Providing Parameter Values Using Nested Functions :: Function Functions (Mathematics)

Mathematics

Providing Parameter Values Using Nested Functions

One way to provide parameters to the polynomial is to write a single M-file that

Accepts the additional parameters as inputs
Invokes the function function
Contains the function called by the function function as a nested function

The following example illustrates how to find a zero of the cubic polynomial x³ + bx + c, for different values of the coefficients b and c, using this method. To do so, write an M-file with the following code.

function y = findzero(b, c, x0)

options = optimset('Display', 'off'); % Turn off Display
y = fzero(@poly, x0, options);

    function y = poly(x) % Compute the polynomial.
    y = x^3 + b*x + c;
    end
end

The main function, findzero, does two things:

Invokes the function fzero to find a zero of the polynomial
Computes the polynomial in a nested function, poly, which is called by fzero

You can call findzero with any values of the coefficients b and c, which are seen by poly because it is a nested function.

As an example, to find a zero of the polynomial with b = 2 and c = 3.5, using the starting point x0 = 0, call findzero as follows.

```
x = findzero(2, 3.5, 0)
```

This returns the zero

```
x =

   -1.0945
```

Parameterizing Functions Called by Function Functions Providing Parameter Values to Anonymous Functions