Mathematics

Viewing Sparse Matrices

MATLAB provides a number of functions that let you get quantitative or graphical information about sparse matrices.

This section provides information about:

• Obtaining information about nonzero elements
• Viewing graphs of sparse matrices
• Finding indices and values of nonzero elements

Information About Nonzero Elements

There are several commands that provide high-level information about the nonzero elements of a sparse matrix:

• nnz returns the number of nonzero elements in a sparse matrix.
• nonzeros returns a column vector containing all the nonzero elements of a sparse matrix.
• nzmax returns the amount of storage space allocated for the nonzero entries of a sparse matrix.

To try some of these, load the supplied sparse matrix west0479, one of the Harwell-Boeing collection.

• load west0479
  whos
    Name           Size         Bytes  Class
  
    west0479     479x479        24576  sparse array 
  

This matrix models an eight-stage chemical distillation column.

Try these commands.

• nnz(west0479)
  
  ans =
  1887
  
  format short e
  west0479
     
  west0479 =
      
    (25,1)      1.0000e+00
    (31,1)     -3.7648e-02
    (87,1)     -3.4424e-01
    (26,2)      1.0000e+00
    (31,2)     -2.4523e-02
    (88,2)     -3.7371e-01
    (27,3)      1.0000e+00
    (31,3)     -3.6613e-02
    (89,3)     -8.3694e-01
    (28,4)      1.3000e+02
      .
      .
      .
     
  
  nonzeros(west0479);
      ans =
      
     1.0000e+00
    -3.7648e-02
    -3.4424e-01
     1.0000e+00
    -2.4523e-02
    -3.7371e-01
     1.0000e+00
    -3.6613e-02
    -8.3694e-01
     1.3000e+02
      .
      .
      .
  

Note    Use Ctrl+C to stop the nonzeros listing at any time.

Note that initially nnz has the same value as nzmax by default. That is, the number of nonzero elements is equivalent to the number of storage locations allocated for nonzeros. However, MATLAB does not dynamically release memory if you zero out additional array elements. Changing the value of some matrix elements to zero changes the value of nnz, but not that of nzmax.

However, you can add as many nonzero elements to the matrix as desired. You are not constrained by the original value of nzmax.

Importing Sparse Matrices from Outside MATLAB

Viewing Sparse Matrices Graphically

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