Displaying your dataweb.stanford.edu/class/physics91SI/cgi-bin/wp-content/uploads/201… · April...

Transcript of Displaying your dataweb.stanford.edu/class/physics91SI/cgi-bin/wp-content/uploads/201… · April...

Displaying your dataPractical Computing for Scientists

Physics 91SI

M. Bellis

Department of PhysicsStanford University

April 19th, 2011

M. Bellis April ’11 Data display 1 / 21
Outline

1 Understanding your dataMatplotlibDisplaying your data

2 Summary

Introduction

• Research is usually about working with new data.• Or about working with old data in a new way.• It behooves you to understand your data.

Data

• Given some distribution of data, look at:• Mean (µ)• Standard deviation (σ)

• Make use of built-in functions in numpy.• Try this with the lists of data you were sent.

legba:~> ipython

In [1]: from numpy import *

In [2]: x = [0, 1, 2, 3, 4]

In [3]: mean(x)

Out[3]: 2.0

In [4]: std(x)

Out[4]: 1.4142135623730951

Data



legba:~> ipython


In [2]: x = [0, 1, 2, 3, 4]

In [3]: mean(x)

Out[3]: 2.0

In [4]: std(x)

Out[4]: 1.4142135623730951

Data



legba:~> ipython


In [2]: x = [0, 1, 2, 3, 4]

In [3]: mean(x)

Out[3]: 2.0

In [4]: std(x)

Out[4]: 1.4142135623730951

Data



legba:~> ipython


In [2]: x = [0, 1, 2, 3, 4]

In [3]: mean(x)

Out[3]: 2.0

In [4]: std(x)

Out[4]: 1.4142135623730951

Data



legba:~> ipython


In [2]: x = [0, 1, 2, 3, 4]

In [3]: mean(x)

Out[3]: 2.0

In [4]: std(x)

Out[4]: 1.4142135623730951

Data



legba:~> ipython


In [2]: x = [0, 1, 2, 3, 4]

In [3]: mean(x)

Out[3]: 2.0

In [4]: std(x)

Out[4]: 1.4142135623730951

Matplotlib

Figure: http://matplotlib.sourceforge.net/

• Plotting library for Python.• Original author: John Hunter• pyplot

• Included in pylab, along with numpy.• pylab aims to be a replacement for MATLAB.• So what does that give us?


http://matplotlib.sourceforge.net/
Coding

Import pylab and use the array object.

legba:~> ipython

In [1]: from pylab import *

In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []

But we don’t see the plot yet.

In [5]: show()

Coding


legba:~> ipython


In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []


In [5]: show()

Coding


legba:~> ipython


In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []


In [5]: show()

Coding


legba:~> ipython


In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []


In [5]: show()

Coding


legba:~> ipython


In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []


In [5]: show()

Coding


legba:~> ipython


In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []


In [5]: show()

Coding


legba:~> ipython


In [2]: x = array([0,1,2,3,4])

In [3]: y = array([0,1,2,3,4])

In [4]: plot(x,y)

Out[4]: []


In [5]: show()

plot

http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.plot

Default is a blue line connecting points, butthere are other plotting options.

Close plot window, and try some of these:

In [6]: plot(x,y,’r--’)

In [6]: plot(x,y,’g-’)

In [6]: plot(x,y,’ks-’,linewidth=4)

In [6]: plot(x,y,’co’)

In [6]: axes().set xlim(-10,10) // Set the range on

the x-axis

Note that you do not have to show() aftereach one.

Note also that unless you close the window,these are overlaid on one another.


plot


Default is a blue line connecting points, butthere are other plotting options.

Close plot window, and try some of these:

In [6]: plot(x,y,’r--’)

In [6]: plot(x,y,’g-’)

In [6]: plot(x,y,’ks-’,linewidth=4)

In [6]: plot(x,y,’co’)

In [6]: axes().set xlim(-10,10) // Set the range on

the x-axis

Note that you do not have to show() aftereach one.

Note also that unless you close the window,these are overlaid on one another.


Your plots

The figure exists in global memory so it is easy to save it as a file.

In [9]: savefig(’myplot.png’)

Use https://afs.stanford.edu to download the image file to your desktop.Upload this image to the Google Doc for this lecture.

https://docs.google.com/present/edit?id=0AaEmDaJ8A2rAZGhwc3pudzhfOTM1Y21wcDk5bjk&hl=en

Let’s take a look at your plots!


https://afs.stanford.eduhttps://docs.google.com/present/edit?id=0AaEmDaJ8A2rAZGhwc3pudzhfOTM1Y21wcDk5bjk&hl=en
Your plots

The figure exists in global memory so it is easy to save it as a file.

In [9]: savefig(’myplot.png’)

Use https://afs.stanford.edu to download the image file to your desktop.Upload this image to the Google Doc for this lecture.

https://docs.google.com/present/edit?id=0AaEmDaJ8A2rAZGhwc3pudzhfOTM1Y21wcDk5bjk&hl=en

Let’s take a look at your plots!


https://afs.stanford.eduhttps://docs.google.com/present/edit?id=0AaEmDaJ8A2rAZGhwc3pudzhfOTM1Y21wcDk5bjk&hl=en
Your data

• If you are lucky, at some point in your life you will get to work on a problem forwhich the answer is not known.

• There’s a reason why people do Sudoku/crossword puzzles/word jumbles: the joy ofsolving a puzzle.

• Your research experience will hopefully help you learn how collect data and gleaninformation from it.

• You also learn how to present that data to others.• Just as importantly you learn how to present that data to to yourself so that you

can make accurate and precise statements about what you are measuring.

• Never forget that the collection of experimental data is a means to an end...notsimply and end in itself.

Your data







Your data







Tufte

• Parts of this lecture are motivated by the following.• Tufte, E., The Visual Display of Quantitative Information

• Can’t recommend this enough.• Examples of the good, the bad and the ugly in the world of charts, plots

and graphs.• Can find Prof. Cabrera’s old monopole data as an example of a well

constructed plot (p.39).

Tufte

• Parts of this lecture are motivated by the following.• Tufte, E., The Visual Display of Quantitative Information

• Can’t recommend this enough.• Examples of the good, the bad and the ugly in the world of charts, plots

and graphs.• Can find Prof. Cabrera’s old monopole data as an example of a well

constructed plot (p.39).

Tufte

Tufte lists his Principles of Graphical Excellence, (p.51)

• Graphical excellence is the well-designed presentation of interesting data - a matter ofsubstance, of statistics, and of design.

• Graphical excellence consists of complex ideas communciated with clarity, precisiion,and efficiency.

• Graphical excellence is nearly always multivariate.• Graphical excellence requires telling the truth about the data.• Graphical excellence is that which gives to the viewer the greatest nunber

of ideas in the shortest time with the least ink in the smallest space

Tufte






Tufte






Tufte






Tufte






Tufte






Binning

• Even the simplest assumptions about how to display your data can affect theconclusions you or others draw.

• Histogramming your data.• Freedom to choose bin size.• Can affect fits to data.

• The following is the same 100 random events from a Gaussian distribution.• µ = 0.0, σ = 1.0

• Plotted with 3 different bin sizes.

Binning





Binning





Binning

10000 bins

Abitrary measurement-4 -2 0 2 4

Num

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100 bins 10 bins

Binning

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Binning

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Constant 0.104± 1.026 Mean 10.68848± -0.08034 Sigma 8.078± 9.954

100 bins


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• Using same fitting tool, wound up with 3 very different widths.• Couldn’t even get a sense of the parent distribution from first plot.• In general the binning should be motivated by the resolution of your measurements.• If your detector/ruler/samples have resolution x, you don’t want to plot your data

with bins of x10

width.

• Don’t not think about your data!• Even if it seems to be super trivial!• Your data should tell a clear story.

Binning

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10 bins


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with bins of x10

width.


Binning

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with bins of x10

width.


Napolean’s march

Figure: Charles Joseph Minard’s display of Napolean’s excursion into Russia.

Train schedule

Figure: 1880’s French train schedule.

John Snow

Figure: John Snow’s map of cholera outbreak (1854).

Cosmic Microwave Background

Figure: Comparison of COBE data with blackbody prediction.

Ratio

Figure: Ratio of cross-sections for e+e− → hadrons to e+e− → µ+µ−, as afunction of center-of-mass energy

.

Household debt

Figure: David Bein. Ration of household debt vs. US GDP.http://www.npr.org/blogs/money/2009/02/household_debt_vs_gdp.html


http://www.npr.org/blogs/money/2009/02/household_debt_vs_gdp.html
Summary

• Collecting your data is not an end in inself.• Your data tell a story. Visualizations help us see that story.• Lots of good tools in Python and Matplotlib!


Understanding your dataMatplotlibDisplaying your data

Summary

Displaying your dataweb.stanford.edu/class/physics91SI/cgi-bin/wp-content/uploads/201… · April...

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Transcript of Displaying your dataweb.stanford.edu/class/physics91SI/cgi-bin/wp-content/uploads/201… · April...