svd_snowfall

svd_snowfall, a Python code which demonstrates the use of the Singular Value Decomposition (SVD) to analyze a set of historical snowfall data.

The snowfall data consists of records for the winters of 1890-1891 to 2016-2017, of the snowfall in inches, over the months from October to May, as measured at Michigan Tech.

This data can be regarded as an 8 by 127 matrix A. Applying the singular value decomposition produces the factors

A = U * S * V'

Licensing:

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

Languages:

svd_snowfall is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

fingerprints, a dataset directory which contains a few images of fingerprints.

time_series, a dataset directory which contains examples of files describing time series.

Reference:

1. Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Danny Sorensen,
   LAPACK User's Guide,
   Third Edition,
   SIAM, 1999,
   ISBN: 0898714478,
   LC: QA76.73.F25L36
2. Gene Golub, Charles VanLoan,
   Matrix Computations, Third Edition,
   Johns Hopkins, 1996,
   ISBN: 0-8018-4513-X,
   LC: QA188.G65.
3. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.
4. Lloyd Trefethen, David Bau,
   Numerical Linear Algebra,
   SIAM, 1997,
   ISBN: 0-89871-361-7,
   LC: QA184.T74.

Source code:

• svd_snowfall.py, the source code.
• svd_snowfall.sh, runs all the tests.
• svd_snowfall.txt, the output file.

• rank_one_approximants.png, a plot of the rank 1 through rank 5 approximants to the 2010 snowfall.
• singular_values.png, a plot of the singular values.
• u_modes.png, a plot of the first 6 U modes = monthly snowfall patterns over a year.
• v_modes.png, a plot of the first 6 V modes = variation over 1890-2010 of snowfall in a given month.