svd_circle

svd_circle, a Python code which analyzes a linear map of the unit circle caused by an arbitrary 2x2 matrix A, using the singular value decomposition (SVD).

The singular value decomposition has uses in solving overdetermined or underdetermined linear systems, linear least squares problems, data compression, the pseudoinverse matrix, reduced order modeling, and the accurate computation of matrix rank and null space.

The singular value decomposition of an M by N rectangular matrix A has the form

        A(mxn) = U(mxm) * S(mxn) * V'(nxn)
      

• U is an orthogonal matrix, whose columns are the left singular vectors;
• S is a diagonal matrix, whose min(m,n) diagonal entries are the singular values;
• V is an orthogonal matrix, whose columns are the right singular vectors;

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

svd_circle is available in a MATLAB version and a Python version.

Related Data and Programs:

svd_lls, a Python code which uses the singular value decomposition (SVD) to construct and plot the best affine and linear relationships in the sense of least square, between two vectors of data.

svd_snowfall, a Python code which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD).

svd_test, a Python code which demonstrates the singular value decomposition (SVD) for a simple example.

Reference:

1. Lloyd Trefethen, David Bau,
   Numerical Linear Algebra,
   SIAM, 1997,
   ISBN: 0-89871-361-7,
   LC: QA184.T74.

Source Code:

• svd_circle.py calls all the tests.
• svd_circle.sh runs all the tests.
• svd_circle.txt the output file.

• svd_circle_1.png a plot of the unit circle.
• svd_circle_2.png a plot of the image of the unit circle.