Project Title

QR Decomposition Example with Classical Gram-Schmidt Process and Modified Gram-Schmidt Process

Project Type

Side Project

Related Article

1. https://medium.com/@kwokanthony/important-decomposition-in-linear-algebra-detailed-explanation-on-qr-decomposition-by-classical-3f8f5425915f
2. https://medium.com/@kwokanthony/detailed-explanation-with-example-on-qr-decomposition-by-householder-transformation-5e964d7f7656

Instruction

• Matrix.py contains the Matrix Class and functions of QR Decomposition.

• All functions below in Matrix.py return Q & R matrix in a tuple.

  • QR_GS() for QR Decomposition by Classical Gram-Schmidt Process
  • QR_MGS() for QR Decomposition by Modified Gram-Schmidt Process
  • QR_Householder() for QR Decomposition by Householder Transformation
  • QR_Givens_Rotation() for QR Decomposition by Givens Rotation

• Examples can be run in main.py:

  • example.cgs() --> Example of QR decomposition by Classical Gram-Schmidt Process

  • example.mgs() --> Example of QR decomposition by Modified Gram-Schmidt Process

  • example.householder() --> Example of QR decomposition by Householder Transformation

  • example.givens_rotation() --> Example of QR decomposition by Givens Rotation

  • example.least_squares_problem() --> Example of Solving Least Square Problem by QR decomposition

• Run main.py to output the QR Decomposition examples.

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