Math::SparseMatrix - Provides basic sparse matrix operations such as creation, reading from file, reading

       Ted Pedersen, University of Minnesota, Duluth.  tpederse at d.umn.edu

       Mahesh Joshi, Carnegie-Mellon University maheshj @ cmu.edu

       Copyright (c) 2006-2008, Ted Pedersen and Mahesh Joshi

       This program is free software; you can redistribute it and/or modify  it  under  the  terms  of  the  GNU
       General  Public License as published by the Free Software Foundation; either version 2 of the License, or
       (at your option) any later version.

       This program is distributed in the hope that it will be useful, but WITHOUT ANY  WARRANTY;  without  even
       the  implied  warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
       License for more details.

       You should have received a copy of the GNU General Public License along with this program; if not,  write
       to

        The Free Software Foundation, Inc.,
        59 Temple Place - Suite 330,
        Boston, MA  02111-1307, USA.

perl v5.34.0                                       2022-06-15                            Math::SparseMatrix(3pm)

       Math::SparseMatrix provides simple sparse matrix functionality such as creation of sparse matrices,
       writing them out to a file, reading matrices from files and reading transpose of a matrix stored in a
       file.

       Math::SparseMatrix - Provides basic sparse matrix operations such as creation, reading from file, reading
       transpose from file and writing to file.

       Math::SparseVector

       The sparse matrix file format that Math::SparseMatrix expects is described below with an example.

       The first line (or the header line) of the file should contain 3 number separated by a single space.  The
       first  number  is the number of rows in the sparse matrix, the second number is the number of columns and
       the third number is the number of non-zero elements present in the stored matrix.

       Each subsequent line represents one row of the sparse matrix, therefore there should be as many number of
       lines after the header line as  the  number  of  rows  mentioned  in  the  header  line.  In  every  line
       representing  a  row, there should be as many pairs of numbers as the number of non-zero elements in that
       row.  The first number in the pair represents the column number of the non-zero element  (column  numbers
       start with 1). The row number is implicitly provided by the line number in the file. The second number in
       the  pair  is  the  actual  non-zero  matrix  element. Numbers in a pair and multiple pairs should all be
       separated by single spaces. If a row does not contain any non-zero element, then an empty line should  be
       present in the file.

       NOTE:  There  should  be no empty lines except those representing empty rows, neither should there be any
       comment lines. Commenting is not supported.

       Consider the sparse matrix of 5 rows and 4 columns below:

         10    0    0    0
          0    0    6    8
          0    0    0    0
          0   21    0    0
          7    0    0    9

       The sparse file representation for the same is:

         5 4 6
         1 10
         3 6 4 8

         2 21
         1 7 4 9

       Notice the empty line in between for the third row.

       1. To begin with, Math::SparseMatrix should be included in your Perl program as follows:
               # include this module for use in your program
               use Math::SparseMatrix;

       2. To create an empty sparse matrix object with the required dimensions, use the following constructor:
               # create a new sparse matrix with 10 rows and 15 columns
               my $spmatrix = Math::SparseMatrix->new(10, 15);

       3. To update the values in the sparse matrix, use the "set" function as follows:
               # set the value at row 5, column 3 to 10
               $spmatrix->set(5, 3, 10);

       4. To retrieve a stored value, use the "get" function as follows:
               # get the value at row 6, column 5 if present, or zero
               $val = $spmatrix->get(6, 5);

       5. A sparse matrix can be written out to a file in the supported format (explained below) as follows:
               # write out the sparse matrix to the file "matrix.txt"
               $spmatrix->writeToFile("matrix.txt");

       6. A new sparse matrix object can be created from a file in the supported  format as follows:
               # create a matrix object by reading the file "matrix.txt"
               my $spmatrix = Math::SparseMatrix->createFromFile("matrix.txt");

       7. A new sparse matrix that is the transpose of the matrix stored in the given input file can be created
       as follows:
               # create the transpose of the matrix stored in "matrix.txt"
               my $spmatrix = Math::SparseMatrix->createTransposeFromFile("matrix.txt");

       8. Finally, to generate the transpose of a matrix stored in a file, read the transpose as in #7 above and
       write out the read transpose to a new file as in #5 above.
               # create the transpose of the matrix stored in "matrix.txt"
               my $spmatrix = Math::SparseMatrix->createTransposeFromFile("matrix.txt");

               # write out the created transpose to another file "transpose.txt"
               $spmatrix->writeToFile("transpose.txt");