SPARSE_ELLPACK
Sparse ELLPACK Matrix File Format

SPARSE_ELLPACK is a data directory which contains examples of the sparse ELLPACK format, a pair of arrays for storing information about a sparse matrix.

The sparse compressed row data structure involves:

• M and N, the number of rows and columns of the matrix (we'll often assume assume the matrix is square, in which case M=N);
• J_MAX, the maximum number of nonzeros in any row.
• A(1:N,1:J_MAX), the nonzero entries for each row. Typically, the diagonal entry comes first, and the other entries in any order. If a row has fewer than J_MAX nonzero entries, then it's important to set the remaining entries to zero.
• J(1:N,1:J_MAX), the column indices for each entry. If a row has fewer than J_MAX entries, then the remaining entries of A are set to zero, and it is only necessary that the corresponding value of J be legal, that is, any column index between 1 and N.

The associated SPARSE_ELLPACK file format to store this information uses 2 separate files, containing the "A" and "J" arrays, one row per line.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

DLAP, a data directory which contains examples of DLAP files, a sparse matrix file format used by the DLAP package;

DSP, a data directory which contains examples of DSP files, a sparse matrix file format, storing just (I,J,A(I,J)), and using one-based indexing.

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

LINPLUS, a C++ library which carries out simple manipulations of matrices in a variety of formats.

SPARSE, MATLAB programs which illustrate the use of MATLAB's SPARSE matrix utilities;

SPARSE_CC, a data directory which contains examples of SPARSE CC files, a three-file format for the sparse compressed column matrix format;

SPARSE_CR, a data directory which contains examples of SPARSE CR files, a three-file format for the sparse compressed row matrix format;

SPARSEKIT, a FORTRAN90 library which implements operations on sparse matrices, including conversion between various formats, by Yousef Saad.

ST, a data directory which contains examples of ST files, the Sparse Triplet format, a sparse matrix file format, storing just (I,J,A(I,J)), and using zero-based indexing.

Example:

Suppose the original matrix is:

          11   0   13    0     0     0  
          21  22    0   24     0     0  
           0  32   33    0    35     0  
           0   0   43   44     0    46  
          51   0    0   54    55     0  
          61  62    0    0    65    66  
      

Then the sparse ELLPACK format would be:

        --------A-------           ------J-------
        11  13    0    0           1   3   *    *  
        22  21   24    0           2   1   4    *  
        33  32   35    0           3   2   5    *  
        44  43   46    0           4   3   6    *  
        55  51   54    0           5   1   4    *  
        66  61   62   65           6   1   2    5  
      

Reference:

1. Yousef Saad,
   Iterative Methods for Sparse Linear Systems,
   Second Edition,
   SIAM, 2003,
   ISBN: 0898715342,
   LC: QA188.S17.

Sample Files:

SIX is a simple example for which M=N=6 and J_MAX = 4.

• six_a_ell.txt, the matrix entries.
• six_j_ell.txt, the column indices.

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