Time for action - instantiating a sparse matrix

1. 1. In Octave, we can define a matrix to be sparse using the sparse function. The simplest way to instantiate a sparse matrix with, say 5 rows and 6 columns, is:

octave:1 > A=sparse(5,6)
A=
Compressed Column Sparse (rows=5, cols=6, nnz=0, [0%])

1. 2. To assign non-zero values to elements in the matrix, you simply use normal assignments, for example:

octave:2> A(1,2) = 42; A(3,:)=3;
octave:3> A
A =
Compressed Column Sparse (rows=5, cols=6, nnz=7, [23%])
(3,1) ->1
(1,2) -> 42
(3,2) -> 1
(3,3) -> 1
(3,4) -> 1
(3,5) -> 1
(3,6) -> 1

1. 3. It is possible to extract the full matrix (and include all the zeros) from sparse matrix by using the full function:

octave:4> B=full(A)
B =
0 42 0 0 0 0
0 0 0 0 0 0
3 3 3 3 3 3
0 0 0 0 0 0
0 0 0 0 0 0

What just happened?

The message returned in Command 1 tells us that Octave interprets the variable as a sparse matrix with 5 rows and 6 columns. The nnz variable indicates the number of...