SVD_SNOWFALL
Singular Value Decomposition of Snowfall Data

SVD_SNOWFALL is a MATLAB library 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 121 seasons from 1890 to 2010, 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 121 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 GNU LGPL license.

Related Data and Programs:

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

SVD_BASIS, a MATLAB program which computes a reduced basis for a collection of data vectors using the SVD.

SVD_DEMO, a MATLAB program which demonstrates the singular value decomposition (SVD) for a simple example.

SVD_FINGERPRINT, a MATLAB program which reads a file containing a fingerprint image and uses the singular value decomposition (SVD) to compute and display a series of low rank approximations to the image.

SVD_TRUNCATED a MATLAB program which demonstrates the computation of the reduced or truncated Singular Value Decomposition (SVD) of an M by N rectangular matrix, in cases where M < N or N < M.

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:

• r8col_normalize_li.m, normalizes the columns of a matrix to have unit infinity norm.
• r8vec_print.m, prints an R8VEC.
• snowfall.txt, the snowfall data.
• timestamp.m, prints the YMDHMS date as a timestamp.

Examples and Tests:

• svd_snowfall_test.m, calls all the tests.
• svd_snowfall_output.txt, the output file.
• svd_snowfall_test01.m, reads and processes the snowfall data.
• svd_snowfall_test02.m, computes and plots the singular values.
• svd_snowfall_test03.m, computes and displays the rank 1 through rank 5 approximants to the 2010 snowfall data.
• svd_snowfall_test04.m, displays the first six U modes in the data.
• svd_snowfall_test05.m, displays the first six V modes in the data.
• 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.

You can go up one level to the MATLAB source codes.