Create an identity matrix and determine the number of nonzeros it contains.

X = eye(4)

X =4×41 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

N = nnz(X)

N = 4

Usennzin conjunction with a relational operator to determine how many matrix elements meet a condition. Since relational operators produce logical matrices of 1s and 0s, thennzfunction counts the 1s where the condition is true.

Create a matrix and determine how many elements are greater than 10.

X = magic(5)

X =5×517 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

nnz(X>10)

ans = 15

The density of a matrix is the ratio of nonzeros to the total number of elements,nnz(X)/numel(X).

Create a sparse matrix representing the finite difference Laplacian on an L-shaped domain and calculate its density.

X = delsq(numgrid('L',20)); spy(X)

d = nnz(X)/numel(X)

d = 0.0194

The result indicates that only about 2% of the elements in the matrix are nonzero.