How do I create a function and run it.

I don't know anything about MATLAB beyond how to create a new script file and type stuff into it.

I copied the following code from a course handout. So I assume it is correct.

    %Program 1.1 Bisection Method
    %Computes approximate solution of f(x)=0
    %Input: function handle f; a,b such that f(a)*f(b)<0,and tolerance tol
    %Output: Approximate solution xc

    xc=bisect(f,a,b,tol)

    if sign(f(a))*sign(f(b)) >= 0
        error('f(a)f(b)<0 not satisfied!') %ceases execution
    end

    fa=f(a)
    fb=f(b)

    while (b-a)/2>tol
        c=(a+b)/2;
        fc=f(c);
        if fc == 0  %c is a solution, done        
            break
        end
    end
    if sign(fc)*sign(fa)<0  %a and c make the new interval
        b=c;fb=fc;
    else                    %c and b make the new interval
        a=c;fa=fc;
    end
    xc=(a+b)/2;

It is supposed to solve a single-variable equation by bisection. I understand the bisection logic and the function flow logic seems obvious to me.

I want to give it a function, say x^5+x=1, and have it bracket in on x and get something close to 0.754877666. What do I type into the MATLAB command window to do this?

Question 2. Where do I find answers to simple questions like this? Is there a list of simple examples somewhere? I have gone through the "onramp" stuff and read the MATLAB Primer, which took hours, without learning how to just pass some variables to a pre-defined function.

[Stephen23]

"Question 2. Where do I find answers to simple questions like this?"

The MATLAB documentation is the most readable, browsable documentation of any language that I have seen or used. It is organized by topic, has links everywhere to related topics and functions, and gives working examples. The introductory tutorials are a good place to start learning fundamental MATLAB concepts:

https://www.mathworks.com/help/matlab/getting-started-with-matlab.html

Ten minutes practicing using the contents (LHS of the page) will be time well spent: click up a level, see the topics, get used to navigating around!

https://www.mathworks.com/matlabcentral/answers/228557-experts-of-matlab-how-did-you-learn-any-advice-for-beginner-intermediate-users

Answer 1

[Richard Zappulla]

Every function in MATLAB uses the following structure:

 function [ouput_vars] = foo(input,vars)
 %
 % Code goes here....
 % 
 end

In your case, you want the first line to read:

 function xc = bisect(funcHandle, a, b, tol)

where funcHandle is a handle for your function. The syntax of a function handle is:

 funcHandle = @(variables)(equation)

To use the function, you simply call the variable name as a function, i.e.

 f_of_x = funcHandle(pi);

Since your bisection method expects a function of the form f(x) = 0, your function handle would be,

 your_fun = @(x)(x^5 + x -1);

Hope this helps!!

[Jay Gourley]

Yes, that helps. Thanks for anticipating that I needed more than just the command to type. Your explanation of the breakdown helps a lot.

Answer 2

[John BG]

function   xc=bisect(f,a,b,tol)
    if sign(f(a))*sign(f(b)) >= 0
        error('f(a)f(b)<0 not satisfied!') %ceases execution
    end
    fa=f(a)
    fb=f(b)
    while (b-a)/2>tol
        c=(a+b)/2;
        fc=f(c);
        if fc == 0  %c is a solution, done        
            break
        end
    end
    if sign(fc)*sign(fa)<0  %a and c make the new interval
        b=c;fb=fc;
    else                    %c and b make the new interval
        a=c;fa=fc;
    end
    xc=(a+b)/2;
end

if you find these lines useful would you please mark my answer as Accepted Answer?

To any other reader, if you find this answer of any help please click on the thumbs-up vote link,

thanks in advance for time and attention

John BG

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