Computer Lab 1: Introduction to Python

Transcription

1 Computer Lab 1: Introduction to Python 1 I. Introduction Python is a programming language that is fairly easy to use. We will use Python for a few computer labs, beginning with this 9irst introduction. The goals of this 9irst lab is to: get you comfortable using Python in both the interactive shell and with a script learn some basic programming learn to program and use a function learn about for loops learn about conditional statements use built- in functions from numpy (Numerical Python) use arrays make a plot There are many online resources including personal.umich.edu/~mejn/computational- physics/ (This second link has an appendix on the difference between python versions.) II. Starting Python There are several ways to use Python. You may use it on your computer (the download is free) or on the computers in the Computer Lab (VAN 201). In the computer lab, after you have logged into one of the computers, open a web browser and set up a CLAS Linux account. Do this by going to Then use to sign in through the web and use the linux account. When you do this, you click the + sign for a new session, and I picked the MATE system tool. Then I was able to open a terminal window from the drop- down Applications menu (Konsole in the System Tools). On my laptop with Python installed, I just open a terminal window (I have a mac with Xquartz.) I then typed (the $ is the command line prompt) on my mac: $ python (On the MATE Konsole, the command line prompt is %, so it looks like % python.) On my mac computer, this results in the output: 1 By M. H. Reno and J. Unmuth- Yockey, version

2 Python (default, Jan , 08:29:18) [GCC Compatible Apple LLVM (clang )] on darwin Type "help", "copyright", "credits" or "license" for more information. >>> The >>> means we are in interactive mode in Python, and the 9irst line says that I have Python 2.7. (There is also a version 3. You can use whatever version you want.) What we will the interactive mode here to begin, although in the last exercise, we will use a Python script instead. To get out of Python interactive mode, type the following (including the parentheses): >>> quit() There are several ways to proceed including: keep working in interactive mode, use IDLE (Integrated Development and Learning Environment) or the Wing IDE (Integrated Development Environment). The IDLE or IDE environment will allow you to save your work, while for the interactive mode, you will need to periodically copy and paste into a word document to show what you have done for the requested tasks. (The tasks are written in italics.) Which ever way you chose, you will print your commands and results to hand in for this lab. In IDLE you can save the 9ile with a.txt extension in text format which will allow you to print the text 9ile. Do this for the following exercises. To use IDLE, instead of typing $ python, type $ idle in the terminal window. This will open a new window, a Python shell with the >>> indicating it is ready to accept statements. Within IDLE, however, it is possible to open a 9ile, say a new 9ile from the drop- down menu in File, and write in the 9irst line print hello world Then save as test.py (9ile name test, 9ile type py for python). Now you have the option under the menu Run to Run Module which will then execute all the lines (of which there is one) in test.py, the output hello world will be in the shell window. You can save the shell window output by using the File menu save copy as testoutput.txt. 2

3 III. Basics Everything after the hashtag # is a comment, namely, nothing after # is executed. In the statements below, after the, type <return> to get the >>>. After <return> on the second line (print <return>), python returns the result (6), etc. >>> #This is a comment statement... >>> print >>> print 2*3 6 >>> print 2**3 #2 to the power 3 8 >>> 2*3**2 #the usual order of operations 18 >>> (2*3)**2 36 Assignment statements set or reset values of variables. Here we have variables a and b: >>> a=2 >>> b=3 >>> print a+b 5 >>> x=a+b >>> print x 5 Assignment statements are not equations. You can reassign values, using the old values. For example, here we have that x=5, and we can increase the value by one in the following way. >>> print x 5 >>> x=x+1 >>> print x 6 (Python also has a special way of writing this by combining + and =: >>> x = 5 >>> x += 1 >>> print x 6 >>> x += 2 >>> print x 8 3

4 but we will stay with the explicit assignment statement for now.) One feature of Python and many other computer programs is that integers are treated differently than real numbers. Look at the following in Python 2.7: >>> 1/2 0 >>> 1./2 0.5 >>> 1/ The 9irst expression 1/2 is the division of integer 1 by integer 2, and the result is the integer 0. If either numerator or denominator is real, then the result returned is real. You can make even the 9irst expression yield 0.5 with the following: >>> from future import division >>> 1/2 0.5 (Before and after future are two underscores.) You may wish to start every interactive session with this line to allow you to avoid getting 0 when you take 1/2. There is another useful symbol called modulo, %. Modulo returns the remainder between two numbers, like this. >>> 8 % 2 # remainder of 8 divided by 2 0 >>> 8 % 3 # remainder of 8 divided by 3 2 >>> 8 % 5 3 >>> 8 % 6 2 Alternatively, it s also like a clock, where counting from 0 to 8 brings you back to the start: >>> 2 % 8 2 >>> 6 % 8 6 >>> 8 % 8 0 >>> 9 % 8 1 >>> 10 % 8 4

5 2 From this you can see % gives the remainder of division between the two numbers. The wording associated with this symbol is like 8 mod 2 equals 0, or 3 mod 8 equals 3. Write some sample lines like the ones listed in this section to test out at least four simple arithmetic operations. Check to see if the case (upper or lower case) of the variable name is relevant in Python. What do you >ind? IV. Functions You can de9ine your own functions. In the code below from my copy and paste, the lines wrap they were all in one line in the terminal: >>> def myfunc(a,b):... """This function takes inputs a and b to form myfunc=(a +b)**2"""... #note that I need to indent four spaces for everything below def... y=(a+b)**2... return y... >>> # <return> after the last (empty) line... >>> a1 = 1 >>> b1 = 1.5 >>> z = myfunc(a1,b1) >>> print z 6.25 >>> a1=2 >>> b1=6 >>> z = myfunc(a1,b1) >>> print z 64 The variables a and b in myfunc are just stand- ins for the variables that you will input when you call the function (here I use a1 and b1). The triple quotes are a comment in the function. After the function is executed (to 9ind z here), the values of a,b and y in myfunc are lost. E.g., >>> print y Traceback (most recent call last): File "<stdin>", line 1, in <module> NameError: name 'y' is not defined 5

6 For a function that you want to use in many places, you can save it (or multiple functions) in a 9ile in the same directory as where you start python (your working directory). Here is an example 9ile that I have called myfunctions.py, in which I have: def myfunc2(a,b): """ myfunc2 = (a+b)**2 """ y = (a+b)**2 return y def myfunc3(a,b): """ myfunc3 = (a+b)**3 """ y = (a+b)**3 return y In Python, I then execute the following commands to get results: >>> from myfunctions import myfunc2, myfunc3 >>> a1 = 2 >>> b1 = 3 >>> z = myfunc2(a1,b1) >>> print z 25 >>> z = myfunc3(a1,b1) >>> print z 125 Another way to get these functions to work is to do the following: >>> import myfunctions >>> a1=2 >>> b1=3 >>> z=myfunctions.myfunc2(a1,b1) >>> print z 25 I need myfunctions. before myfunc2 because myfunc2 resides in the myfunctions module. Yet another way to do this is to make a nickname (alias) for myfunctions (here called mf): >>> import myfunctions as mf >>> a1 = 2 >>> b1 = 3 >>> z = mf.myfunc2(a1,b1) >>> print z 25 I can 9ind the contents of myfunctions (nicknamed mf) by dir (mf): 6

7 >>> dir (mf) [' builtins ', ' doc ', ' file ', ' name ', ' package ', 'myfunc2', 'myfunc3'] Make up two functions of your own and try them out, by saving them in a >ile and importing them, to get results. Hand in both your functions and how they run in Python. V. `For loops Now we will learn the bread and butter of iterations. Whenever you want to iterate over data or have a task repeat you will use a `for loop. mini- section on `range function as part of the `for loops, one will often use the function `range. This function returns a list of numbers. >>> range(0, 5) [0, 1, 2, 3, 4] and it starts from zero and goes up to N- 1, for whatever N you put in. Here, N=5, so the list of 5 numbers goes from 0 to 4. Now lets see a for loop and range together: >>> for i in range(0, 5): >>> print i Here you can see in an example what the for loop does and how the range function is involved. for i in range(0, 5): means in english: for each thing that the range function makes: meaning for each number in the list [0, 1, 2, 3, 4]:. The print i means in english print the current thing, in this case print the current number. FYI using `i is not needed, the only words in this case that need to be there are for, and in, you could have wrote for x in range(0, 10): and then printed all the numbers from 0 to 9. Just like in function de9initions, everything you want to do for i in the range speci9ied you must put in lines indented the same way. Try to anticipate what the following code will do: >>> x = 0 >>> for i in range(0, 5): >>> x = x + i >>> print x 7

8 after thinking about it for a minute, run it and see what happens. Take one more minute to try and understand what happened > x was set to zero > we told the computer to loop through the numbers [0, 1, 2, 3, 4] using the variable i > the computer evaluates the right side of the equal sign (x + i), in this case (0 + 0), and assigns that value to x. > it then prints the value of x. > the computer evaluates the right side of the equal sign (x + i), in this case (0 + 1), and assigns that value to x. > it then prints the value of x. > the computer evaluates the right side of the equal sign (x + i), in this case (1 + 2), and assigns that value to x.... Make a for loop that prints 0, 2, 4, 6, 8, 10. Make another for loop that does what ever you want it to so long as it doesn t return an error and it does what you thought it would! VI. Conditional Statements Now we will use some logic with english words, in the form of conditional statements. This is done with the words if, elif, and else. We will use an example to show their use: >>> x = 4 # declare the value of x >>> if (x < 4): # test to see if x is less than four >>> print x is smaller than 4 >>> elif (x == 4): # test to see if x equals four >>> print x is 4! >>> else: # what to do if the other situations are false >>> print x must be larger than 4 x is 4! The computer goes through this line by line and checks the condition in each case. First it checks to see if x is less than 4, when that turns out to be false, it moves on without running the indented code below. Then on to the else- if statement and checks to see if x equals 4. That part turned out to be true and so it ran the code indented underneath. It never made it to the else part because one of the cases was true before getting there so it just skipped that part. You can include as many elif statements you want, or not at all. In fact you can just use only the if part if you want. 8

9 >>> x = 2 # declare the value of x >>> if (x < 12): # check to see if x is less than twelve >>> x = 5 # change the value of x to 5 >>> print x # print the value of x 5 Let me do one more example that is somewhat practical. I will make a function that is the square wave function. Here you can see the value of a function and using conditionals. def square_wave(t, period): # define the function, it s name and the arguments it has returns the value of the step function for any t. y = t % period # make a new variable in the interval of the period if (y <= period/2.): # check to see if the variable is less than or equal to half the period return 1.0 # if yes, return 1 else: return -1.0 # if not, return 0. Write your own conditional set-up, it can be anything you want as long as it doesn t return an error and it does what you wanted it to do! VII. Built-in Functions: numpy module Good news, there are many built in functions. To access basic functions like trigonometic functions and the square root, you need to import numpy (short for Numerical Python). You can 9ind the complete list of functions in numpy with the dir (numpy) command after you import it. A common nickname is np. We will use trigonometric functions. In the code below, I show that pi is de9ined in numpy, but that numpy must be identi9ied (with nickname np here) every time you use pi: use np.pi, not pi. >>> import numpy as np >>> print np.pi >>> x = np.sin(pi/2) Traceback (most recent call last): File "<stdin>", line 1, in <module> NameError: name 'pi' is not defined >>> print np.sin(np.pi/2) 1.0 Evaluate the cosine function at 30, 60 and 90 degrees. Note that the inputs to the trigonometric functions are in radians. Use Python to do all the conversions. VIII. Arrays 9

10 Numpy also allows for arrays. You can think of an array as a row or column vector (although whether it is a row or column is a little bit more technical), or n1 by n2 matrix for integers n1 and n2, etc. We will look at one- dimensional arrays. Since we will be looking at trig functions, let s call the array theta, and we will give it 21 values. For a start, we can set all the values to zero: >>> theta = np.zeros(21) >>> print theta [ ] or ones: >>> theta = np.ones(21) >>> print theta [ ] or 21 values equally spaced between pi and +pi: >>> theta = np.linspace(-np.pi,np.pi,21) >>> print theta [ ] The arrays start with the label 0: theta[0] is the first value, and this one ends with theta[20], so there are 21 values in all. We can print: >>> print theta[0] We can get the sine of theta for each of the 21 values with the following: >>> y = np.sin(theta) >>> print y [ e e e e e e e e e e e e e e e e e e e e e-16] Notice that the output is in scienti9ic notation: e.g., = 3.09e- 01, and there is 10

11 some round- off error so that y[0] is a number close to zero, but not exactly zero. For 25 equally spaced values of theta between pi and pi, use Python to evaluate cosine(theta). IX. Plotting Python has a particularly easy to use graphing module called matplotlib.pylab. Lets plot our sine function. First import matplotlib.pylab (nickname plt), then add a few commands. Using y=sin(theta) and theta from the previous section: >>> import matplotlib.pylab as plt >>> plt.plot(theta,y) [<matplotlib.lines.line2d object at 0x10c2e3750>] >>> plt.xlabel('angle [rad]') <matplotlib.text.text object at 0x10c260050> >>> plt.ylabel('sin(theta)') <matplotlib.text.text object at 0x10c273f50> >>> plt.axis('tight') ( , , -1.0, 1.0) >>> plt.show() The output from the last command appears in a new window as a.png 9ile. As you can see from the 9igure on the next page, the tight command presets the minimum and maximum values of the axes based on minimum and maximum x and y values. 11

12 Let s make this look a little nicer, and we can also plot the cosine function on the same 9igure. I can do this interactively (which I just tried to do, and made mistakes, so needed to redo) or this time, I will make a python script named sincos.py. The contents are below: # sincos.py # standard starting commands from future import division import numpy as np import matplotlib.pylab as plt theta = np.linspace(- np.pi,np.pi,21) y = np.sin(theta) z = np.cos(theta) plt.plot(theta,y,linestyle='- ',color='blue',label='sine') plt.plot(theta,z,linestyle='- - ',color='magenta',label='cosine') plt.axis([- np.pi,np.pi,- 1.1,1.1]) plt.xlabel('$\\theta$ [rad]') plt.ylabel('$f(\\theta)$') plt.legend(frameon=false) plt.show() 12

13 Then in the terminal command line (not in Python), I type the following to get the 9igure: $ python sincos.py You can see that I can get Greek letters, labeled lines, etc. The Greek letters come from using a computer typesetting program called LaTeX (see the Appendix). Sometimes Python gets confused with the backslash \ used in LaTeX because to continue a line in Python, a backslash is used. The double backslash \\ seems to work with LaTeX. Your exercises for this part are 1) to plot (sin(2 theta))**2 for the angle range of pi to pi, and 2) to make up another function f(x) to plot between x=1-100 on a log-log plot. You will need to look on the internet to see the commands to do a log-log plot. In the plot window for 2), use matplotlib commands to write the function that you used. Please hand a copy of the commands you use, plus the plot for each of these two exercises. X. Final Remarks 13

14 As you could see with the previous exercise, there are extensive online resources for Python with lots of sample code. Something you want to do? Search for some key words and then do it! Appendix. LaTeX LaTeX is a typesetting system that is used in the preparation of manuscripts. The American Physical Society journals require electronic submission, and manuscripts submitted in a form that they can use directly are eligible for a reduction of page charges. LaTeX is one of the formats. We use LaTeX here to generate Greek letters. In normal LaTeX, to get a symbol, one uses the $ to indicate the beginning of a math symbol (which Greek letters are) and another $ to indicate the end. The symbol for the Greek letter beta is \beta. In LaTeX, $\beta$ results in β. As mentioned above, Python gets confused with backslash \, so by using $\\beta$, Python will not get confused. In normal LaTeX, you can t use \\ for this. To lookup symbols in LaTeX use For more information about LaTeX, check out project.org/ 14