# spfun

Apply function to nonzero sparse matrix elements

## Description

example

F = spfun(func,S) applies the function func to the nonzero elements of a sparse matrix S. The input argument func is a function handle to a function that takes one input argument.

This operation preserves the sparsity of the original matrix S unless the function func returns zero for some nonzero elements of S.

## Examples

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Create a 4-by-4 sparse diagonal matrix.

S = diag(sparse(1:4))
S =
(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 =
(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)

## Input Arguments

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Input matrix. This matrix is typically (but not necessarily) sparse.

If S is a full matrix, then F = spfun(func,S) applies the function func to the nonzero elements of S and returns F as a sparse matrix.

Data Types: double | logical
Complex Number Support: Yes

Function to apply to the elements of the input array, specified as a function handle. The function should operate on S element-wise. For more information about function handles, see Create Function Handle.

Example: @(n) n+1

## Tips

• If func returns zero for inputs that are zero, you can use func(S) to return the same results as calling spfun on a sparse matrix S.