ENGR (Socolofsky) Week 07 Python scripts

Transcription

1 ENGR (Socolofsky) Week 07 Python scripts A couple programming examples for this week are embedded in the lecture notes for Week 7. We repeat these here as brief examples of typical array-like operations in programs. We also include a longer example showing many of the things you can do with array-like data types in Python. A common task with array-like data is to do some operation on each element of the array. Program prog 00.py demonstrates operating on each element of a list using a for loop 1 # prog_ 00. py 2 # 3 # Demonstrate adding two arrays of data using a for loop 4 # 5 # S. Socolofsky 6 # ENGR # September # Let V contain the voltage measured by an analog temperature probe 10 V = [3.57, 3.46, 3.67, 3.44, 3.55] 11 T = [] # Initialize empty list to hold computed temperatures # Compute the temperature in deg F from the calibration curve given by 14 # T = * V , where V is the voltage reading of the sensor 15 a = b = for i in range ( len (V )): 18 T. append (a * V[i] + b) # Return the results 21 print (' The measured temperatures in deg F are :') 22 print (T) Code execution for prog 00.py yields The measured temperatures in deg F are: [ , , , , ]

2 We can accomplish the same task as shown in prog 00.py using the numpy array data type, but without the need to use a for loop. This is because the np.array data type automatically performs math operations element-by-element. We demonstrate an example using numpy in prog 01.py 1 # prog_ 01. py 2 # 3 # Demonstrate making elementwise computations using numpy 4 # 5 # S. Socolofsky 6 # ENGR # September import numpy as np # Let V contain the voltage measured by an analog temperature probe 12 V = np. array ([3.57, 3.46, 3.67, 3.44, 3.55]) # Compute the temperature in deg F from the calibration curve given by 15 # T = * V , where V is the voltage reading of the sensor 16 a = b = T = a * V + b # Return the results 21 print (' The measured temperatures in deg F are :') 22 print (T) Code execution for prog 01.py yields The measured temperatures in deg F are: [ ] 2

3 A final program script.py demonstrates many features of array-like data types in Python. 1 # script. py 2 # 3 # This is a general program to demonstration data types for array - like data 4 # 5 # In this script we will consider three sets of data. First, we will consider 6 # an array of values, for example the output of a temperature sensor in 7 # voltage. These values will be 8 # 9 # vals = [5.45, 5.30, 4.95, 4.97, 4.87, 5.01, 4.88] 10 # 11 # Second, we will consider a database of keyword - value pairs. These will be 12 # the names and ages of three people in a medical records database : 13 # 14 # Name Age 15 # # John # Kathy # Elsa # David # 21 # In the thrid example, we will let one set of data be the x- coordinates of 22 # a function we want to plot, and we will compute the corresponding 23 # y- coordiantes from the function 24 # 25 # f( t) = A sin ( omega t) + bt 26 # 27 # S. Socolofsky 28 # ENGR # August import numpy as np 32 import matplotlib. pyplot as plt # Lists # We can literally store any Python object in a list. 37 my_list = ['John ', 47, [5.45, 5.30, 4.95, 4.97, 4.87, 5.01, 4.88], 38 'A sin ( omega t) + bt '] # We return values from lists using the index to a list element. Python 41 # starts counting at zero 42 print (' Element number 1 of my strange list is ' + str ( my_list [ 1 ])) # Lists are mutable, so I can change values in a list 45 my_list [ 1] = '47 years old ' # And lists are iterators, so they can be used in a for loop 48 print ('\ nmy strange list contains :') 49 for thing in my_list : 3

4 50 print ( thing ) # Normally, when we use lists, we store similar data throughout the list. 53 # Let 's store the voltages from a temperature sensor in a list volts 54 volts = [5.45, 5.30, 4.95, 4.97, 4.87, 5.01, 4.88] # To do math on the elements of a list, we have to do it element - by - element 57 # using a loop. I could store the corresponding temperature values in a new 58 # list temperature if I know the calibration coefficients between voltage 59 # and temperature 60 a0 = a1 = temperature = [] # initialize an empty list to store the result 63 for voltage in volts : 64 # Append lists to lists 65 temperature += [ a0 * voltage + a1] print ('\ nthe temperature values in my new list are :') 68 print ( temperature ) # You can also add data to a list using. append () 71 volts. append (5.06) # And you can slice lists using : 74 print ('\ nhere are some subsamples of my voltage data :') 75 print (' volts = ' + str ( volts )) 76 print (' volts [0:3] = ' + str ( volts [0:3 ])) 77 print (' volts [-1] = ' + str ( volts [-1 ])) 78 print (' volts [3:] = ' + str ( volts [3 :])) 79 print (' volts [2] = ' + str ( volts [2 ])) 80 print (' etc... ') # Tuples # Tuples are like lists, but once created, they cannot be changed 85 volts = (5.45, 5.30, 4.95, 4.97, 4.87, 5.01, 4.88) # There is no. append () method since tuples are immutable. If you need to add 88 # something to a tuple, you have to create a new tuple. I can add two 89 # tuples, but if one of my tuples only contains one data point, ( 5. 06) is 90 # interpreted as a float inside (). Instead, I have to put a comma after the 91 # number, which tells Python to consider as the only element in a tuple : 92 volts = volts + ( 5. 06,) 93 print ('\ nmy new tuple that contains voltages is:') 94 print (' ' + str ( volts )) # You slice tuples similarly to lists. We will use tuples a lot once we learn 97 # how to create a user - defined function since the result of the function is 98 # returned in a tuple # Dictionaries # Dictionaries are special lists in which the user gets to name the index to 4

5 103 # the list using a keyword 104 patients = {'John ' : 47, 'Kathy ' : 36, 'Elsa ' : 27, 'David ' : 19} # You still use [] to index a dict, but you put the keyword within [] instead 107 # of an index number. Python can tell you the names of the keywords : 108 print ('\ nthe keywords of my medical record dictionary are :') 109 print (' ' + str ( patients. keys ())) # I can index the dictionary several ways : 112 print ('\ njohn is ' + str ( patients ['John ']) + ' years old \n') 113 for key in patients. keys (): 114 print (' ' + key + ' is ' + str ( patients [ key ]) + ' years old ') # Numpy Arrays # Numpy arrays are specialized lists intended to be used as mathematical 119 # objects. We have to import numpy to use it, and we create arrays with the 120 # numpy function array () # If you pass a list of numbers to np. array, it will create a numpy array 123 # object 124 np_volts = np. array ( volts ) # Indexing of numpy arrays looks the same as for lists. 127 print ('\ nhere are some subsamples of my numpy array of voltage data :') 128 print (' np_volts = ' + str ( np_volts )) 129 print (' np_volts [0:3] = ' + str ( np_volts [0:3 ])) 130 print (' np_volts [-1] = ' + str ( np_volts [-1 ])) 131 print (' np_volts [3:] = ' + str ( np_volts [3 :])) 132 print (' np_volts [2] = ' + str ( np_volts [2 ])) 133 print (' etc... ') # But math is very different. 136 print ('\ nif we multiply our list volts by 3, we get ') 137 print ( 3 * volts ) 138 print ('\ nif we multiply our numpy array np_ volts by 3, we get ') 139 print (3 * np_volts ) 140 print (' This last operation is the same as multiplying our list ') 141 print ('element -by - element within a for loop.') # Hence, numpy arrays are ideal for mathematics. Consider a vector ( 3. 4, 144 # 5.7, 2.6) and (8.4, 4.5, 6.7) 145 vec_a = np. array ([3.4, 5.7, 2.6]) 146 vec_b = np. array ([8.4, 4.5, 6.7]) 147 print ('\ nvector a is ' + str ( vec_a )) 148 print (' Vector b is ' + str ( vec_b )) 149 print ('\ nvector a has magnitude ' + str (np. sqrt (np. inner ( vec_a, vec_a )))) 150 print ('Vector b has magnitude ' + str (np. sqrt (np. inner ( vec_b, vec_b )))) 151 print (' Vector a + b is ' + str ( vec_a + vec_b )) 152 print (' The inner product a dot b is ' + str ( np. inner ( vec_a, vec_b ))) 153 print (' The cross product a x b is ' + str ( np. cross ( vec_a, vec_b ))) # The fact that numpy arrays can do math element - by - element makes computing 5

6 156 # and plotting functions easy 157 t = np. linspace ( 0., 100., num =500) # 500 points between 0 and a = b = omega = 1./ y = a * np. sin ( omega * t) + b * t # We can print out a few data points using slices 164 print ('\ ntable of time and position data :') 165 print ('t = ' + str (t[0:-1:100 ])) 166 print ('y = ' + str (y[0:-1:100 ])) # Matplotlib # Another advantage of numpy arrays is that we can plot them using the 171 # matplotlib package and pyplot module. 172 plt. plot (t, y, 'b-') 173 plt. ylabel ('f(t), (m)') 174 plt. xlabel ('t, (s)') 175 plt. grid ( True ) 176 plt. show () # This ends our introduction to array - like data types for this week. Code execution for script.py yields Element number 1 of my strange list is 47 My strange list contains: John 47 years old [5.45, 5.3, 4.95, 4.97, 4.87, 5.01, 4.88] A sin (omega t) + bt The temperature values in my new list are: [ , , , , , , ] Here are some subsamples of my voltage data: volts = [5.45, 5.3, 4.95, 4.97, 4.87, 5.01, 4.88, 5.06] volts[0:3] = [5.45, 5.3, 4.95] volts[-1] = 5.06 volts[3:] = [4.97, 4.87, 5.01, 4.88, 5.06] volts[2] =

7 etc... My new tuple that contains voltages is: (5.45, 5.3, 4.95, 4.97, 4.87, 5.01, 4.88, 5.06) The keywords of my medical record dictionary are: dict_keys([ John, Kathy, Elsa, David ]) John is 47 years old John is 47 years old Kathy is 36 years old Elsa is 27 years old David is 19 years old Here are some subsamples of my numpy array of voltage data: np_volts = [ ] np_volts[0:3] = [ ] np_volts[-1] = 5.06 np_volts[3:] = [ ] np_volts[2] = 4.95 etc... If we multiply our list volts by 3, we get (5.45, 5.3, 4.95, 4.97, 4.87, 5.01, 4.88, 5.06, 5.45, 5.3, 4.95, 4.97, 4.87, 5.01, 4.88, 5.06, 5.45, 5.3, 4.95, 4.97, 4.87, 5.01, 4.88, 5.06) If we multiply our numpy array np_volts by 3, we get [ ] This last operation is the same as multiplying our list element-by-element within a for loop. Vector a is [ ] Vector b is [ ] Vector a has magnitude Vector b has magnitude Vector a + b is [ ] The inner product a dot b is The cross product a x b is [ ] 7

8 Table of time and position data: t = [ ] y = [ ] f(t), (m) t, (s) Plot created by matplotlib.pyplot. 8