Creating a Nested Function

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?

Answer 1

[Azzi Abdelmalek]

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

function root = new_name(x)

[Kelly]

I did that and I didn't get an error. However when I used the command whos I didn't see two functions. Only the first function calls it's variables and runs. The second doesn't seem to be doing anything. Am I not"nesting" the functions correctly?

[Azzi Abdelmalek]

whos displays variables in base workspace, the variables inside any function are not displayed. each function has its own workspace

[Azzi Abdelmalek]

Also, if the first function is working and you are not getting errors, means the second function is also working

[Kelly]

Ok, but when I go to plot the functions do I need to call both functions or just the main? The main function is the newton raphson method for finding roots and the whole purpose of this nested function is to adapt the newton method to use the central difference method to numerically derive the roots.

[Azzi Abdelmalek]

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]

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]

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