PHY224 Practical Physics I. Lecture 2

Transcription

1 PHY224 Practical Physics I Python Review Lecture 2 Sept , 2013 Summary Functions and Modules Graphs (plotting with Pylab) Scipy packages References M H. Goldwasser, D. Letscher: Object oriented programming in Python, Pearson 2008 G. Daniell and J. Flynn: School of Physics and Astronomy, University of Southampton (Computing Module for PHYS2022) used by permission Eric Jones: Introduction to Scientific Computing with Python: Enthought SciPy 2007 Conference, CalTech. Scipy:

2 Control structures: for and while loops for iterating_var in sequence: body #statement(s) while condition: body #statements executed if condition is true

3 Control structures: Conditionals (if f statements) if condition: body #statements executed only if condition is true If th diti l t t T th b d i tdif th If the condition evaluates to True, the body is executed; if the condition evaluates to False, the body is bypassed. The condition can be an arbitrary expression that evaluates to a Boolean.

4 Functions Python contains a large library of standard functions which can be used to make programs more concise and modular. In addition to this, you may build your own functions as useful tools for particular applications. Functions must be defined dfi dby using the following syntax: def function(arguments): body #expressions and conditions that define the function

5 Functions Let s define a function that does...nothing! Example 2_2 def f(): pass the first line is the function declaration or function header all the following indented dlines are the function body the pass statement does nothing The pass statement is present here because all functions and all code blocks must have at least one statement

6 Functions: defining your own. Independent work We shall write the code to calculate a sequence named after Leonardo of Pisa, also known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics. In the book/movie Da Vinci code, a certain bank vault is open by entering which represents 1, 1, 2, 3, 5, 8, 13, 21 (the first 8 terms of the Fibonacci sequence). The first two numbers in the Fibonacci series are 1 and 1. To obtain each number of the series, you simply add the two numbers that came before it. In other words, each number of the series is the sum of the two numbers preceding it.

7 Define and calculate the Fibonacci function 1, 1, 2, 3, 5, 8, 13, 21 (the first 8 terms of the Fibonacci sequence) Each number of the series is the sum of the two numbers preceding it. How to build the program: Figure out how the sequence works Define the function In the function body, initialize the calculation (you will have two terms) Write a loop of your choice

8 Functions: defining your own Example2_3: the Fibonacci function def fib(n): a, b = 1,1 while b < n: print b, a, b = b, a + b Run fib(100) and fib(1000) in the Python Shell. Save your work as fibonacci.py (we shall use itlater)

9 Modules Let s say you have defined a very useful function which you d like to use in the future, without copying the entire code in each program. In Python, a file containing function definitions and/or executable statements to be loaded (imported) into an interactive session is called a module. The file name is the module name with the suffix.py added. d

10 Modules: making your own Your own modules: We shall use the Fibonacci function defined earlier to illustrate how to make a module. Your function was saved as fibonacci.py on your memory stick. If this is to be used as a module, then Python has to be able to find it. Python has a list of folders, called the module search path where it looks for files to import. If you keep all your Python code in the same directory, you can add this directory to the search path.

11 Modules: making your own Example 2_5: How to make a module. Use the Python shell import fibonacci dir() The built in dir() function without any argument returns a list of string objects, representing the identifiers of the current namespace. By using this form of import statement, we created a module object. Check it out: fibonacci dir(fibonacci) fibonacci.fib #fib(n) was the function we defined fibonacci.fib(100) #runs the file

12 Modules: making your own How to use the module search path Here is how to do this: Work in the Python shell import sys print sys.path If the path does not contain the folder you want, do the following: sys.path.append(... ) #This could be the removable drive address

13 Modules: standard modules Python comes with a vast library of standard modules, which give access to operations that are not part of the core language. Here is how to access a standard module, using math as an example: Example 2_4: Work in the Python shell Import the module: import math # Import statement print math.sin(0.5) # Use objects from the module Use abbreviations: import math as m print m.sin(0.5) print m.pi Import all objects from a module: from math import * print cos(pi/3), log(54.3), sqrt(6)

14 Some problematic cases Example 2_6. Return to VIDLE from math import sin x = 0.00 while x<3.0: print x, sin(x)/x x = x / Run the program. Note that although sin(x)/x has a well defined limit as x 0, the computer does not know it and has to be instructed how to check for this possibility.

15 Some problematic cases You would need to define a function to do the checking when x is likely to be zero. Try this: from math import sin def sinlimit(x): if x==0: return 1 else: return sin(x)/x x=0.0 while x<3.0: print x, sinlimit(x) x=x+0.25 Run the program. Explain how the code works, line by line and overall.

16 Plotting with Pylab Let us begin by plotting a damped cosine oscillation. Do this : import pylab from numpy import* x=arange(0,8*pi,0.05*pi) #generating the x-values pylab.plot(x,cos(x)) #plotting cos(x) vs. x pylab.plot(x,cos(x)*exp(-x/20.0)) #plotting damped cos(x) vs.x pylab.xlabel('x') #labeling the x-axis pylab.title('oscillation and damped oscillation') pylab.savefig('pylabplot.png') #plot is saved in the cwd, see below pylab.show() ### finding the location where the plot is saved ### import os #importing the operating system currdir = os.getcwd() #getting the current working directory (cwd) print 'Plot saved in:', currdir

17 Independent work Plot sin(x) and cos(x/2) for 0 < x < 5π. Savefigureyour cwd.

18 How to read lab data in a Python array from numpy import * data = loadtxt("myfile.txt") # myfile.txt contains 4 columns of numbers t,z = data[:,0], data[:,3] # data is 2D numpy array t,x,y,z = loadtxt("myfile.txt", unpack=true) # to unpack all columns t,z = loadtxt("myfile.txt", usecols = (0,3), unpack=true) # to select just a few columns data = loadtxt("myfile.txt", skiprows = 7) # to skip 7 rows from top of file data = loadtxt("myfile.txt", delimiter=';') # use ';' as column separator instead of whitespace data = loadtxt("myfile.txt", dtype = int) # file contains integers instead of floats You will find a text file (mydata.txt) in the 2nd Yr Lab files folder. - Load the data in an array - Unpack all columns. - Clean the top of the file (header, zeros) - Load data in the (x, t) format. - Plot x vs. t

19 Scipy packages Optimization (scipy.optimize): p many applications We shall use the least square program from scipy to build the data fitting program: from scipy.optimize import leastsq Numerical integration (scipy.integrate) integrate) Special functions (scipy.special): over 200 functions (Airy, Bessel, Gamma,...etc.) Statistics (scipy.stats): over 80 continuous distributions, 10 standard discrete distributions, basic statistical calculations (mean, std, var, etc.)...and many others

20 What s next? Computational exercises begin on Sept. 23 Background knowledge for exercises 1 3: Simple pendulum, equation of motion, solution (position(angle) vs. time), energy vs. time, phase plot. Pendulum at large angle: same as above Pendulum at large angle with damping: same as above P h l di i l i l i i Python: loops, conditionals, arrays, numerical integrators, scipy, pylab.