RB

RB, a data directory which contains examples of the RB or Rutherford Boeing Sparse Matrix File Format, used to store a sparse matrix in a file.

Since most of the matrix is presumably zero, a great deal of storage can be saved if only the nonzero entries are stored. The file format offers a choice of two suitable representations for the nonzero data: a compressed column storage (CCS) format, or a format suitable for finite element matrices.

The two representations, compressed column storage or finite element, may then be stored in a file using either the Rutherford Boeing format (RB) or a Matrix Market format (MM).

Often, a sparse matrix has associated information, such as eigenvectors, or special right hand sides. The RB format offers a way to include such information in files, so that it is associated with the sparse matrix and retrieved as needed. The Harwell-Boeing format, a predecessor to the RB format, required all supplementary information to be included in the same file as that storing the sparse matrix.

Licensing:

The information on this web page is distributed under the MIT license.

Related Programs and Data:

HB, a data directory which contains examples of HB files, the Harwell Boeing sparse matrix file format;

MM, a data directory which contains examples of MM files, the Matrix Market Sparse Matrix File Format;

Reference:

1. Ronald Boisvert, Roldan Pozo, Karin Remington,
   The Matrix Market Exchange Formats: Initial Design,
   Technical Report NISTIR-5935,
   National Institute of Standards and Technology, December 1996.
2. Iain Duff, Roger Grimes, John Lewis,
   User's Guide for the Harwell-Boeing Sparse Matrix Collection,
   Technical Report TR/PA/92/86,
   CERFACS, October 1992.
3. Iain Duff, Roger Grimes, John Lewis,
   Sparse Matrix Test Problems,
   ACM Transactions on Mathematical Software,
   Volume 15, Number 1, March 1989, pages 1-14.
4. Iain Duff, Roger Grimes, John Lewis,
   The Rutherford-Boeing Sparse Matrix Collection,
   Technical Report RAL-TR-97-031,
   Rutherford Appleton Laboratory, 1997.

Sample Files:

EXAMPLE1 is a 5x5 real general matrix. Thanks to Liang Tang for suggestion a correction to the RB file.

• example1.rb, the matrix file in Rutherford Boeing format.
• example1.mm, the matrix file in Matrix Market format.

EXAMPLE2 is a 10x10 square symmetric matrix in elemental form. The matrix is formed as the sum of 6 symmetric 3x3 matrices and one symmetric 4x4 matrix. Because symmetry is specified, only the diagonal and lower triangle of these matrices are to be supplied.

• example2.hb, the matrix file in Rutherford Boeing format.
• example2.mm, the matrix file in Matrix Market format.

EXAMPLE3 is a 5x5 square matrix in elemental form. The matrix is not symmetric, but it is structurally symmetric. The matrix is formed as the sum of 4 square finite element matrices.

• example3.rb, the matrix file in Rutherford Boeing format.
• example3.mm, the matrix file in Matrix Market format.

EXAMPLE4 is a 4x5 small rectangular matrix in elemental form. The matrix is formed as the sum of 3 rectangular finite element matrices.

• example4.rb, the matrix file in Rutherford Boeing format.
• example4.mm, the matrix file in Matrix Market format.