Tutorial 2 PHY409 Anadi Canepa Office, TRIUMF MOB 92 B ( )

Transcription

1 Tutorial 2 PHY409 Anadi Canepa canepa@triumf.ca Office, TRIUMF MOB 92 B ( ) Alan Manning mannin2@phas.ubc.ca Mohammad Samani samani@physics.ubc.ca

2 During the 1 st tutorial We learnt What Python is How to import packages How to produce a 1D plots, scauer plots, histograms We used matplotlib numpy 13/9/2013 Python TutoWal 2

3 HW #1 (due today) 1. Install python 2. Install matplotlib, numpy, scipy (the order mauers!) 3. (Install Spyder - opwonal) 4. Write a script to plot sin(x): 1. Range [0:2π] 2. Add labels to the axis, Wtle, legend 5. Save the plot in pdf format 13/9/2013 Python TutoWal 3

4 The goal of today is to learn to fit 1. Example #1: Polynomial order 0 1. Read in text file 2. Store data 3. Fit them and compute uncertainwes on the fit parameter 2. Example #2: ExponenFal (hands- on) 1. Modify the model 2. Compute uncertainwes on the fit parameters 3. Example #3: Gaussian (hands- on) 1. Handling histograms 13/9/2013 Python TutoWal 4

5 Example #1 1. Read in a text file containing data points 2. Handle the data 3. Fit the data Module courtesy of Prof. C. Gay 13/9/2013 Python TutoWal 5

6 Input file and script hlp://trshare.triumf.ca/~canepa/python/tutorial2/ input_p0.txt fiuest_p0.py 13/9/2013 Python TutoWal 6

7 Important Concepts 1. Objects 2. Module 3. Package 13/9/2013 Python TutoWal 7

8 (1) Objects Everything in Python is an object Strings, funcwons, classes The name is used to access the object The dot operator is used to access the object auributes str. index ( e ) Variable name Delimiter AUribute Argument 13/9/2013 Python TutoWal 8

9 (2) Modules A module is a file containing Python funcwons definiwons and executable statements The file name is the module name with the suffix.py appended Modules can be imported in scripts and in modules Whenever you run a simple Python script, the interpreter treats it as a module called main, which gets its own namespace 13/9/2013 Python TutoWal 9

10 (3) Packages Packages are a way of structuring Python s module namespace For example, the module name A.B designates a sub- module named B in a package named A 13/9/2013 Python TutoWal 10

11 Modules: import statement import pylab as plb import scypy as sy import numpy as np import matplotlib.pyplot as plt from math import sqrt from scipy.opwmize import leastsq Import module (pylab) with a given alias Access the funcwons using this alias Import sub- module (pyplot) from package (matplotlib) Import name (sqrt) from module (math) 13/9/2013 Python TutoWal 11

12 How to read in a text file data = np.loadtxt( mydata.txt, skiprows=2) FuncWon loadtxt of numpy to read in the text file Returns an ndarray (mulwdimensional container of items of the same type) 13/9/

13 Working with the N- dimensional array ndarray can be indexed: print data[1,2] x y σ X ndarray can be sliced: x = data[:,0] y = data[:,1] sigma = data[,:2] x y σ X X X X 13/9/2013 Python TutoWal 13

14 Least- square fi]ng MinimizaWon of: Where f(x) is the model we want to use to fit the data 13/9/2013 Python TutoWal 14

15 Define the model funcfon def func(x, a): return a*pow(x,0) a * x 0 x 1 x 2 x n keyword def followed by the funcwon name and parentheses input parameters or arguments should be placed within these parentheses code block within every funcwon starts with a colon (:) and is indented statement return [expression] exits a funcwon, opwonally passing back an expression to the caller 13/9/2013 Python TutoWal 15

16 Fit the data (I) Define the residual funcwon def residual (coeff, x, y, sigma): return (y- func(x, coeff[0]))/sigma Call the leastsq funcwon imported from scipy.opwmize p = leastsq (residuals, coeff, args=(x, y, sigma)) 13/9/2013 Python TutoWal 16

17 Fit the data (II) Leastsq returns the value of the fiued parameter print "Fit value: ", p[0] It can also return the uncertainty if we request the full output p, cov, infodict, mesg, ier = leastsq (residuals, coeff, args=(x, y, sigma), full_output=true) print "Fit value: ", p[0] s_sq = (infodict['fvec']**2).sum()/(len(y)- 1) cov_scaled = cov*s_sq print Uncertainty", sqrt(cov_scaled[0]) 13/9/2013 Python TutoWal 17

18 Plo]ng the results Some formarng. (see script) Plot the data with error bars and overlay the fit result plt.errorbar(x, y, sigma, linestyle='', marker='o ) plt.plot(x,func(x, p[0])) plt.show() 13/9/2013 Python TutoWal 18

19 Example #1: Result 13/9/2013 Python TutoWal 19

20 Example #2 Download the input file input_exp.txt from: hlp://trshare.triumf.ca/~canepa/python/tutorial2/ Fit the data to the exponenwal: 13/9/2013 Python TutoWal 20

21 Example #2 (I) Replace the polynomial fit with the exponenwal fit Warning: number of free parameter changes from 1 to 2 coeff = [0,0] def func(x, a, b): return a * np.exp(- b * x) def residuals (coeff, x, y, sigma): return (y- func(x, coeff[0],coeff[1]))/sigma 13/9/2013 Python TutoWal 21

22 Example #2 (II) Replace the polynomial fit with a n exponenwal fit Warning: number of free parameter changes from 1 to 2 p = leastsq (residuals, coeff, args=(x,y,sigma), full_output=true) print "Fit values for a, b", p[0][0], p[0][1] 13/9/2013 Python TutoWal 22

23 Example #3 Generate a sample of 1000 events distributed according to a Gaussian distribuwon (mean =0, variance = 1) Fill a histogram with the data Fit the histogram to a Gaussian (take into account the uncertainty on the bin content) Print the mean and the variance 13/9/2013 Python TutoWal 23

24 Example #3 (I) Extract the bin content using the return values of matplotlib.pyplot hist tuple : (bincontents, binedges, patches) 13/9/2013 Python TutoWal 24

25 Example #3 (II) x = np.random.randn(10000) bincontents, binedges, patches = plt.hist(x,bins=60,range=(- 3,3)) binwidth = binedges[1]- binedges[0] nbins = len(bincontents) bincenters = range(nbins) binerrors = range(nbins) for i in range(len(bincontents)): bincenters[i] = (binedges[i+1]+binedges[i])/2 binerrors[i] = sqrt(bincontents[i]) 13/9/2013 Python TutoWal 25

26 In today s tutorial We learnt 1. How to read in a text file 2. Store its content in arrays 3. Define and call funcwons 4. Fit data 5. Print fit results 6. Plot fit results Slides, scripts and input files can be found at: hlp://trshare.triumf.ca/~canepa/python/tutorial2/ 13/9/2013 Python TutoWal 26

27 More material 13/9/2013 Python TutoWal 27

28 Name A name in Python is roughly analogous to a variable in just about any other language, but with a few extras. Because of Python s dynamic nature, you can apply a name to just about anything. a = 5.0 a = a a = [1,2,3] def fun(): print Hello a = fun 13/9/2013 Python TutoWal 28

29 Name Space A namespace is a space that holds names. Each module gets it s own global namespace Once you import that module into your script, you can access the names by prefixing them with the module name Each namespace is also completely isolated 13/9/2013 Python TutoWal 29

30 Math package FuncWons from the "math" package do not operate on numpy arrays (which you should always be using instead of lists) Use funcwons from numpy to do this. Example: import numpy import math x = numpy.asarray([0,2,3,4,5]) y = math.sqrt(x) #Error! y = numpy.sqrt(x) #No error 13/9/2013 Python TutoWal 30