Function Functions in MATLAB

Function functions refer to functions that have other function names or handles as input parameters.

For example, MATLAB has a function called fzero. This function is used to find the independent variable for which the function value passed to it is 0. For instance, the statement fzero(‘cos’, [0 pi]) can determine when cos(x) is 0 in the interval [0, pi]. The statement fzero(‘exp(x) – 2’, [0 1]) can determine when the function exp(x) – 2 is 0 in the interval [0, 1].

>> fzero('cos',[0 pi])    % Find the x that makes the function value of cos x zero in the interval 0 to pi
ans =
    1.5708

>> fzero('exp(x) - 2',[0 1])
ans =
    0.6931

In MATLAB, there are two specialized functions eval and feval that are key to handling function functions.

The function eval evaluates a string as if it were typed in the command window. This function allows MATLAB to construct executable statements during execution. The syntax for the function eval is:

 eval(string)

For example:

>> x = eval('sin(pi/4)') % Calculate the value of sin(x) at pi/4
x =
    0.7071

The following example constructs a string and evaluates it using the function eval:

 x = 1;
 str = ['exp(' num2str(x) ') - 1'];
 res = eval(str)

In this case, the content of the variable str is the string ‘exp(1) – 1’, and eval computes the result as 1.7183.

The function feval computes the value of a named function defined by an M-file at specified input values. The syntax for the function feval is

 feval(fun,value)

For example, to compute sin(x) at x = pi/4:

>> x = feval('sin',pi / 4)
x =
    0.7071

Summary:

• fzero is used to find the zeros of a function within a specified interval.
• feval is used to compute the value of a function at a specified point. The calling form is:feval(fun,value)
• eval is used to compute the value of a function at a specified point. The calling form is:eval(string)

Happy learning~~