14.4.2 Defining sparse matrices
A matrix is sparse if most of its elements are 0. To specify a
sparse matrix, it is easier to define the non-zero elements.
This can be done with a table (see Section 14.4.1).
The matrix command (see Section 14.2.4) or the
convert command (see Section 10.1.10) can then
turn the table into a matrix.
Example
First, define the non-zero elements.
| A:=table((0,0)=1,(1,1)=2,(2,2)=3,(3,3)=4,(4,4)=5) |
or:
| purge(A);
A[0..4,0..4]:=[1,2,3,4,5] |
This table can be converted to a matrix with either the
convert command or the matrix command.
or:
|
| |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎣ | | 1 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 | 0 |
| 0 | 0 | 3 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 5 |
| ⎤
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| | | | | | | | | | |
|