Physics 2660: Fundamentals of Scientific Computing Lecture 9 News and Announcements
•  HW08 is assigned – due 6pm Sunday 3 April at 6pm
•  Reminder: Use piazza for asking questions and pay aBention to the discussions there
•  Office hours reminder:
–  My office hours are in Room 022-­‐‑C (our computer lab) from 3:30-­‐‑5pm on Tuesdays or by appointment
–  TA office hours, also in Room 022-­‐‑C
•  Mondays 5-­‐‑8pm
•  Tuesdays 5-­‐‑8pm
•  Lab09 will be this week Thursday as normal
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Review and Today’s Outline
•  Last time:
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Exam
Structures
Libraries Statistics
•  Today:
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Review of exam
More on strings
More on arrays and pointers
Debugging
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Exam Review
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Exam Results
•  Average:
•  Multiple choice went fairly well
16 14 N_students –  Mult choice: 39.33/46
–  WriBen: 40.63/54
Mul4ple Choice: Max 46 –  Performance on this portion of the exam was reasonable
8 6 2 0 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 Score [points] Wri=en Por4on: Max 54 N_students •  Short answer: •  Code examination:
10 4 –  Some repeats from in-­‐‑
lecture examples
–  Touched on material across the first 7 weeks
–  Lenient on the ten-­‐‑word-­‐‑
max criteria
12 9 8 7 6 5 4 3 2 1 0 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 Score [points] 5
Multiple Choice: Challenging Top Five Multiple Choice: Challenging Top Five Short Answer: Notes
•  Don’t ever forget the mathematical form of the Gaussian distribution!
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Example Code: Notes
This is actually a poorly-­‐‑
asked question, since the answer is simply “YES”.
while(..) does not strictly need { } brackets, since execution statement s just one line
also, the argument of the while (..) statement is a conditional – remember that conditionals all evaluate to some value (0 implies ‘false’, non-­‐‑zero implies ‘true’
type this code up yourself and see if it compiles!
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Example Code: Notes
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Algorithm: Notes
•  Simply wanted exactly a response like HW01
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Algorithm: Notes
•  Simply wanted exactly a response like HW01
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Extra Credit
Extra Credit: Max 5 35 30 N_students 25 20 15 10 5 0 0 1 2 3 4 5 Scores [points] 13
Extra Credit
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Monte Carlo Integration
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Multiple Measurements
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Multiple Measurements
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Multiple Measurements
Important vocabulary:
-­‐‑ mean
-­‐‑ variance -­‐‑ standard deviation or RMS
The standard deviation has an intimate relationship to the definition of the Gaussian (aka normal) distribution.
Here the standard deviation of the sample of measurements is usually the best estimate of the standard deviation of the parent distribution.
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Standard Deviation
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The Importance of the Gaussian Distribution
•  If ploBed, our measurements will look approximately like a Gaussian Distribution.
–  Is this magic?
–  No!
•  Recall the Central Limit Theorem, paraphrased
–  Any collection of random measurements of some variable will resemble a Gaussian
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The Importance of the Gaussian Distribution
•  If ploBed, our measurements will look approximately like a Gaussian Distribution.
–  Is this magic?
–  No!
•  Recall the Central Limit Theorem, paraphrased
–  Any collection of random measurements of some variable will resemble a Gaussian
•  Back to the whale:
–  Our random measurements here are the results of MC integration of the whale shape
–  An infinite number of such measurements would be a perfect Gaussian
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But…What about the True Value?
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But…What about the True Value?
The change to using N-­‐‑1 is called Bessel’s Correction. Read more here What happens below as N gets very large?
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Computing the Standard Deviation
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Uncertainty on the Mean
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Uncertainty on the Mean
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Confidence Levels
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Back to the Whale!
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Back to the Whale!
The thing that maBers is the TOTAL number of points that are thrown!
It does not maBer if they are in 100, 10 or even 1 experiment – it is the number of points.
What if we treated each single randomly-­‐‑thrown point as a single measurement?
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Back to the Whale!
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Back to the Whale!
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More on Character Strings
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Arrays of Characters
*
Single characters are nice but …many in succession can be more meaningful to us.
Array of characters are called a string.
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Arrays and Pointers
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String Utilities: strlen
What is going on?!
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Character Encoding
•  American Standard Code for Information Interchange (ASCII):
–  ~first new widely adopted code for laBer communication since Morse code
–  Ea. character represented by 8 bits
–  128 characters supported
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26x2 leBers of the english alphabet
10 single-­‐‑digit numerals
33 symbols, incl. “space”
33 control characters
–  Facilitates communication between terminal and computer
–  Other standards are used today (eg., UTF-­‐‑8, others) but the spirit is the same
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String Termination and Arrays
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String Utilities: strcmp
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More on Arrays and Pointers
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Recall…
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Incrementing a Pointer
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Array Names ARE Pointers Already!
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Array Names ARE Pointers Already -­‐‑-­‐‑ proof
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Pointer Arithmetic
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Storage of 2D Arrays
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Memory and 2D Arrays
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2D Arrays and Pointer Arithmetic: I
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2D Arrays and Pointer Arithmetic: II
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2D Arrays and Pointer Arithmetic: III
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Using 1D Notation for 2D Arrays
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All Arrays Are Linear in Memory
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Example: Structs and Functions
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Example: The Gravity Problem
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Example: The Gravity Problem
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Example: The Gravity Problem
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Example: The Gravity Problem
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Example: The Gravity Problem
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Example: The Gravity Problem
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Example: The Gravity Problem
You will also need to write functions for:
-­‐‑ calculating the distance between objects
-­‐‑ the difference between objects’ positions, using vectors
-­‐‑ calculating the total force on each object
-­‐‑ calculating the center of mass for the array of objects
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We’ll pick up from there next time.
Have a good rest of the week and see you at labs on Thursday!
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