Transcript What is Python?

Introduction to Data Analysis in Python
for Physics Laboratories
Dr. Peter T. Gallagher & Dr. Matthias Möbius
School of Physics
Trinity College Dublin
Trinity College Dublin
School of Physics
What is Python?
• Python is an interactive language that allows you to write
programs to:
– Plot data
– Analyse data
– Model data
• It is straight-forward to learn, relatively fast, and widely
used in physics, astronomy, mathematics, computer
science, etc. It’s also free!
Scientific PYthon Development EnviRonment
(Spyder)
• Spyder is an interactive development environment (IDE) that is freely
available for Mac, PC and Linux.
• General information on Spyder is available at:
http://code.google.com/p/spyderlib/
• For installation on your home computer or laptop, you can consult
http://code.google.com/p/spyderlib/wiki/Installation
(available on PC, Mac and Linux)
Starting Spyder
• Log into Windows 7. If you are in Linux restart and boot into
Windows at the boot menu.
• Click on Spyder icon on your desktop:
(Note: A black screen may appear for 30sec. Just wait.)
• This will start the Spyder IDE, a screenshot of which is
shown on the next slide.
Spyder IDE
Help &
Variable
Explorer
Editor
Console
Set your global directory
•
Go to “Tools” and click on “Preferences”. Set global directory to your network
folder (usually S:\). You may want to create a new folder for your Python scripts.
e.g. S:\Python and change the global directory accordingly.
•
Also, select “the global working directory” for “open file” and “new file”. Do not
store the files on the local disk (C:\) !
Variables in calculations
Enter the following in the Console to see what happens:
>>> print “hello world”
>>> m = 1
>>> c = 2.9e8
Now use the variable explorer to find
about the variables m and c.
Now do a some arithmetic:
>>> energy = m*c**2
>>> print energy
out more
Python Modules
•
We often use modules to extend the core functionality of Python. Of particular interest:
– NumPy: Python package for scientific computing. Includes mathematical functions
such as square root, trigonometric functions etc. Also provides array data
structure for multidimensional arrays.
– Matplotlib: This package is used to make 2D and 3D plots.
– SciPy: This contains many widely used standard numerical routines. E.g. curve
fitting, numerical integration etc.
•
To make use of this functionality, modules have to be imported into your script.
>>> import numpy as np
>>> import scipy as sp
>>> import matplotlib.pyplot as plt
•
Note: “as np”, “as sp”, “as plt” allows us to use a shorthand for invoking function from
the modules. Also, these modules are loaded by default in the interactive console
window - type scientific for more information.
Entering scientific data
•
Define array of integer values:
>>> x = array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ])
•
The arange() function makes this easier:
>>> x = arange( 1, 11, 1 )
•
Now define array of measured floating point values:
>>> y = array([ 23., 49., 68., 79., 85., 99., 105., 130., 140., 160. ])
•
Check that entered arrays are the same length using len()
>>> len( x ) == len( y )
Plotting scientific data
•
Now plot y versus x
>>> plt.plot( x, y )
•
You should never connect the data points with lines! Use a symbols instead:
>>> plt.plot( x, y, ’o’ )
or
>>> plt.plot( x, y, ’r+’ )
•
Now add a title and label the axis
>>>
>>>
>>>
>>>
plt.plot( x, y, ‘ro’ )
xlabel( ‘Time [sec]’ )
ylabel( ‘Velocity [km/sec]’ )
title(‘Velocity versus time’)
Python plotting interface
Plotting scientific data
• An easy way of plotting data is using
>>> plt.scatter( x, y )
The following functions are useful for logarithmic plots
>>> plt.loglog( x, y )
>>> plt.semilogx( x, y )
>>> plt.semilogy( x, y )
Plotting error bars
• Now let’s add uncertainties to the y values:
>>> y_sig = array( [ 15., 17., 14., 15., 18., 12., 16., 13., 20., 19. ])
• Check that there are 10 elements in the array
>>> len( y_sig )
• Now plot the data with the uncertainties in the y-axis
>>>
>>>
>>>
>>>
plt.errorbar( x, y, y_sig, fmt = ‘o’ )
xlabel( ‘Time [sec]’ )
ylabel( ‘Velocity [km/sec]’ )
title(‘Velocity versus displacement’)
Plotting error bars
Fitting the data
• Let’s see if we can fit the data with a straight line.
• Assume a model of the form y = m * x + c
• This is a 1st order polynomial, so use:
>>>> p = polyfit( x, y , 1)
• Returns best-fit values for slope p[0] and intercept p[1]
using a least-squares fit.
Fitting the data
• Print the best-fit values:
>>> print p
or
>>> p
• Can also access each individual best-fit values:
>>> slope= p[ 0 ]
>>> intercept = p[ 1 ]
or
>>> slope, intercept = p
Plotting data, error bars and fit
• Therefore can define best-fit
>>> y_model = slope * x + intercept
• Finally, plot the data together with the best fit:
>>>
>>>
>>>
>>>
>>>
>>>
errorbar( x, y, y_sig, fmt = ‘bo’, label = ‘Data’)
xlabel( ‘Time [sec]’ )
ylabel( ‘Velocity [km/sec]’ )
title(‘Velocity versus displacement’)
plot( x, y_model, ‘r’, label = ‘Fit’ )
legend( loc = 'upper left’ )
Plotting data, error bars and fit
Calculating the Slope and Intercept
• Can also use least squares method to explicitly calculate the slope (m) and
intercept (c) for a linear model (y = m * x + c)
>>>
>>>
>>>
>>>
>>>
n = len( x )
s_x = sum( x )
s_y = sum( y )
s_xx = sum( x**2 )
s_xy = sum( x*y )
>>> denom = n * s_xx - s_x**2
>>> c = ( s_xx * s_y - s_x * s_xy ) / denom
>>> m = ( n * s_xy - s_x * s_y ) / denom
• Derivation at http://mathworld.wolfram.com/LeastSquaresFitting.html
• Slope (m) and intercept (c) should be the same as using p = polyfit(x,y,1)
Calculating Uncertainties in Slope and Intercept
• Calculate uncertainties in intercept and slope
>>> sigma = sqrt(sum( ( y - ( c + m*x ) )**2 ) / ( n – 2 ) )
>>> sigma_c = sqrt( sigma**2 * s_xx / denom )
>>> sigma_m = sqrt( sigma**2 * n / denom )
• Print best-fit values and uncertainties
>>> print ‘Slope (m): ‘, m, '+-', sigma_m, ’Units'
>>> print ‘Intercept (c): ', c, '+-', sigma_c, ’Units'
Putting it all together in a script
Putting it all together in a script
• Here’s what the script on the previous slide will produce:
• Note the numbers need to be rounded to appropriate number of significant figures.
• The script will also produce the plot below.
Plotting Greek symbols
• You can plot Greek symbols by preceding a string with an r for raw string:
>>> plt.errorbar( x, y, y_sig, fmt = ‘o’ )
>>> xlabel( r‘$\theta$ [sec]’ )
• More at http://matplotlib.org/users/mathtext.html
Subscripts and superscripts
• You can plot superscripts and and subscripts using the following:
>>> plt.errorbar( x, y, y_sig, fmt = ‘o’ )
>>> xlabel( ‘$t^{2}$ [sec]’ )
>>> ylabel( ‘$a_{n-1}$’ )
• Below are given some other examples:
Additional Reading
How to Create a Graph in Python:http://www.thetechrepo.com/main-articles/465how-to-create-a-graph-in-python
A First Program: Straight Line Fitting:https://alexandria.astro.cf.ac.uk/Joomlapython/index.php/week4-straight-line-fitting
Good general introduction to Python for data analysis:http://www.astro.unibonn.de/~rschaaf/Python2008/
Codecademy’s excellent introduction to Python
basics:http://www.codecademy.com/tracks/python
Khan Academy’s excellent introduction to
Python:http://www.khanacademy.org/science/computer-science