ST
Sparse Triplet Matrix File Format

ST, the "sparse triplet format", is a simple data structure and a file format for storing sparse matrices.

The sparse triplet data structure simply records, for each nonzero entry of the matrix, the row, column and value. Thus, the information in the data structure might be

• M and N, the number of rows and columns in the (original full) matrix;
• NZ_NUM, the number of nonzero elements in the matrix;
• ROW(1:NZ_NUM), the row indices of the nonzero elements;
• COL(1:NZ_NUM), the column indices of the nonzero elements;
• VAL(1:NZ_NUM), the values of the nonzero elements;

The sparse triplet file format is an ASCII file of NZ_NUM lines, with each line corresponding to a nonzero entry of the matrix, and containing the row index, column index and value of that entry, separated by spaces.

Related Data and Programs:

DSP is a sparse matrix file format that is identical to the ST format, except that it uses 1-based indexing, which is suitable for FORTRAN77, FORTRAN90 and MATLAB programming.

LINPLUS is a library of routines for matrix tasks, which includes routines for matrices stored in the DSP format. LINPLUS is available in a C++ version, and a FORTRAN90 version, and a MATLAB version,

MGMRES is a C++ routine which applies the restarted GMRES iterative technique to a sparse linear system stored in the DSP format.

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
      

        0  0  11.0
        0  3  14.0
        0  5  16.0
        1  1  22.0
        1  3  25.0
        1  5  26.0
        2  2  33.0
        2  3  34.0
        2  5  36.0
        3  0  41.0
        3  2  43.0
        3  3  44.0
        3  5  46.0
      

ST File Characteristics:

• ASCII format;
• each line has the form I J A(I,J)
• the I and J indices are zero-based.

Reference:

1. Timothy Davis,
   Direct Methods for Sparse Linear Systems,
   SIAM, 2006.

Routines to write a matrix to a file in the ST format:

• LINPLUS is a C++ library which supports the DSP format, essentially a one-based version of the ST format. LINPLUS includes a routine DSP_WRITE which can write a DSP or ST matrix to a file.

Routines to read a matrix from a file in the ST format:

• LINPLUS is a C++ library which supports the DSP format, essentially a one-based version of the ST format. LINPLUS includes a routine DSP_READ which can read a DSP or ST matrix from a file.

Routines to convert another file to ST format:

• DSP_TO_ST is an executable FORTRAN90 program which can read a matrix stored in a DSP file and write a copy of the matrix stored in the ST format.
• HB_TO_ST is an executable FORTRAN77 program which can read a Harwell-Boeing sparse matrix file and rewrite the information as a Sparse Triplet file.

Routines to convert a ST file to another format:

• ST_TO_DSP is an executable FORTRAN90 program which can read a matrix stored in a ST file and write a copy of the matrix stored in the DSP format.

Sample ST Files:

• 5by5.st, a 5 by 5 matrix.
• ash219.st
• bcsstk01.st
• bcsstk16.st
• fs_183_1.st
• kershaw.st, the 4 by 4 Kershaw matrix.
• lp_afiro.st
• mbeacxc.st
• t1.st
• west0067.st

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