How to Implement the Bisection Root-Finding Method in MATLAB?

[dillonmhudson]

Homework Statement

Create and test a MATLAB function called bisection that implements the bisection root finding method. You will have to use a function handle and exit flag coding.

Homework Equations

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The Attempt at a Solution

% bisection.m

function [root, err, iter, exitFlag] = bisection (fun, lb, ub, errMax, iterMax)

% This function performs the bisection algorithm on a function to
% locate a root of the function (location where it crosses zero). The
% function must be of a single variable and must return a scalar result
% (i.e., a scalar function of a scalar argument). 
% 
% The approximation loop is controlled by three termination criteria:
%  - estimate of the approximation error is less than errTol
%  - number of iterations is greater than iterMax
%  - function value magnitude is less than funTol
%
% The initial bracket controls the search. The initial bracket must be
% defined such that the sign of the function is opposite at each end of the
% bracket (to ensure a zero crossing exists between the two. THERE IS NO
% ERROR CHECKING for this in the current code.
%
% Inputs:  @fun = function that is the subject of the root-finding
%          lb = lower bound of the bisection search bracket
%          ub = upper bound of the bisection search bracket
%          errMax = maximum acceptable relative approximation error
%          iterMax = maximum number of iterations
%
% Outputs: root = approximation of root location
%          err = relative approximation error of solution
%          iter = number of iterations taken to find the solution
%          exitFlag = indicates termination status of function
% 
% Exit Flag Encoding: 1: Alrogithm terminated normally (due to error being
%                        sufficiently small)
%                     0: Alrogithm terminated due to maximum number of
%                        iterations being reached
%                    -1: Algorithm terminated due to invalid bracket 
%                        specification (no root in bracket)
%                    -2: Algorithm terminated due to invalid return value
%                        from function fun (e.g., NaN, Inf, empty brakets)

%%%%%%%%%%%%%%%%%%%%%%%%%%
% GENERAL INITIALIZATION %
%%%%%%%%%%%%%%%%%%%%%%%%%%
iter = 0;       % iteration counter variable
done = false;   % Boolean variable to control looping
root = (ub+lb)/2; % initial approximation of root location 
err = 100*abs([ub-lb]/[ub+lb]); % estimate of error

if fun(lb)*fun(ub)>0
    exitFlag = -1;
    error('invalid bracket: exitFlag = %g\n',exitFlag);

elseif fun(root)+errMax>0 && fun(root)-errMax<0;
    exitFlag = 1;
    err = 100*abs([ub-lb]/[ub+lb]); % estimate of error
    done=true;
        
elseif fun(lb)+errMax>0 && fun(lb)-errMax<0;
    exitFlag = 1;
    err = 100*abs([ub-lb]/[ub+lb]); % estimate of error
    root=lb;
    done=true;
        
elseif fun(ub)+errMax>0 && fun(ub)-errMax<0;
    exitFlag = 1;
    err = 100*abs([ub-lb]/[ub+lb]); % estimate of error
    root=ub;
    done=true;

elseif fun(lb)==NaN || Inf || -Inf || isempty(lb);
    exitFlag = -2;
    error('invalid lower bound: exitFlag = %g\n',exitFlag);
    done = true;

elseif fun(ub)==NaN || Inf || -Inf || isempty(ub);
    exitFlag = -2;
    error('invalid upper bound: exitFlag = %g\n',exitFlag);
    done = true;

else
    return;
     
end

%%%%%%%%%%%%%%%%%%%%%%
% MAIN ITERATION LOOP
%%%
while ~done
    
    iter = iter+1;      % increment iteration counter
    
        % determine which way to go with next bracket
    if fun(lb)*fun(root)<0
        ub = root;
    else
        lb = root;
    end
    
    % update approximation of root location based on new bracket
    root = (ub+lb)/2;     
    
    err = 100*abs([ub-lb]/[ub+lb]); % estimate of error
        
    % loop control -- check for termination criteria
    if err<errMax
        exitFlag = 1;
        done = true;
    elseif iter >= iterMax
        exitFlag = 0;
               
        % if the next line executes, it means at least one of the
        % termination criteria was true
        done = true;    
    end

end

Example of function call:

[root, err, iter, exitFlag] = bisection (@(x)x^3-3*x,-4,2,.0001, 1000)

My problem with the code is that the error flag -2 keeps popping up when I am trying to find a root

 

[Office_Shredder]

Two things: first, Doing fun(lb)==NaN doesn't work. Try it out, NaN==NaN returns 0, not 1. There's a function isnan that you should use instead,
isnan(fun(lb))

Second, you have a serious parenthesis problem. fun(lb)==NaN || Inf doesn't do (fun(lb)==NaN)||(fun(lb)==Inf), it does (fun(lb)==NaN) || Inf and Inf counts as true so your program always takes that part of the if statement and runs it

 

[dillonmhudson]

Ok, thanks that helps. Between you and a TA I got it to work so thank you!