CC
Compressed Column (CC) Sparse Matrix File Format

CC is a data directory which contains examples of files in the Compressed Column (CC) format for storing sparse matrices.

The sparse compressed column 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);
• NZ_NUM, the number of nonzero entries in the matrix.
• COL(1:N+1), the location in ROW and A of the first entry associated with each column; the last entry of COL indicates where the first entry of column N+1 would go.
• ROW(1:NZ_NUM), the row indices of the nonzero entries; entries are grouped by column. Within each column, the entries are presumed to be ascending sorted by row;
• A(1:NZ_NUM), the nonzero entries;

The associated CC file format to store this information uses 3 separate files, containing the column, row, and entry information separately. The value of M can be inferred from the maximum value to occur in the row file. The value of N can be inferred from the length of the column file (minus 1), and the value of NZ_NUM from the length of the row or entry files.

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:

CR, a data directory which contains examples of Compressed Row (CR) files, a three-file format for the sparse compressed row matrix format;

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 Harwell Boeing (HB) files, a sparse matrix file format;

LINPLUS, a C++ library which carries out simple manipulations of matrices in a variety of formats, including matrices stored in symmetric, banded, and sparse formats.

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:

The 4 by 6 matrix

        11   0   0  14   0  16
         0  22   0   0  25  26
         0   0  33  34   0  36
        41   0  43  44   0  46
      

COL:

        1
        3
        4
        6
        9
       10
       14
      

ROW:

        1  (column 1 begins)
        4
        2  (column 2 begins)
        3  (column 3 begins)
        4
        1  (column 4 begins)
        3
        4
        2  (column 5 begins)
        1  (column 6 begins)
        2
        3
        4
      

ENTRY:

        11.0  (column 1 begins)
        41.0
        22.0  (column 2 begins)
        33.0  (column 3 begins)
        43.0
        14.0  (column 4 begins)
        34.0
        44.0
        25.0  (column 5 begins)
        16.0  (column 6 begins)
        26.0
        36.0
        46.0
      

CC File Characteristics:

• A matrix is described by three files.
• Each file is in the ASCII format;
• Each line contains a single value.
• depending on the programming language being used, the indices in the ROW and COLUMN arrays may be 0-based or 1-based.

Reference:

1. Timothy Davis,
   Direct Methods for Sparse Linear Systems,
   SIAM, 2006,
   ISBN: 0898716136,
   LC: QA188.D386.
2. Tim Kelley,
   Iterative Methods for Linear and Nonlinear Equations,
   SIAM, 2004,
   ISBN: 0898713528,
   LC: QA297.8.K45.
3. Yousef Saad,
   Iterative Methods for Sparse Linear Systems,
   Second Edition,
   SIAM, 20003,
   ISBN: 0898715342,
   LC: QA188.S17.

Sample Files:

X01 is a simple example for which M=N=5 and NZ_NUM=12.

• x01_a.txt, the matrix entries.
• x01_i.txt, the row indices.
• x01_j.txt, the column pointers.

X02 is related to a finite difference approximation (-1,2-1) of the second derivative at a set of 20 equally spaced points in 1D. Thus M=N=20 and NZ_NUM=58.

• x02_a.txt, the matrix entries.
• x02_i.txt, the row indices.
• x02_j.txt, the column pointers.
• x02_b.txt, a right hand side b.
• x02_x.txt, the solution of the linear system A*x=b.

X03 is related to a finite difference approximation (-1,-1,4,-1,-1) of the second derivative at a 5 by 5 grid of equally spaced points in 2D. Thus M=N=25 and NZ_NUM=105.

• x03_a.txt, the matrix entries.
• x03_i.txt, the row indices.
• x03_j.txt, the column pointers.
• x03_cc_setup.f90, a FORTRAN90 program which set up the arrays.

You can go up one level to the DATA page.