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ASEN 5070Statistical Orbit determination I
Fall 2012
Professor George H. BornProfessor Jeffrey S. Parker
Lecture 4: Coding and Linear Algebra Review
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Homework 1 due today
Homework 2 due in 7 days
I will most likely not be available during my Monday office hours. Definitely use the TAs – I hear they’re bored.
Announcements
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Quiz Results
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Quiz Results
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Quiz Results
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Quiz Results
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Quiz Results
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Quiz Results
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Quiz Results
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Quiz Results
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Coding hints and tricks◦ MATLAB: ways to speed up your code◦ Python: intro
Review of Linear Algebra
Review of Statistics Tuesday
Today’s Lecture
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ode45’s default tolerance: 1e-6 What should you set it to be?
First: 1 slide on integration tolerances
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Matlab Overview
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Generic Tips: Pre-allocate
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Learn to use help function/online resources
% Comment your code!!!
Name functions and outputs descriptively
Generic Tips: Misc.
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Symbolic Toolbox
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Use to convert STM from matrix to a vector so it can be numerically integrated
reshape() Command
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Python is a free, open source programming language that runs on nearly everything.
Resources:◦ http://www.python.org/◦ Python 3 Tutorial: http://docs.python.org/py3k/tutorial /◦ IDEs:
Xcode Emacs / xemacs / vi
Python
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Python is high-level◦ No memory management requirements by the
user. Hurrah!
Python is object oriented.◦ Matlab is a little, but Python is a lot.
Python can do anything that Matlab can do, but differently.◦ Some things are easier, some harder.
Python
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Working on some example tutorials that parallel the Matlab tutorials.
Python
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Questions on Coding?
Quick Break
Next topics:◦ Review of Linear Algebra◦ Review of Statistics
Questions
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Notation
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Matrix Multiplication
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Fundamentals
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Fundamentals
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Matrix Rank
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Matrix Rank
Example: What is the rank of the following matrices?
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Matrix Rank
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Quadratic Forms
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Quadratic Forms
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A triangular matrix has non-zero elements on the diagonal and above (upper triangular) or below (lower triangular).
A unitary triangular matrix has diagonal elements equal to 1.
Triangle Matrices
Example of a upper triangular matrix
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The square root of an matrix, P, is defined as P=AA, where is the square root of P.
A symmetric positive semidefinite matrix has a unique symmetric positive semidefinite square root.
If , where P is symmetric positive semidefinite and S is upper triangular, then an orthogonal matrix Q exists so that
Matrix Square Root
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Determinants
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Determinants
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Matrix Trace
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Eigenvalues and Eigenvectors
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Eigenvalues and Eigenvectors
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Example:
Eigenvalues and Eigenvectors
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Derivatives
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Derivatives
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Maxima and Minima
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Maxima and Minima
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Maxima and Minima
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Maxima and Minima
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Maxima and Minima
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Example:
Maxima and Minima
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Example:
Maxima and Minima
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Matrix Inversion Theorems
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Matrix Inversion Theorems
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Homework 1 due today
Homework 2 due in 7 days
Next quiz active Monday at 1pm.
Final Thoughts
