MATLAB Newton Raphson Method with a function with array/matrix variables

clc; close all; clear all;

syms x; 
g = [1 2 3 4 5]

for i= 1:5 
    f=g(i)*exp(x)-1; %Enter the Function here
    df=diff(f); %The Derivative of the Function
    y = newtonraphson(x,f, df, 5, 0.001);
    fprintf('%.4f', y);
end

function y = newtonraphson(x, f, df, n, x0)
    rounding = 5*10^-(n+1);
    
    for i=1:100
        f0=vpa(subs(f,x,x0)); %Calculating the value of function at x0
        f0_der=vpa(subs(df,x,x0)); %Calculating the value of function derivative at x0
        y=x0-f0/f0_der; % The Formula
        err=abs(y-x0);
        
        if err<rounding %checking the amount of error at each iteration
            break;
        end
        x0=y;
    end
    
    y = y - rem(y,10^-n);
    fprintf('The Root is : %f \n',y);
    fprintf('No. of Iterations : %d\n',i);
end

I am learning to use newton raphson method to solve equations.

My function works when g is a single value, say 1 or x. This is without the for loop, for a basic equation.

I added the for loop as I wanted g to have a matrix/array input. Would appreciate the guidance. Thank you!

[Kenneth Chia]

Error using symengine

Dimensions do not match.

Error in sym/privBinaryOp (line 1034)

Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});

Error in * (line 329)

X = privBinaryOp(A, B, 'symobj::mtimes');

Error in test_newton (line 7)

f=g*exp(x)-1; %Enter the Function here

[Kenneth Chia]

I got this error message. My code is not 1034 long. Only 32.

Am not sure why there is an error with my equation on line 7.

Answer 1

[Alan Stevens]

You could do it like this

f = @(x,g) g.*exp(x) - 1;
df = @(x,g) g.*exp(x);
g = [1 2 3 4 5];

for i= 1:numel(g) 
    x0 = 0.001;
    y = newtonraphson(f, df, g(i), numel(g), x0);
    fprintf('%.4f  \n', y);
end

function y = newtonraphson(f, df, g, n, x0)
    rounding = 5*10^-(n+1);
    
    for i=1:100
        f0 = f(x0,g); %Calculating the value of function at x0
        f0_der=df(x0,g); %Calculating the value of function derivative at x0
        y=x0-f0/f0_der; % The Formula
        err=abs(y-x0);
        
        if err<rounding %checking the amount of error at each iteration
            break;
        end
        x0=y;
    end
    
    y = y - rem(y,10^-n);
    fprintf('The Root is : %f \n',y);
    fprintf('No. of Iterations : %d\n',i);
end

[Kenneth Chia]

Thank you! It works!

I also solved my problem too! I just needed a new variable to store my computed values.

syms x;

g = [1 2 3 4 5];
mat = [];

for i= 1:5 
    f=g(i)*exp(x)-1; %Enter the Function here
    df=diff(f); %The Derivative of the Function
    y = newtonraphson(x,f, df, 5, 0.001);
    mat(i) = y;  
    fprintf('%.4f', mat(i));
end

function y = newtonraphson(x, f, df, n, x0)
    rounding = 5*10^-(n+1);
    for i=1:100
        f0=vpa(subs(f,x,x0)); %Calculating the value of function at x0
        f0_der=vpa(subs(df,x,x0)); %Calculating the value of function derivative at x0
        y=x0-f0/f0_der; % The Formula
        err=abs(y-x0);
        if err<rounding %checking the amount of error at each iteration
            break;
        end
        x0=y;
    end
    
    y = y - rem(y,10^-n);
    
    fprintf('The Root is : %f \n',y);
    fprintf('No. of Iterations : %d\n',i);
end