Post on 11-Nov-2021
transcript
Python Introduction &Linear Algebra Review
Kuan FangCS 231A
01/15/20211
Outline● Python Introduction
● Linear Algebra and NumPy
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Outline● Python Introduction
● Linear Algebra and NumPy
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Python
High-level, interpreted programming language
Python will be used in all the homeworks and recommended for the project.
We’ll cover some basics today
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Why Python?● Python is high-level.
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Why Python?● Python is accessible.
Interpreter/Terminal IDE Jupyter Notebook6
Why Python?● Python has many many awesome packages.
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How to Set up Python?1. Find a computer:
a. Your Linux/Mac/Windows/... machines.b. Use Stanford Corn machines:
https://web.stanford.edu/group/farmshare/cgi-bin/wiki/index.php/Main_Pagec. iMac computers in Stanford Libraries.
2. Follow this guide: https://wiki.python.org/moin/BeginnersGuide/Download3. Choose your favourite editor or IDE:
a. Sublimeb. Vimc. Spyderd. PyCharme. Eclipsef. Jupyter Notebook
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Variable
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Comment
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List
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List
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List
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List Indexing
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List Indexing
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Dictionary (Similar to Map in Java/C++)
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Dictionary
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Dictionary Indexing
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Control Flow
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Control Flow
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List Comprehension
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Function
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Outline● Python Introduction
● Linear Algebra and NumPy
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Why use Linear Algebra in Computer Vision?As you’ve seen in lecture, it’s useful to represent many quantities, e.g. 3D points on a scene, 2D points on an image.
Transformations of 3D points with 2D points can be represented as matrices.
Images are literally matrices filled with numbers (as you will see in HW0).
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Vector Review
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Vector Review
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Matrix Review
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Matrices and Vectors in Python (NumPy)
import numpy as npAn optimized, well-maintained scientific computing package for Python.
As time goes on, you’ll learn to appreciate NumPy more and more.
Years later I’m still learning new things about it!
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np.ndarray: Matrices and Vectors in Python
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np.ndarray: Matrices and Vectors in Python
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np.ndarray: Matrices and Vectors in Python
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Other Ways to Create Matrices and VectorsNumPy provides many convenience functions for creating matrices/vectors.
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Matrix Indexing
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Dot Product
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Cross Product
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Cross Product
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Matrix Multiplication
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Basic Operations - Dot Multiplication
Matrix multiplication in NumPy can be defined as the dot product between a matrix and a matrix/vector.
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Basic Operations - Element-wise Multiplication
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Orthonormal Basis= Orthogonal and Normalized Basis
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Transpose
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Basic Operations - Transpose
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Matrix Determinant
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Matrix Inverse
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Basic Operations - Determinant and Inverse
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Matrix Eigenvalues and Eigenvectors
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Matrix Eigenvalues and Eigenvectors
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Basic Operations - Eigenvalues, Eigenvectors
NOTE: Please read the NumPy docs on this function before using it, lots more information about multiplicity of eigenvalues and etc there.
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Singular Value Decomposition
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Singular Value Decomposition
Image source: Wikipedia50
Singular Value Decomposition
Image source: Wikipedia51
Singular Value Decomposition
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Singular Value Decomposition
Recall SVD is the factorization of a matrix into the product of 3 matrices, and is formulated like so:
M = UΣVT
Caution: The notation of SVD in NumPy is slightly different. Here V is actually VT in the common notation.53
More InformationPython Documentation: https://docs.python.org/2/index.html
NumPy Documentation: https://docs.scipy.org/doc/numpy-1.13.0/user/index.html
The Matrix Cookbook: https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
CS231N Python Tutorial: http://cs231n.github.io/python-numpy-tutorial/
Office hours!The rest of the internet!
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Thanks!Questions
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