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
18901891 to 20162017, 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'
and it is the purpose of this code to consider what these
factors indicate about the snowfall data.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL 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:

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

Gene Golub, Charles VanLoan,
Matrix Computations,
Third Edition,
Johns Hopkins, 1996,
ISBN: 080184513X,
LC: QA188.G65.

David Kahaner, Cleve Moler, Steven Nash,
Numerical Methods and Software,
Prentice Hall, 1989,
ISBN: 0136272584,
LC: TA345.K34.

Lloyd Trefethen, David Bau,
Numerical Linear Algebra,
SIAM, 1997,
ISBN: 0898713617,
LC: QA184.T74.
Source code:

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 18902010 of snowfall
in a given month.
Last revised on 03 May 2017.