylabel('Probability') plt.title('Histogram of IQ') plt.axis([40, 160, 0, 0.03])

16. Show Histograms 16

17. ∏ Estimation 17  Rings a bell? (recitation 4) def estimate_pi(error): term = 1 summ = 0 k = 1 while term > error: term = 1.0/k**2 summ += term k += 1 summ = sqrt(summ*6.0) return summ

18. ∏ Estimation 18  Create estimations of π by different error values pi_est = [] err_val = range(2, 12) err_vec = [10**(-x) for x in err_val] for err in err_vec: pi_est.append(estimate_pi(err))

19. ∏ Estimation – Build Plot 19 margin = 0.01 plt.plot([err_val[0]-1, err_val[-1]+1],[pi, pi], 'b-', err_val, pi_est, 'go') plt.axis([err_val[0]-1, err_val[-1]+1, min(pi_est)- margin, max(pi_est)+ margin ]) # document plot plt.xlabel('-log10 error') plt.ylabel('Estimation') plt.title('Pi Estimation') plt.legend(('python pi','estimation'), loc=4) # show plot and save as an image plt.show() plt.savefig('pi.png')

20. ∏ Estimation - Result 20

21. How to Find Bugs 21

22. 22 A unit is the smallest testable part of an application. The goal of unit testing is to isolate each part of the program and show that the individual parts are correct Pros: simplifies integration with other units, “living documentation” (how to use the code), helps design. The hw tests are examples of unit testing How to Find Bugs

23. 23  Mission: create 1000 lists of 25 guesses (random numbers) from 0,1,2,3 nSuits, nCards, nPlayers = 4, 25, 1000 players_guess=[] cards_list=[0]*nCards # create guesses for player in range(nPlayers): for card in range(nCards): # create one guess cards_list[card ]= random.randrange(0,nSuits) players_guess.append(cards_list)

24. How to Find Bugs 24 Investigate the lists created: >>> players_guess[0] [1, 1, 3, 3, 2, 2, 2, 3, 1, 2, 3, 1, 3, 0, 0, 3, 2, 0, 2, 0, 3, 2, 2, 3, 2] >>> players_guess[1] [1, 1, 3, 3, 2, 2, 2, 3, 1, 2, 3, 1, 3, 0, 0, 3, 2, 0, 2, 0, 3, 2, 2, 3, 2] >>> players_guess[2] [1, 1, 3, 3, 2, 2, 2, 3, 1, 2, 3, 1, 3, 0, 0, 3, 2, 0, 2, 0, 3, 2, 2, 3, 2] Oh, No, Bug! How to Find Bugs

25. 25 Trace the code step by step. In this case – by iterations. We begin by tracing the outer loop: for player in range(3): # 1000 is a lot! for card in range(nCards): cards_list[card ]= random.randrange(0,nSuits) players_guess.append(cards_list) print cards_list How to Find Bugs

26. 26 Output: [2, 3, 3, 0, 2, 1, 2, 0, 2, 3, 2, 2, 2, 1, 1, 0, 0, 2, 2, 1, 2, 3, 0, 0, 3] [1, 2, 3, 3, 2, 0, 0, 1, 0, 0, 1, 2, 2, 3, 3, 1, 2, 1, 0, 0, 2, 0, 1, 3, 3] [2, 2, 2, 0, 3, 1, 3, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1] The problem is not here. What is players_guess? >>> players_guess [[2, 2, 2, 0, 3, 1, 3, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1], [2, 2, 2, 0, 3, 1, 3, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1], [2, 2, 2, 0, 3, 1, 3, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1]] Notice anything? How to Find Bugs

27. 27 Ok, we found the problem, but what is the reason? And the solution? Main suspect: players_guess.append(cards_list) Is this drawing correct? How to Find Bugs players_guess cards_list

28. 28 There is only one list – which is mutated every iteration.  Found the problem. Solution? players_guess cards_list How to Find Bugs

29. 29 for player in range(nPlayers): # create cards list inside the loop cards_list=[0]*nCards for card in range(nCards): cards_list[card]= random.randrange(0,nSuits) players_guess.append(cards_list) How to Find Bugs

30. 30  Mission: replace first and last character in a string def switch(s): first = s [0] last = s [-1] s = s.replace(s[0], last ) s = s.replace(s[-1], first ) return s >>> switch(‘abcd’) abca >>> switch(‘banana’) bbnbnb How to Find Bugs

31. 31 Add ‘print’ def switch(s): first = s [0] last = s [-1] s = s.replace(s[0], last ) s = s.replace(s[-1], first ) return s How to Find Bugs

32. 32 >>> switch('abcd') 'abca' >>> switch('banana') 'bbnbnb‘  Let’s add ‘print’ commands inside switch: print s s = s.replace(s[0], last ) print s s = s.replace(s[-1], first ) return s How to Find Bugs

33. 33 >>> switch('abcd') abcd dbcd 'abca' >>> switch('banana') banana aanana 'bbnbnb‘  Observations? How to Find Bugs

34. 34 Observation: replace changes all occurances of the character in the string – we only want one specific change. >>> help(str.replace) replace(...) S.replace(old, new[, count]) -> string Solution: s = s.replace(s[0], last, 1 ) s = s.replace(s[-1], first, 1 ) How to Find Bugs

35. 35 >>> switch('abcd') abcd dbcd 'abcd' >>> switch('banana') banana aanana 'banana‘ Observation: The first letter is changed twice! Solution: replace doesn’t work for us, use a different method! How to Find Bugs

36. 36 New code: return s[-1]+s[1:-1]+s[0] >>> switch('abcd') 'dbca' >>> switch('banana') 'aananb’ How to Find Bugs

37. 37 class Nothing: def set_value(self, value): self.value = value def print_value(value): print value not_a_thing = Nothing() not_a_thing.set_value(“nowhere”) not_a_thing.print_value() >>> ??? How to Find Bugs