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<html>
<head>
<title>
SVD_SNOWFALL - Singular Value Decomposition of Snowfall Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SVD_SNOWFALL <br> Singular Value Decomposition of Snowfall Data
</h1>
<hr>
<p>
<b>SVD_SNOWFALL</b>
is a C++ library which
demonstrates the use of the Singular Value Decomposition (SVD)
to analyze a set of historical snowfall data,
with plots created by GNUPLOT.
</p>
<p>
The snowfall data consists of records for the 123 seasons from
1890 to 2012, of the snowfall in inches, over the months from
October to May, as measured at Michigan Tech.
</p>
<p>
This data can be regarded as an 8 by 123 matrix A.
Applying the singular value decomposition produces the
factors
<blockquote>
A = U * S * V'
</blockquote>
and it is the purpose of this library to consider what these
factors indicate about the snowfall data.
</p>
<p>
The sample problem writes files that can be processed by GNUPLOT
to create plots.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SVD_SNOWFALL</b> is available in
<a href = "../../c_src/svd_snowfall/svd_snowfall.html">a C version</a> and
<a href = "../../cpp_src/svd_snowfall/svd_snowfall.html">a C++ version</a> and
<a href = "../../f77_src/svd_snowfall/svd_snowfall.html">a FORTRAN77 version</a> and
<a href = "../../f_src/svd_snowfall/svd_snowfall.html">a FORTRAN90 version</a> and
<a href = "../../m_src/svd_snowfall/svd_snowfall.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../datasets/fingerprints/fingerprints.html">
FINGERPRINTS</a>,
a dataset directory which
contains a few images of fingerprints.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/svd_basis/svd_basis.html">
SVD_BASIS</a>,
a C++ program which
applies the Singular Value Decomposition (SVD) to a set of vectors,
extracting dominant modes;
</p>
<p>
<a href = "../../cpp_src/svd_demo/svd_demo.html">
SVD_DEMO</a>,
a C++ program which
demonstrates the singular value decomposition (SVD) for a simple example.
</p>
<p>
<a href = "../../cpp_src/svd_truncated/svd_truncated.html">
SVD_TRUNCATED</a>,
a C++ program which
demonstrates the computation of the reduced or truncated
Singular Value Decomposition (SVD) that is useful for cases when
one dimension of the matrix is much smaller than the other.
</p>
<p>
<a href = "../../datasets/time_series/time_series.html">
TIME_SERIES</a>,
a dataset directory which
contains examples of files describing time series.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford,
James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum,
Sven Hammarling, Alan McKenney, Danny Sorensen,<br>
LAPACK User's Guide,<br>
Third Edition,<br>
SIAM, 1999,<br>
ISBN: 0898714478,<br>
LC: QA76.73.F25L36
</li>
<li>
Gene Golub, Charles VanLoan,<br>
Matrix Computations,
Third Edition,<br>
Johns Hopkins, 1996,<br>
ISBN: 0-8018-4513-X,<br>
LC: QA188.G65.
</li>
<li>
David Kahaner, Cleve Moler, Steven Nash,<br>
Numerical Methods and Software,<br>
Prentice Hall, 1989,<br>
ISBN: 0-13-627258-4,<br>
LC: TA345.K34.
</li>
<li>
Lloyd Trefethen, David Bau,<br>
Numerical Linear Algebra,<br>
SIAM, 1997,<br>
ISBN: 0-89871-361-7,<br>
LC: QA184.T74.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "svd_snowfall.cpp">svd_snowfall.cpp</a>, the source code.
</li>
<li>
<a href = "svd_snowfall.hpp">svd_snowfall.hpp</a>, the include file.
</li>
<li>
<a href = "svd_snowfall.sh">svd_snowfall.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "svd_snowfall_prb.cpp">svd_snowfall_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "svd_snowfall_prb.sh">svd_snowfall_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "svd_snowfall_prb_output.txt">svd_snowfall_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
The snowfall data itself must be read into the program from a file:
<ul>
<li>
<a href = "snowfall.txt">snowfall.txt</a>,
the snowfall data.
</li>
</ul>
</p>
<p>
The second test function writes "command" and "data" files that can be used
by gnuplot to create plots.
<ul>
<li>
<a href = "singular_values_commands.txt">singular_values_commands.txt</a>,
a command file.
</li>
<li>
<a href = "singular_values_data.txt">singular_values_data.txt</a>,
a data file.
</li>
<li>
<a href = "singular_values.png">singular_values.png</a>,
the resulting plot.
</li>
</ul>
</p>
<p>
The third test function writes "command" and "data" files that can be used
by gnuplot to create plots.
<ul>
<li>
<a href = "approx_commands.txt">approx_commands.txt</a>,
a command file.
</li>
<li>
<a href = "approx_data.txt">approx_data.txt</a>,
a data file.
</li>
<li>
<a href = "approx0.png">approx0.png</a>,
the 2012 snowfall (red).
</li>
<li>
<a href = "approx1.png">approx1.png</a>,
the 2012 snowfall (red) and rank 1 approximation (blue).
</li>
<li>
<a href = "approx2.png">approx2.png</a>,
the 2012 snowfall (red) and rank 2 approximation (blue).
</li>
<li>
<a href = "approx3.png">approx3.png</a>,
the 2012 snowfall (red) and rank 3 approximation (blue).
</li>
<li>
<a href = "approx4.png">approx4.png</a>,
the 2012 snowfall (red) and rank 4 approximation (blue).
</li>
<li>
<a href = "approx5.png">approx5.png</a>,
the 2012 snowfall (red) and rank 5 approximation (blue).
</li>
</ul>
</p>
<p>
The fourth test function writes "command" and "data" files that can be used
by gnuplot to create plots of the first 6 U modes, which form a basis
for average snowfall as a function of the month.
<ul>
<li>
<a href = "umode_commands.txt">umode_commands.txt</a>,
a command file.
</li>
<li>
<a href = "umode_data.txt">umode_data.txt</a>,
a data file.
</li>
<li>
<a href = "umode1.png">umode1.png</a>,
basis vector 1 for snowfall as a function of month.
</li>
<li>
<a href = "umode2.png">umode2.png</a>,
basis vector 2 for snowfall as a function of month.
</li>
<li>
<a href = "umode3.png">umode3.png</a>,
basis vector 3 for snowfall as a function of month.
</li>
<li>
<a href = "umode4.png">umode4.png</a>,
basis vector 4 for snowfall as a function of month.
</li>
<li>
<a href = "umode5.png">umode5.png</a>,
basis vector 5 for snowfall as a function of month.
</li>
<li>
<a href = "umode6.png">umode6.png</a>,
basis vector 6 for snowfall as a function of month.
</li>
</ul>
</p>
<p>
The fifth test function writes "command" and "data" files that can be used
by gnuplot to create plots of the first 6 V modes, which form a basis
for total yearly snowfall behavior as a function of the year.
<ul>
<li>
<a href = "vmode_commands.txt">vmode_commands.txt</a>,
a command file.
</li>
<li>
<a href = "vmode_data.txt">vmode_data.txt</a>,
a data file.
</li>
<li>
<a href = "vmode1.png">vmode1.png</a>,
basis vector 1 for total yearly snowfall as a function of year.
</li>
<li>
<a href = "vmode2.png">vmode2.png</a>,
basis vector 2 for total yearly snowfall as a function of year.
</li>
<li>
<a href = "vmode3.png">vmode3.png</a>,
basis vector 3 for total yearly snowfall as a function of year.
</li>
<li>
<a href = "vmode4.png">vmode4.png</a>,
basis vector 4 for total yearly snowfall as a function of year.
</li>
<li>
<a href = "vmode5.png">vmode5.png</a>,
basis vector 5 for total yearly snowfall as a function of year.
</li>
<li>
<a href = "umode6.png">umode6.png</a>,
basis vector 6 for snowfall as a function of month.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is TRUE (1) if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DAXPY</b> computes constant times a vector plus a vector.
</li>
<li>
<b>DDOT</b> forms the dot product of two vectors.
</li>
<li>
<b>DNRM2</b> returns the euclidean norm of a vector.
</li>
<li>
<b>DROT</b> applies a plane rotation.
</li>
<li>
<b>DROTG</b> constructs a Givens plane rotation.
</li>
<li>
<b>DSCAL</b> scales a vector by a constant.
</li>
<li>
<b>DSVDC</b> computes the singular value decomposition of a real rectangular matrix.
</li>
<li>
<b>DSWAP</b> interchanges two vectors.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two I4's.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of a R8.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_SIGN</b> returns the sign of a R8.
</li>
<li>
<b>R8COL_NORMALIZE_LI</b> normalizes an R8COL with the column infinity norm.
</li>
<li>
<b>R8COL_REVERSE</b> reverses the order of columns in an R8COL.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads the data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_MM_NEW</b> multiplies two matrices.
</li>
<li>
<b>R8MAT_MMT_NEW</b> computes C = A * B'.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_SVD_LINPACK</b> gets the SVD of a matrix using a call to LINPACK.
</li>
<li>
<b>R8MAT_SVD_LOW_RANK</b> forms a rank R approximation using the SVD.
</li>
<li>
<b>R8ROW_REVERSE</b> reverses the order of the rows of an R8ROW.
</li>
<li>
<b>R8VEC_CUM0_NEW</b> computes the cumulutive sums of an R8VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_SUM</b> returns the sum of an R8VEC.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_R8</b> reads an R8 value from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 09 May 2013.
</i>
<!-- John Burkardt -->
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