spfun

Create a 4-by-4 sparse diagonal matrix.

S = diag(sparse(1:4))

S = 4x4 sparse double matrix (4 nonzeros)
   (1,1)        1
   (2,2)        2
   (3,3)        3
   (4,4)        4

Apply the exponential function to the nonzero elements of S. The resulting matrix has the same sparsity pattern as S.

F = spfun(@exp,S)

F = 4x4 sparse double matrix (4 nonzeros)
   (1,1)       2.7183
   (2,2)       7.3891
   (3,3)      20.0855
   (4,4)      54.5982

Because spfun only applies to nonzero elements of S, the value of F(i) is zero whenever S(i) is zero. This is different from applying the function to all elements of S. For example, compare the result to applying the exponential function to all elements of S. The exp(S) function returns 1 for the elements of S that are 0s.

full(exp(S))

ans = 4×4

    2.7183    1.0000    1.0000    1.0000
    1.0000    7.3891    1.0000    1.0000
    1.0000    1.0000   20.0855    1.0000
    1.0000    1.0000    1.0000   54.5982

Create a random 50-by-50 sparse matrix with density 0.02, where the matrix has 50 nonzero elements. Plot the sparsity pattern of the matrix S.

rng default;
S = sprand(50,50,0.02);
spy(S)

Evaluate the quadratic function $$x^2+x+1$$ to the nonzero elements of S. The evaluated function using spfun has the same sparsity pattern as the matrix S.

fun = @(x) x.^2 + x + 1;
F = spfun(fun,S);
spy(F)