accuracy of fzero in finallzeros.m

Hi,

I am trying to solve a non-linear equation for multiple roots. I use a routine called findallzeros.m which calls fzero to find the roots. The routine works fine, however I can't figure out how to set the required accuracy (normally done by the TolX option of fzero) of the solution.

Any helpfull suggestions would be very much appreciated.

The matlab code:

.m

    function  x  =  findallzeros( fhandle, xguess, maxroots)
    %
    %    x = findallzeros( fhandle, xguess, maxroots)
    %   ==================================
    %
    %   attemps to find multiple roots of a function.
    %
    %  fhandle = function handle, prefix by @
    %  xguess = a scalar value used as initial guess
    %           ( = 0   if not supplied )
    %  maxroots = the number of roots needed
    %           ( = 1   if not supplied )

    %   (c) 2005 by Tomas Co
    %   @ Michigan Technological University

    x   = [ ];                

    if nargin==1
        xguess =0;
        maxroots = 1;
    end

    if nargin==2
        maxroots  = 1;
    end

    nroots = 0;

    while nroots<maxroots
        if  abs(feval(fhandle,xguess,[ ]))<=1e-16,
            xroot=xguess;
            % xguess results in zero value of objective function fhandle
            % --> xroot = xguess
        else
    %         options = optimset('TolX',2*eps(x));     
    %         options = optimset('TolX',1e-12);        
            [xroot,val,flag,output] = fzero(fhandle,xguess,[ ],x);
            % val is the value of the objective function (should converge
            % to zero).
            % x is the vector of old roots ?
            % flag describes the exit condition of fzero;
            % when flag = 1, fzero converged to solution xroot;
            % when flag < 0, fzero could not find a solution
            if flag <= 0
                return
            end
        end
        x=[x,xroot];
        nroots=nroots+1;
        xguess=xguess+0.1;
    end

the function:

      function f = test( x,oldroots )
      % this funcion is called by the findallzeros function to find all roots 
      % of function f

      aspectratio = 5;                             %aspect ratio of spherocylinder: L/D
      denom = pi./6 + (pi./4).*aspectratio;
      C1STAR = 2.*aspectratio.^(2)./denom;         %coefficient one of excluded volume expression
      %--------------------------------------------------------------------------
      %   calculate Aresn_alpha = f
      %--------------------------------------------------------------------------
      y = 0.425;                                     %packing fraction
      G = (4.*y - 3.*y.^2)./(8.*(1-y).^2);         %scaling factor: Areshs/8Nkt

      % Calculate modified Bessel functions I2 and I3
      I2 = besseli(2,2.*x);
      I3 = besseli(3,2.*x);

      I2prime = 2.*(I3 + I2./x); %derivative of I2(2*alpha) to alpha

      Q1 = G.*C1STAR.*pi;
      dummy1 = (1/sinh(x).^2).*( I2prime./2 - coth(x).*I2 );
      f = 1./x - atan(sinh(x)).*cosh(x)./sinh(x).^2 + Q1.*dummy1; 

      if length( oldroots ) > 0 ,
          f = f/polyval( poly ( oldroots ), x );
      end
      end

Note that fhandle = @test.

Thanks in advance!

Thijs

Answer 1

[Walter Roberson]

Uncomment the line

% options = optimset('TolX',1e-12);

and change the tolerance to whatever you want.

Then on the next line, change

[xroot,val,flag,output] = fzero(fhandle,xguess,[ ],x);

to

[xroot,val,flag,output] = fzero(@(g) fhandle(g,x),xguess,options);

Warning: the existing code is not correct even for using the default tolerance. Unless perhaps it was supported in a much earlier MATLAB, additional arguments cannot be passed to the target function by including the arguments directly in the fzero() call.