## Creating a Nested Function

### Kelly (view profile)

on 29 Mar 2013

I am trying to create a nested function, but I get an error saying that the variable that I've chosen is already being used even though that's the variable that I need as an input for my second function to compute the equation.

```function [root,numit,err] = newton(x,tol,fx,ddx)
err = abs(fx(x));
numit = 0;
while(err > tol && numit < 1000);
numit = numit + 1;
x = x - fx(x)/ddx(x);
err = abs(fx(x));
end
```
```    if (numit == 1000)
disp('Maxed out on iterations.')
err;
end```
```root = x;
```
```    function root = x
dx = 0.001;
for i = 2:length(x)-1;
fx = exp(cos(x) + sin(x)) - 2;
dxf=(diff(2:i)-diff(1:(i-1)))/2*dx';
end```
```    root = dxf(x);
end
end```

root is my desired output and it is denoted by x. I keep getting an error about x being used as a variable and in the nested function in the same scope. What am I doing wrong?

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### Azzi Abdelmalek (view profile)

on 29 Mar 2013
Edited by Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

on 29 Mar 2013

Change the name of your nested function, because you are using x as function name and variable

```function root = new_name(x)
```

Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

on 29 Mar 2013

You do not need to call the nested function, it's called by the main function. If your main function is correct, provide the values of x,tol,fx,ddx then call your function

```[root,numit,err] = newton(x,tol,fx,ddx)
```
Kelly

### Kelly (view profile)

on 29 Mar 2013

Ok, I got all the computations to work correctly. Now I'm stuck on plotting. I'm creating a 1x2 and the first plot is just the exact derivative of the function and the second should be the numerical approximation.

```clc; clear all; close all;
% Equation 1
tol = 0.001; % for central difference dx == tol
ns = 5;
a = 0;
b = 7;
```
```fx = inline('exp(cos(x) + sin(x)) - 2');
ddx = inline('(exp(cos(x) + sin(x)))*(cos(x)-sin(x))');
```
```% Incremental Search Method
[nroots,low,high] = increm_mod(fx,a,b,ns,tol);
```
```for j = 1:length(low)
fprintf('\n')
disp(['The First Equation has ',num2str(nroots),' roots.'])
```
``` fprintf('\n')
fprintf('-----------------------------------------------------------------')
fprintf('\n')
disp('USING THE NEWTON-RAPHSON METHOD:')
fprintf('\n')```
```% Newton Estimate
guess = 2*(a + b)/3;
[root_n(j),numit_n,err_n(j)] = newton(low(j),tol,fx,ddx);
disp(['Root # ',num2str(j),' = ',num2str(root_n(j))])
disp(['Error # ',num2str(j),' = ',num2str(err_n(j))])
disp(['Number of Iterations # ',num2str(j),' = ',num2str(numit_n)])
fprintf('\n')
```
` end`
``` n = 0;
ns = 100;
dx = (b-a)/ns;
for j = a:dx:b
n = n+1;
f_p(n) = fx(j);
x_p(n) = j;
end```
```      figure(1)
subplot(2,1,1)
plot(x_p,f_p);
hold on
grid on
plot(fx,dx,'ko')%%%%%%%% here's is my problem
xlabel('x-values')
ylabel('fx')
title('Solution Using Newton-Raphson')
subplot(2,1,2)
plot(root_n,root_err,'ko')
xlabel('x values')
ylabel('my function')```

I'm not sure if I'm plotting the right variables for the derivative because my function and derivative are inline functions.

Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

on 29 Mar 2013

If the answer helped, accept the answer and post a new question.

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