Physics 2660: Fundamentals of Scientific Computing Lecture 7 News and Announcements
•  Welcome back from Spring Break!
•  HW06 has been assigned and will be due Saturday 19 March at 6pm
•  Office hours reminder:
–  My office hours are in Room 022-­‐‑C (our computer lab) from 3:30-­‐‑4:30 on Tuesdays or by appointment
–  TA office hours, also in Room 022-­‐‑C
•  Mondays 5-­‐‑8pm
•  Tuesdays 5-­‐‑8pm
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News and Announcements
•  Mid-­‐‑term exam has been rescheduled for Tuesday 22 March at 7pm
•  Inability to access the class wiki for the last 36 hours puts you at a disadvantage, especially coming off of Spring Break
•  Wiki access issue is at the level of UVa IT professionals who maintain the server on which our class wiki is hosted
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Review and Today’s Outline
•  Last time:
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Pointers to functions
Arrays in C
Passing arguments to main(….)
Making re-­‐‑usable code
•  Tonight!
–  Exam 1
•  Today:
–  Histograms
–  Making nice plots of data
–  Statistics: Our first entrypoint
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Data Visualization: Histograms
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What is a Histogram?
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Elements of a Histogram
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Elements of a Histogram
-­‐‑  range
-­‐‑  number of bins
-­‐‑  number of total entries
-­‐‑  number of entries in each bin -­‐‑  number outside range
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Why Are Histograms So Useful?
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Histograms in C as a Structure
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Operations With / On Histograms
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Histogram Operations: Function Prototypes
We will use these functions in lab this week!
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Histogram Operations: Function Examples
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Histogram Operations: Function Examples
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How to Make a Histogram
•  Biggest mistake made by young scientists in my experience:
–  They have taken some nice data, they maybe have some model that they are testing, done a good job
–  They want to convey the message from their experiment through some visualization of their data, a plot –  And then they make a plot like this:
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How to Make a Histogram
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How to Make a Histogram
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How to Make a Histogram
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How to Make a Histogram
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How to Make a Histogram
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How to Make a Histogram
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How to Make a Histogram
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How to Make a Histogram
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Statistics: Our First Entrypoint
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Making a Measurement: Truth
•  Let’s say I want to measure some physical observable.
•  Examples:
–  the acceleration due to gravity near the Earth’s surface
–  the speed of light
–  the mass of the Higgs boson
N
•  Each such measureable has a single value – the truth:
Make N repeated measurements of some quantity x. A perfect apparatus and data collection scheme would yield the true value every time!
x [units]
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Making A Measurement: Data
Why do we see a range of measured values?
•  imperfections in our instruments
•  limitations in our measurements
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GeWing to the Truth
How do we go from to arrive at
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Use Statistics:
The best we can achieve is the center distribution.
Its shape depends on the measurement’s uncertainty.
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The Story of Measurement
•  A measurement is not about the central value one finds
•  A measurement is truly about its uncertainty
–  The central value in fact is MEANINGLESS and OF NO USE without understanding and reporting the associated uncertainty
•  Two types of uncertainty:
–  Systematic uncertainty: Features of the measurement device or technique that shift (aka “bias”) the measured result away from the true value
•  Biases can often be corrected if discovered
•  Eg: Imagine you are measuring athletes running the 40-­‐‑yard dash. You discover however the length they run is in fact 42 yards long. This can in principle be corrected
–  Statistical or random uncertainty: Features of the measurement device or technique that shift the measured result by a different amount in each akempt (hence, random)
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Statistical or Random Uncertainty
“Uncertainty” and “error” are used interchangeably, often inappropriately.
I will try to use “uncertainty” universally – and you should as well.
If we try to measure the value many 2mes, and have only random uncertain2es in our measurement, we might see a distribu2on of results that follows this red curve. probability distribution
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The Gaussian Distribution µμ = “mean”, average value of the distributions
σ2 = “variance”, characterizes the width
σ = “standard deviation”
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We’ll pick up from here next time. See you then.
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