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NumPy Beginner's Guide

You're reading from   NumPy Beginner's Guide An action packed guide using real world examples of the easy to use, high performance, free open source NumPy mathematical library.

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Product type Paperback
Published in Apr 2013
Publisher Packt
ISBN-13 9781782166085
Length 310 pages
Edition 2nd Edition
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Author (1):
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Ivan Idris Ivan Idris
Author Profile Icon Ivan Idris
Ivan Idris
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Table of Contents (19) Chapters Close

Numpy Beginner's Guide Second Edition
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
1. NumPy Quick Start FREE CHAPTER 2. Beginning with NumPy Fundamentals 3. Get in Terms with Commonly Used Functions 4. Convenience Functions for Your Convenience 5. Working with Matrices and ufuncs 6. Move Further with NumPy Modules 7. Peeking into Special Routines 8. Assure Quality with Testing 9. Plotting with Matplotlib 10. When NumPy is Not Enough – SciPy and Beyond 11. Playing with Pygame Pop Quiz Answers Index

Time for action – decomposing a matrix


It's time to decompose a matrix with the singular value decomposition. In order to decompose a matrix, perform the following steps:

  1. First, create a matrix as follows:

    A = np.mat("4 11 14;8 7 -2")
    print "A\n", A

    The matrix we created looks like the following:

    A
    [[ 4 11 14]
     [ 8  7 -2]]
    
  2. Decompose the matrix with the svd function.

    U, Sigma, V = np.linalg.svd(A, full_matrices=False)
    print "U"
    print U
    print "Sigma"
    print Sigma
    print "V"
    print V

    The result is a tuple containing the two orthogonal matrices U and V on the left- and right-hand sides and the singular values of the middle matrix.

    U
    [[-0.9486833  -0.31622777]
     [-0.31622777  0.9486833 ]]
    Sigma
    [ 18.97366596   9.48683298]
    V
    [[-0.33333333 -0.66666667 -0.66666667]
     [ 0.66666667  0.33333333 -0.66666667]]
    
  3. We do not actually have the middle matrix—we only have the diagonal values. The other values are all 0. We can form the middle matrix with the diag function. Multiply the three matrices. This is shown, as...

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