You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: conformal.m
    path of file: ./repos/chebfun
    
    the code of the file until where you have to start completion: function [f, finv, pol, polinv] = conformal(C, varargin)
%% CONFORMAL  Conformal map to unit disk
%   [F, FINV] = CONFORMAL(C, ctr) computes a conformal map F of the region
%   bounded by the complex periodic chebfun C to the unit disk and its inverse
%   FINV, with F(ctr) = 0 and F'(ctr) > 0.  Both maps are represented by
%   function handles evaluating rational functions.  If ctr is omitted it is

    
function [f, finv, pol, polinv] = conformal(C, varargin)
%% CONFORMAL  Conformal map to unit disk
%   [F, FINV] = CONFORMAL(C, ctr) computes a conformal map F of the region
%   bounded by the complex periodic chebfun C to the unit disk and its inverse
%   FINV, with F(ctr) = 0 and F'(ctr) > 0.  Both maps are represented by
%   function handles evaluating rational functions.  If ctr is omitted it is
%   set to 0.
%
%   CONFORMAL(..., 'tol', tol) uses tolerance tol instead of the default 1e-5.
%
%   CONFORMAL(..., 'plots') produces plots of the map and its inverse.
%
%   CONFORMAL(..., 'numbers') prints various quantities.
%
%   CONFORMAL(..., 'poly') uses a less robust algorithm based on polynomials
%                          instead of the Kerzman-Stein integral equation.
%
%   [F, FINV, POL, POLINV] = CONFORMAL(...) returns the poles of F and FINV.
%
%   This experimental code is good for smooth simple regions, but easy to break.
%
%   Examples:
%
%   C = chebfun('exp(pi*1i*t)','trig')*(1+.15*randnfun(.2,'trig'));
%   [f, finv] = conformal(C, 'plots');                               % random
%
%   C = chebfun('2*cos(t)+1i*(sin(t)+2*cos(t).^3)',[0 2*pi],'trig'); % Ellacott
%   conformal(C, 'poly', 'plots');                                   % blade
%
%   C = chebfun('exp(pi*1i*t)*(1+.3*cos(6*pi*t))','trig');
%   conformal(C, 'plots', 'tol', 1e-8, 'numbers');                   % snowflake
%
%   s = chebfun('s'); C = join(s-.5i,1+.5i*s,.5i-s,-1-.5i*s);
%   conformal(C, 'poly', 'plots');                                   % rectangle
%
% References:
% 
% A. Gopal and L. N. Trefethen, Representation of conformal maps by
% rational functions, Numer. Math. 142 (2019), 359--382.
%
% L. N. Trefethen, Numerical conformal mapping with rational 
% functions, Comp. Meth. Funct. Th. 20 (2020), 369-387.
%
% See also CONFORMAL2.

%%
%   Default algorithm:
%     (1) Solve discretized Kerzman-Stein integral equation
%     (2) Use AAA to approximate f and its inverse by rational functions
%
%   Alternative algorithm if 'poly' is specified:
%     (1) Use least-squares to find harmonic u s.t. u(z) = -log(abs(z-ctr)) on C
%     (2) Set w = u+iv (v = harmonic conjugate of u)
%     (3) Set f = z*exp(w(z-ctr));
%     (4) Use AAA to approximate f and its inverse by rational functions
%
%   Although in principle these algorithms should be embedded in the
%   Chebfun constructor, for simplicity in this numerically challenging
%   area we have not done that.
%
% This code was written by L. N. Trefethen in September 2019.  The
% Kerzman-Stein part originates with Anne Greenbaum and Trevor Caldwell.

t1 = tic;
[ctr, tol, plots, numbers, poly] = parseinputs(C, varargin{:});
err = Inf;
scl = norm(C-ctr, inf);

if poly == 0               % DEFAULT ALGORITHM: KERZMAN-STEIN INTEGRAL EQUATION

    M = 300;
    while err > tol
        M = M + 300;
        [g, Z, W] = kerzstein((C-ctr)/scl, M, 0);
        Z = Z*scl + ctr;
        gc = trigcoeffs(g);
        err = norm(gc([1:10 end