SVD_SNOWFALL
Singular Value Decomposition of Snowfall Data

SVD_SNOWFALL is a FORTRAN77 library which demonstrates the use of the Singular Value Decomposition (SVD) to analyze a set of historical snowfall data, with plots created by GNUPLOT.

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'

The sample problem writes files that can be processed by GNUPLOT to create plots.

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 FORTRAN77 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.

GNUPLOT, FORTRAN77 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

SVD_BASIS, a FORTRAN90 program which computes a reduced basis for a collection of data vectors using the SVD.

SVD_DEMO, a FORTRAN77 program which demonstrates the singular value decomposition (SVD) for a simple example.

SVD_TRUNCATED, a FORTRAN90 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:

• svd_snowfall.f, the source code.
• svd_snowfall.sh, BASH commands to compile the source code.

Examples and Tests:

• svd_snowfall_prb.f, a sample calling program.
• svd_snowfall_prb.sh, BASH commands to compile and run the sample program.
• svd_snowfall_prb_output.txt, the output file.

The snowfall data itself must be read into the program from a file:

• snowfall.txt, the snowfall data.

The second test function writes "command" and "data" files that can be used by gnuplot to create plots.

• singular_values_commands.txt, a command file.
• singular_values_data.txt, a data file.
• singular_values.png, the resulting plot.

The third test function writes "command" and "data" files that can be used by gnuplot to create plots.

• approx_commands.txt, a command file.
• approx_data.txt, a data file.
• approx0.png, the 2012 snowfall (red).
• approx1.png, the 2012 snowfall (red) and rank 1 approximation (blue).
• approx2.png, the 2012 snowfall (red) and rank 2 approximation (blue).
• approx3.png, the 2012 snowfall (red) and rank 3 approximation (blue).
• approx4.png, the 2012 snowfall (red) and rank 4 approximation (blue).
• approx5.png, the 2012 snowfall (red) and rank 5 approximation (blue).

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.

• umode_commands.txt, a command file.
• umode_data.txt, a data file.
• umode1.png, basis vector 1 for snowfall as a function of month.
• umode2.png, basis vector 2 for snowfall as a function of month.
• umode3.png, basis vector 3 for snowfall as a function of month.
• umode4.png, basis vector 4 for snowfall as a function of month.
• umode5.png, basis vector 5 for snowfall as a function of month.
• umode6.png, basis vector 6 for snowfall as a function of month.

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.

• vmode_commands.txt, a command file.
• vmode_data.txt, a data file.
• vmode1.png, basis vector 1 for total yearly snowfall as a function of year.
• vmode2.png, basis vector 2 for total yearly snowfall as a function of year.
• vmode3.png, basis vector 3 for total yearly snowfall as a function of year.
• vmode4.png, basis vector 4 for total yearly snowfall as a function of year.
• vmode5.png, basis vector 5 for total yearly snowfall as a function of year.
• umode6.png, basis vector 6 for snowfall as a function of month.

List of Routines:

• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DAXPY computes constant times a vector plus a vector.
• DDOT forms the dot product of two vectors.
• DNRM2 returns the euclidean norm of a vector.
• DROT applies a plane rotation.
• DROTG constructs a Givens plane rotation.
• DSCAL scales a vector by a constant.
• DSVDC computes the singular value decomposition of a matrix.
• DSWAP interchanges two vectors.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• R8COL_NORMALIZE_LI normalizes an R8COL with the column infinity norm.
• R8COL_REVERSE reverses the order of columns in an R8COL.
• R8MAT_COPY copies an R8MAT.
• R8MAT_DATA_READ reads data from an R8MAT file.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_MM multiplies two R8MAT's.
• R8MAT_MMT multiplies computes C = A * B' for two R8MAT's.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8MAT_SVD_LINPACK gets the SVD of a matrix using a call to LINPACK.
• R8ROW_REVERSE reverses the order of the rows of an R8MAT.
• R8VEC_CUM0 computes the cumulutive sums of an R8VEC.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_SUM sums the entries of an R8VEC.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.