Time for action - using imagesc

1. 1. Let us first consider a one dimensional problem with 20 grid points. The coefficient matrix is generated by calling cmat_1d:

octave:5> A=cmat_1d(20);

1. 2. To set the gray colour map, use (also see Chapter 3):

octave:6> colormap("gray");

1. 3. To make a scaled image of the matrix, we use:

octave:7> imagesc(full(A))

• The result is shown in the left-hand side figure below.

What just happened?

Notice that in Command 7, we use the full matrix of A because imagesc does not currently support sparse matrices. It is easy to see that matrix elements indeed follow the matrix given by Equation (6.14).

For the two-dimensional problem, we can do the same. The result is shown in the right figure for a domain discretized into a 5 x 5 grid. For this grid size, we have 16 boundary points which are given by ones (white) on the matrix diagonal and only 9 interior points given by -4 (black)—see Equation (6.17). The so-called "fringes" on each side of the diagonal represent...