How do I take input from a user (equation in terms of x) and convert it into an equation matlab would understand and use this to perform a differentiation in order to perform a newton-raphson method.

function y=newtraph(varargin)

% newtraph: Newton-Raphson root location zeroes

% y=newtraph(varargin):

% uses Newton-Raphson method to find the root of func

% input:

% func = name of function

% dfunc = name of derivative of function

% xr = initial guess

% es = desired relative error (default = 0.0001)

% maxit = maximum allowable iterations (default = 50)

% p1,p2,... = additional parameters used by function

% output:

% root = real root

% ea = approximate relative error

% iter = number of iterations

xr=input('input initial guess: ');

func=input('input function in terms of x: ');

func=vectorize(char(func));

eval(['f = @(x) ' func]);

dfunc=diff(func,x,1);

es=0.0001;

maxit=20;

iter = 0;

while (1)

xrold = xr;

xr = xr - func(xr)/dfunc(xr);

iter = iter + 1;

if xr ~= 0, ea = abs((xr - xrold)/xr); end

if ea <= es iter >= maxit, break, end

end

root = xr;

display(root);

end

% this is the error message I keep getting:

 % ??? Error using ==> input

% Undefined function or variable 'x'.

%Error in ==> newtraph at 18

% func=input('input function in terms of x: ');

Answer 1

[Sergio E. Obando]

You could use something like this:

syms f(x)
xr=input('input initial guess: ');
func=input('input function in terms of x: ','s');
f(x) = str2sym(func)
dfunc=diff(f,x)
func = matlabFunction(f)
dfunc = matlabFunction(dfunc)

Otherwise, a numerical approach may look like this:

func = @(X) X.^2 - 4;
dfunc = @(X) 2*X;
nIter = 1000;
tol = 0.001;
x = zeros(1,nIter);
x(1) = 1;
for ii = 1:nIter
    
    x(ii+1) = x(ii) - f(x(ii))/dfdx(x(ii));
    if abs(f(x(ii+1))) < tol
        disp(x(ii+1));
        break
    end
end