Programming for Engineers in Python. Recitation 3

Transcription

1 Programming for Engineers in Python Recitation 3

2 Plan Modules / Packages Tuples Mutable / Imutable Dictionaries Functions: Scope Call by Ref / Call by Val Frequency Counter

3 Python Code Hierarchy Statement function Module Package

4 Modules All modules and their contents (functions, constants) can be found at >>> import math # mathematical functions >>> dir(math) [' doc ', ' name ', ' package ', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'erf', 'erfc', 'exp', 'expm1', 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum', 'gamma', 'hypot', 'isinf', 'isnan', 'ldexp', 'lgamma', 'log', 'log10', 'log1p', 'modf', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'trunc'] >>> math.pi # a constant >>> math.sqrt(16) # a function 4.0 >>> math.log(8, 2) 3.0

5 Modules Cont. >>> import os #operating system interfaces >>> os.rename( my_file.txt, your_file.txt ) >>> os.mkdir( new_dir ) >>> for root, dirs, files in os.walk('lib/ '): print root, "consumes", print sum(getsize(join(root, name)) for name in files), print "bytes in", len(files), "non-directory files" >>> os.times()[0] # user time

6 Packages NumPy support for large, multi-dimensional arrays and matrices high-level mathematical functions SciPy Optimization linear algebra integration special functions signal and image processing And more

7 Installing Packages Download NumPy: Choose Download numpy win32-superpackpython2.7.exe SciPy: Choose Download scipy win32-superpackpython2.6.exe

8 Mutable vs. Immutable Can we change lists? >>> a_list = [1,2,3] >>> a_list[2] 3 >>> a_list[2] = Inigo Montoya >>> a_list [1,2, Inigo Montoya ] The assignment has mutated the list!

9 Mutable vs. Immutable What about strings? >>> name = Inigo Montoya >>> name[0] ' I' >>> name[5] ' ' >>> name[3] = t Traceback (most recent call last): File "<pyshell#14>", line 1, in <module> name[3] = 't' TypeError: 'str' object does not support item assignment Immutable!

10 Assignments to List Variables >>> orig_list = [1,2,3] >>> copy_list = orig_list >>> orig_list = [6,7,8,9] >>> copy_list ] 1,2,3] >>> orig_list ] 6,7,8,9] So far - no surprises

11 Assignments to List Variables >>> copy_list = orig_list >>> orig_list[0] = 1000 >>> orig_list ] 1000,7,8,9] >>> copy_list ] 1000,7,8,9] Surprise!

12 Memory Assignments to List Variables List assignment orig_list = [6,7,8,9] creates: a list object, [6,7,8,9] a reference from the variable name, orig_list, to this object. Memory orig_list [6,7,8,9]

13 Assignments to List Variables The assignment copy_list = orig_list does not create a new object, just a new variable name, copy_list, which now refers to the same object. Memory orig_list [6,7,8,9] copy_list

14 Assignments to List Variables Mutating list elements, orig_list[0] = 1000, does not create a new object and does not change existing references. Memory orig_list [1000,7,8,9] copy_list

15 Tuples A tuple is just like a list, only it is immutable. Syntax: note the parentheses! >>> t = ( don t, worry, be, happy ) # definition >>> t ( dont, worry, be, happy ) >>> t[0] # indexing 'dont' >>> t[-1] # backwords indexing worry' >>> t[1:3] # slicing ( worry, be )

16 Tuples >>> t[0] = do # try to change Traceback (most recent call last): File "<pyshell#2>", line 1, in <module> t[0]= do TypeError: 'tuple' object does not support item assignment No append / extend / remove in Tuples!

17 Tuples So what are tuples good for? Faster than lists Safe code When immutable types are required (coming next).

18 Dictionaries A dictionary is a set of key-value pairs. >>> dict_name = {key1:val1, key2:val2, } Keys are unique and immutable, values are not. Example: Map names to heights: >>> heights = { Alan Harper :1.76, John Smith :1.83, Walden Schmidt :1.90} >>> heights {'Walden Schmidt': 1.9, 'John Smith': 1.83, 'Alan Harper': 1.76} Note:The pairs order changed

19 Dictionaries Add a new person: >>> heights[ Lyndsey Makelroy ] = 1.70 >>> heights {'Lyndsey Makelroy': 1.7, 'Walden Schmidt': 1.9, John Smith': 1.83, 'Alan Harper': 1.76} What happens when the key already exists? >>> heights[ John Smith ] = 2.02 >>> heights {'Lyndsey Makelroy': 1.7, 'Walden Schmidt': 1.9, 'John Smith': 2.02, 'Alan Harper': 1.76} Solutions?

20 Dictionaries Idea: Add address to the key >>> heights = {[ Alan Harper, Malibu ]:1.76} Traceback (most recent call last): File "<pyshell#46>", line 1, in <module> heights = {['Alan Harper', 'Malibu']:1.76} TypeError: unhashable type: 'list What s the problem? Fix: >>> heights = {( Alan Harper, Malibu ):1.76} >>> heights {('Alan Harper', 'Malibu'): 1.76}

21 Dictionaries Useful methods: D.get(k[,d]) - D[k] if k in D, else d (default None). D.has_key(k) - True if D has a key k, else False D.items() - list of (key, value) pairs, as 2-tuples D.keys() - list of D's keys D.values() - list of D's values D.pop(k[,d]) - remove specified key and return the value. If key is not found, d is returned.

22 Functions Scope Consider the following function, operating on two arguments: def linear_combination(x,y): y=2*y return (x+y) The formal parameters x and y are local, and their life time" is just the execution of the function. They disappear when the function is returned. 3, 4 linear_combination 11 x, y

23 Functions Scope >>> a=3 >>> b=4 >>> linear combination(a,b) 11 # this is the correct value >>> a 3 >>> b 4 # b has NOT changed The change in y is local - inside the body of the function.

24 Functions Scope >>> x=3 >>> y=4 >>> linear_combination(x,y) 11 # this is the correct value >>> x 3 >>> y 4 The y in the calling environment and the y in the function are not the same variable!

25 Functions Call by Val / Call by Ref Functions have arguments that appear in their prototype: def linear_combination(x,y): When you call a function, you must assign values to the function s arguments: >>> linear_combination(3, 4) What happens when you pass variables? >>> linear_combination(a, b)

26 Functions Call by Val / Call by Ref What is the difference? Run ta3_switch.py to find out!

27 Functions Call by Val / Call by Ref What is the difference? Run ta3_add.py to find out!

28 Functions Call by Val / Call by Ref There are two possibilities: Call by Value pass a s value to x and b s value to y a, b A_function a=3 b=4 x = 3 y = 4 Call by Reference pass a s address to x and b s address to y a, b Another_function a=[1,2] b=[3, 4] x y

29 Functions Call by Reference In Python Call by reference A function can mutate its parameters. When the address does not change, the mutations effect the original caller's environment. Remember: Assignment changes the address! That explains why y=2*y is not visible in the caller's environment.

30 Functions Call by Reference def increment(lst): for i in range(len(lst)): lst[i] = lst[i] +1 # no value returned Now let us execute it in the following manner >>> list1=[0,1,2,3] >>> increment(list1) >>> list1 [1, 2, 3, 4] # list1 has changed! lst was mutated inside the body of increment(lst). Such change occurs only for mutable objects.

31 Functions Call by Reference Consider the following function: def nullify(lst): lst=[ ] # no value returned Now let us execute it in the following manner >>> list1=[0,1,2,3] >>> nullify(list1) >>> list1 [0, 1, 2, 3] # list1 has NOT changed! Why?

32 Functions - Information Flow To conclude, we saw two ways of passing information from a function back to its caller: Using return value(s) Mutating a mutable parameter

33 Frequency Counter Assume you want to learn about the frequencies of English letters. You find a long and representative text and start counting. Which data structure will you use to keep your findings? s u p e r c a l i f r a g i l i s t i c e x p i a l i d o c i o u s

34 Frequency Counter str1 = 'supercalifragilisticexpialidocious # count letters charcount = {} for char in str1: charcount[char] = charcount.get(char, 0) + 1 # sort alphabetically sortedchartuples = sorted(charcount.items())

35 Frequency Counter # print for chartuple in sortedchartuples: print chartuple[0], =, chartuple[1] a = 3 c = 3 d = 1 e = 2 f = 1 g = 1

36 Simulation Guess Cards צורה שם עברי שם אנגלי צבע עלה/פיק שחור Spades לב אדום Hearts יהלום/מעוין אדום Diamonds תלתן שחור Clubs

37 Simulation Reminder In class: Simulated a rare disease by: Generating its distribution in the entire population, assume we received 2% Generating a sample of 1000 people. For every person toss a coin with 2% chance of heads (have the disease) and 98% of tails (don t have the disease) Check whether the number of sick people is significantly higher then expected (20 people) Repeat for 100 diseases

38 Simulation - Cards Scenario: Generate 25 playing cards. Guess which series every card belongs to. One card - there is an equal chance that the card belongs to each of the four series, hence - 25% chance for being correct. Two cards 16 options with equal chance 6.25% chance n cards 4 n options, 1/ 4 n chance of being correct in all guesses. For 25 cards the chance of being always correct drops to almost 0.

39 Simulation - Comparison Role Diseases Cards Number of Guesses Number of Observations Rate (Expectation) 100 diseases 1000 people Generated per each disease 1000 people 25 cards 25% per series

40 Exercise - Dice Odds In backgammon, there are 36 combinations of rolling the dice. We are interested in the sum of the two dice. Therefore: count the number of combinations for every possible sum find the chance of getting it.

41 Exercise - Dice Odds Create the following data structure: Each combination of two dice is a tuple. All combinations are held in a dictionary, where the key is the sum of the combination. Each value in the dictionary is a list of tuples that is, all combinations that sum to key Keys Values [ (1, 1) ] [ (1, 2), (2, 1) ] [ (1, 3), (2, 2), (3, 1) ]

42 Exercise - Dice Odds The general outline is: rolls = {} Loop with d1 from 1 to 6 Loop with d2 from 1 to 6 newtuple ( d1, d2 ) # create the tuple oldlist dictionary entry for d1+d2 newlist oldlist + newtuple update dictionary entry Loop over all keys in the dictionary print key, length of the list Let s Play!

43 Exercise - Dice Odds rolls = {} for d1 in range(1, 7): # first dice for d2 in range(1, 7): # second dice t = (d1, d2) key = d1+d2 val = rolls.get(key, []) # update list val.append(t) rolls[key] = val for key in rolls.keys(): print key, len( rolls[key] ) # print result

44 Exercise - Dice Odds >>>