% this takes the interval [a,b], and starts by integrating on an interval 
% with n mesh-points.  It then takes finer and finer meshes until the error
% is less than the given tolerance (tol).
%
% It then returns the area, the error, the mesh-size, and the number of
% flops it took to perform the integral using the trapezoidal rule:
% function [area,h,error,t_run] = trap_filter(a,b,n,tol)

function [area,h,error,t_run] = trap_filter(a,b,n,tol)

% set the initial error to be larger than tol so that we can enter the
% following while loop:
error = 2*tol;

% enter the while loop.  CAREFUL, need to take the absolute value of the
% error since if it's negative we'd exit the while loop immediately.
while abs(error) > tol, 

% set the flops count to zero:
  flops(0);
% call the trapezoidal rule subroutine with n mesh-points:
  [area,h,error] = trap(a,b,n);
  t_run = flops;
% now want to double the number of intervals and try again.  There
% are (n-1) intervals, so we want 2*(n-1) = 2n-2 intervals and 
% 2n-1 mesh-points.  Since n is the present number of mesh-points,
% we replace n with 2n-1:
  n = 2*n-1;

end