Function functions of fixed-point iteration

Hello,

I'm trying to make function functions, but I have an error in the last row and I don't know that's wrong:

clc;
close all;
clear all;
syms x;
fun=@(x)-0.0641*x^3+1.0889*x^2-3.8260*x+0.6364;
n=input('Enter the number of decimal places:');
x0 = input('Enter the intial approximation:');
[t]=F[@fun, x0,n]

My function F is:

function [t] = F(fun, x0, n)
%   Detailed explanation goes here
g=diff(fun); 
epsilon = 5*10^-(n+1)
i=1;
rng(0,'twister'); 
alpha = -2/vpa(subs(g,x,x0));
x_current = x0;
while i~=200
    phi_of_x_at_x_current= x_current + (alpha*vpa(subs(fun,x,x_current))); 
 
err=abs(phi_of_x_at_x_current-x_current); 
if  abs(1+alpha*vpa(subs(g,x,x_current)))>=1 
    alpha = -1*(2/vpa(subs(g,x,x0))*rand);
    i=1;
elseif err<epsilon
break
end
x_current =  phi_of_x_at_x_current;
i=i+1;
end
phi_of_x_at_x_current = phi_of_x_at_x_current - rem(phi_of_x_at_x_current,10^-n);
fprintf('Answer: %f \n',phi_of_x_at_x_current);
end

[KALYAN ACHARJYA]

Is this you are looking for?

syms x;
fun1=@(x)-0.0641*x^3+1.0889*x^2-3.8260*x+0.6364;
n=input('Enter the number of decimal places:');
x0 = input('Enter the intial approximation:');
[t]=F(fun1,x0,n);
Please note that I have changed the fun name to fun1

[KALYAN ACHARJYA]

@madhan ravi Comment

I think it would be better to remove @(x) Kalyan, what do you think? Because diff command doesn’t work for function handle unless evaluated.

[KALYAN ACHARJYA]

syms x;
fun1=-0.0641*x^3+1.0889*x^2-3.8260*x+0.6364;
n=input('Enter the number of decimal places:');
x0 = input('Enter the intial approximation:');
[t]=F(fun1,x0,n)

Result:

Enter the number of decimal places:2
Enter the intial approximation:3
epsilon =
    0.0050
Undefined function or variable 'x'.
Error in F (line 7)
alpha = -2/vpa(subs(g,x,x0));
Error in ans_may19 (line 8)
[t]=F(fun1,x0,n)
>> 

[KALYAN ACHARJYA]

I am sure, this doesnot work

[t]=F[@fun, x0,n]

[madhan ravi]

Haven’t checked the code perhaps:

fun1(x)=-0.0641*x^3+1.0889*x^2-3.8260*x+0.6364;
t=F(fun1(x),x0,n)

Answer 1

[Sulaymon Eshkabilov]

Hi,

You were almost there and just overlooked at one point with: g=diff(fun); that requires symbolic differentiaion w.r.t the variable x. Another very minor point is output variable name t that was assigned but not given any output value within F.m. I have chosen phi_of_x_at_x_current that can be changed to any output calc's from F.m

Here is the corrected codes. Note that I have done some name changes not to get confused with fun and g which are substitute with FF and G. I like upper cases for the sake of visibility.

function phi_of_x_at_x_current = F(FF, x0, n)
%   Detailed explanation goes here
syms x
G=diff(FF, x);
epsilon = 5*10^-(n+1);
i=1;
rng(0,'twister');
alpha = -2/vpa(subs(G,x,x0));
x_current = x0;
while i~=200
    phi_of_x_at_x_current= x_current + (alpha*vpa(subs(FF,x,x_current)));
    err=abs(phi_of_x_at_x_current-x_current);
    if  abs(1+alpha*vpa(subs(G,x,x_current)))>=1
        alpha = -1*(2/vpa(subs(G,x,x0))*rand);
        i=1;
    elseif err<epsilon
        break
    end
    x_current =  phi_of_x_at_x_current;
    i=i+1;
end
phi_of_x_at_x_current = phi_of_x_at_x_current - rem(phi_of_x_at_x_current,10^-n);
fprintf('Answer: %f \n',phi_of_x_at_x_current);
end

clc;
close all;
clear variables
syms x
FF=@(x)-0.0641*x^3+1.0889*x^2-3.8260*x+0.6364;
n=input('Enter the number of decimal places:   ');
x0 = input('Enter the intial approximation:    ');
OUT = F(FF, x0, n);

>> Enter the number of decimal places:   3
>> Enter the intial approximation:    55
Answer: 12.188000 

Good luck.

[madhan ravi]

Answers moved for a consistent thread:

Sulaymon Eshkabilov:

Hi,

It looks like that your matlab version is a bit older than what I am using and there is a problem in Symbolic math toolbox of matlab of older versions in data type conversion (automatic conversion). In later versions, this issue is resolved and automatically done.

Fo my curiosity what version of MATLAB are you are?

Now all problems are resolved. You would need to use this functiton file.

function phi_of_x_at_x_current = F(FF, x0, n)
%   Detailed explanation goes here
syms x
G=diff(FF, x);
epsilon = 5*10^-(n+1);
i=1;
rng(0,'twister');
alpha = -2/vpa(subs(G,x,x0));
x_current = x0;
while i~=200
    phi_of_x_at_x_current= x_current + (alpha*vpa(subs(FF,x,x_current)));
    err=abs(phi_of_x_at_x_current-x_current);
    if  abs(1+alpha*vpa(subs(G,x,x_current)))>=1
        alpha = -1*(2/vpa(subs(G,x,x0))*rand);
        i=1;
    elseif err<epsilon
        break
    end
    x_current =  double(phi_of_x_at_x_current);
    i=i+1;
end
phi_of_x_at_x_current = double(phi_of_x_at_x_current) - rem(double(phi_of_x_at_x_current),10^-n);
fprintf('Answer: %f \n',phi_of_x_at_x_current);
end

Let me know your success.

Good luck and all the best.

pragiedruliai:

Hey,

Thank you for taking the time to find a solution.

Unfortunately, I can't stand why this code still doesn't work on my computer... I copied and pasted your code. It is written:

Error using subs
Expected input number 1, S, to be one of these types:
sym
Instead its type was function_handle.
Error in sym/subs (line 60)
validateattributes(F, {'sym'}, {}, 'subs', 'S', 1);
Error in F (line 11)
    phi_of_x_at_x_current= x_current + (alpha*vpa(subs(FF,x,x_current)));
Error in mini_2 (line 8)
OUT = F(FF, x0, n);

Sulaymon Eshkabilov:

Did you get it now corrected code running?