The University of Florida Sparse Matrix Collection

From the abstract of the paper The University of Florida Sparse Matrix Collection:

The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (such as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (such as optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs). The collection is widely used by the sparse matrix algorithms community for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.

Sample Gallery of the University of Florida Sparse Matrix Collection:

Click on the thumbnails below for a close-up.

The images above of matrices in the UF Sparse Matrix Collection were created by Yifan Hu, AT&T. As of April 2009, it contains 2255 problems (some of which are sequences of dozens of matrices). The largest has a dimension of almost 29 million, with 760 million nonzero entries. The matrices are available in three formats: MATLAB mat-file, Rutherford-Boeing, and Matrix Market. Note that the MATLAB mat-files can only be read by MATLAB 7.0 or later.

This collection is managed by Tim Davis, but ``editors'' of other collections are attributed, via the Problem.ed field in each problem set. Problem.author is the matrix creator. Other collections are always welcome.

Click here for a paper describing the collection (Nov. 2008).

Browse the collection:

• Browse the collection by matrix group
• Browse all the matrices (sorted by matrix id). New matrices are always at the end of this list.
• Browse all the matrices (sorted by dimension)
• Browse all the matrices (sorted by name)
• Browse all the matrices (sorted by nnz)
• Browse all the matrices (sorted by symmetry)
• Browse all the matrices (sorted by type)
• Browse all the matrices (sorted by group)
• See the ChangeLog for recent changes.
• Highlights:
  • Some of the matrices have xyz coordinates, which are plotted on the matrix web pages. See the Cunningham, Engwirda, Pajek, and Pothen matrix sets. Check out the Commanche helicopter:
    
• Problem domains

MATLAB interface:

• Click here for the UFget MATLAB interface for simple access to the collection, right inside your MATLAB workspace. From inside MATLAB, UFget will download a matrix, cache it locally, and load it into your MATLAB workspace. No need to use a browser to get a matrix. You can even use the built-in index to search for matrices that fit your criteria ... all inside MATLAB. A future version of Mathematica will also include this feature. For example, to download all symmetric matrices into MATLAB, in increasing size as measured by nnz(A):

      index = UFget ;           % get index of the UF Sparse Matrix Collection 
      ids = find (index.numerical_symmetry == 1) ;
      [ignore, i] = sort (index.nnz (ids)) ;
      ids = ids (i) ;
      for id = ids
  	Prob = UFget (id)     % Prob is a struct (matrix, name, meta-data, ...)
  	A = Prob.A ;          % A is a symmetric sparse matrix
      end
  

Software:

The SuiteSparse collection of packages includes all of the software that I used to generate these web pages, and to manage the matrices themselves (creating the Matrix Market and Rutherford/ Boeing files, for example). You don't need SuiteSparse to access the matrices, however.

Downloading matrices:

The simplest method for downloading the matrices in MATLAB *.mat format is with UFget, right inside MATLAB itself.

You can download them from the web as well, with a browser. Right-click the matrices in your browser and "save as..." a file on your system. Alternatively, try using the wget program, which can download entire directories (or even the entire collection) in a single command. For example, to download the Oberwolfach directory in the Rutherford/Boeing format, do:

wget -r -l 1 -np http://www.cise.ufl.edu/research/sparse/RB/Oberwolfach
To download the entire collection in Rutherford/Boeing format:
wget -r -l 2 -np http://www.cise.ufl.edu/research/sparse/RB
To download the entire collection in MATLAB format:
wget -r -l 2 -np http://www.cise.ufl.edu/research/sparse/mat
To download the entire collection in Matrix Market format:
wget -r -l 2 -np http://www.cise.ufl.edu/research/sparse/MM
Direct access to the matrix directories, useful for wget access:
• MATLAB format
• Rutherford/Boeing format
• Matrix Market format

References:

• To cite this collection, use the following:
  • The University of Florida Sparse Matrix Collection T. A. Davis, Submitted to ACM Transactions on Mathematical Software
  • Algorithm 8xx: UFget, a MATLAB interaface to the University of Florida Sparse Matrix Collection T. A. Davis, Submitted to ACM Transactions on Mathematical Software
  • Duff, I.S, Grimes, R. G, and Lewis, J. G, Sparse matrix test problems, ACM Transactions on Mathematical Software, vol 15, no. 1, pp 1-14, 1989. This describes the Harwell-Boeing collection which is the starting point of the UF Sparse Matrix Collection (the first 292 matrices).
  • The URL: http://www.cise.ufl.edu/research/sparse/matrices, submitted to ACM Trans. on Mathematical Software.
  • See also NA Digest, vol. 92, no. 42, October 16, 1994, NA Digest, vol. 96, no. 28, July 23, 1996, and NA Digest, vol. 97, no. 23, June 7, 1997.
• The Rutherford-Boeing format is described in the document Rutherford-Boeing Sparse Matrix Collection
• See the Matrix Market for a description of the Matrix Market format.

To submit matrices to this collection:

Sparse matrices from real applications are critical to the development of sparse matrix algorithms. Many sparse matrix algorithm developers use the matrices at this site to test their methods. If you would like the next generation of sparse matrix methods to work well on matrices from your problem domain, then please submit matrices to the collection, at: http://www.cise.ufl.edu/~web-gfs (user "davis"). If you upload a file there, I will automatically be notified via email.

Use any reasonable format; just tell me what you use. I prefer either the Matrix Market format, or a MATLAB *.mat file.

Another simple method is the triplet format. The triplet format is a simple ascii file with nz lines; each line contains a row index, column index, and numerical value of one entry in the matrix (two values for a complex matrix, the real part followed by the imaginary part). Duplicates are OK - these are summed in the output matrix. The triplets can be in any order. If the matrix dimension cannot be inferred from the row and column indices, please tell me what they are in another file or email message.

If you wish to include other data (right-hand-sides, solutions, cost vector c for a linear programming problem, and so on), use a separate file for each matrix in your problem. A dense vector of length n should appear as a file with n lines, and one entry per line (or use the Matrix Market format for dense matrices).

Sources of some matrices and related links

Graph drawings, by Yifan Hu

For a demo of how Yifan's algorithm works, see the GraphPlot function, which he wrote for Mathematica, or you can view it here by right-clicking the figure below and selecting "Play". (or just click "reload" on your browser).

Below is Yifan Hu's graph drawing of the Chen/pkustk01 matrix that I obtained from Pu Chen, Beijing University. The matrix is a model of the Beijing Botanical Garden Conservatory. Overlayed on top of the graph is a picture of the actual building.