function out = cdemo(n,auto,m)
%
% April 2006. 
% A simple driver to run typical examples for ccf 
% for negative parameter values also include Alex Burnett's implementations
% The value of "auto" is palnned to be used for the speed of the animations
%
% More basic examples: 
% z, conj(z), i*z, 1/z, real(z), z.^2, z.^3
% 1./(z.^2-1), (z.^2+1)./(z.^2-1)
% finite Taylor and Laurent approximations
% exp(z), sin(z), cos(z)
% exp(1/z), sin(1/z)
% sqrt(z), -sqrt(z), log(z), sqrt(z^2-1)

if (nargin < 3), m    = 3; end
if (nargin < 2), auto = 0.3; end
if (nargin < 1), n    = 0;   end

%% polynomial and rational functions
%% n=0 : k-th powers
if n==0 for k=0:20; ccf([1 zeros(1,k)],3,111,0), figure(gcf), pause(0.3), end, end
%% n=1 : polynomials (z^k-1)
if n==1 for k=0:20; ccf([1 zeros(1,k-1) -1],3,111,0), figure(gcf), pause(auto), end, end
%% n=2 : polynomial functions: merging m singularities 
if n==2 for k=-2:0.1:2; ccf([1 zeros(1,m-1) k^3]), figure(gcf), pause(auto/2), end, end
%% n=3 : rational functions: merging m singularities 
if n==3 for k=-2:0.1:2; ccf([zeros(1,m) 1;1 zeros(1,m-1) k^3]), figure(gcf), pause(auto/2), end, end
%% n=4 : rational functions 
if n==4 for k=0:5; ccf([1 zeros(1,k) 1;1 zeros(1,k) -1]), figure(gcf), pause(auto), end, end
%% n=5 : pole-zero cancellation, increasing control gain k of transfer function 
if n==5 for k=[-10:0.5:20] ; ccf([1 0 9;1 k 9],10); figure(gcf), pause(0.01), end, end


%% zoom out of elementary exp, trig, and hyperbolic functions
%% n=6 : zoom out of exp
if n==6 for k=1:20; ccf('exp(z)',k,111,0), figure(gcf), pause(auto), end, end
%% n=7 : zoom out of sin
if n==7 for k=1:20; ccf('sin(z)',k,111,0), figure(gcf), pause(auto), end, end
%% n=8 : zoom out of cos
if n==8 for k=1:20; ccf('cos(z)',k,111,0), figure(gcf), pause(auto), end, end
%% n=9 : zoom out of sinh
if n==9 for k=1:20; ccf('sinh(z)',k,111,0), figure(gcf), pause(auto), end, end

%% zoom in on elementary exp, trig, and hyperbolic functions at 1/z
%% n=11 : zoom out of exp
if n==11 for k=1:20; ccf('exp(1./z)',100/(3/2)^k,111,0), figure(gcf), pause(auto), end, end
%% n=12 : zoom out of sin
if n==12 for k=1:20; ccf('sin(1./z)',100/(3/2)^k,111,0), figure(gcf), pause(auto), end, end
%% n=13 : zoom out of cos
if n==13 for k=1:20; ccf('cos(1./z)',100/(3/2)^k,111,0), figure(gcf), pause(auto), end, end
%% n=14 : zoom out of sinh
if n==14 for k=1:20; ccf('sinh(1./z)',100/(3/2)^k,111,0), figure(gcf), pause(auto), end, end


%% Taylor approximations of transcendental functions
%% n=21 : zoom out of exp
if n==21 for N=[1:30]; 
        ccf([fliplr(1./cumprod(1:N)),1],10,111,-3); 
        figure(gcf), pause(auto); end; end;
%% n=22 : zoom out of exp
if n==22 for N=[1:30]; 
        ccf([fliplr(real(1./cumprod(i*[1:N]))),1],10,111,-3); 
        figure(gcf), pause(auto); end; end;
%% n=23 : zoom out of exp
if n==23 for N=[1:30]; 
        ccf([fliplr(imag(1./cumprod(i*[1:N]))),0],10,111,-3); 
        figure(gcf), pause(auto); end; end;
%% n=24 : zoom out of exp
% nice mistake -- lots of double roots for "obvious reasons"
if n==24 for N=[1:30]; 
        ccf([fliplr(imag(1./cumprod(i*[1:N]))),1],10,111,-3); 
        figure(gcf), pause(auto); end; end;
%

%% Successive (symmetric) Laurent expansion
%% series for 1/(z-1)(z-2) on the annulus
if n==31
    N=40;r=2;R=3;C=[[-(1/R).^[N+1:-1:1],r.^[0:N-1]];[zeros(1,N),1,zeros(1,N)]];
    for k=0:N; ccf(C(:,N+1-k:N+1+k),2*abs(R)); figure(gcf), pause(auto); end;
end
% Remainder terms for the same:
%% series for 1/(z-1)(z-2) on the annulus
if n==32
    N=40;r=2;R=3;C=[[-(1/R).^[N+1:-1:1],r.^[0:N-1]];[zeros(1,N),1,zeros(1,N)]];
   for k=0:N; ccf(C(:,N+1-k:N+1+k),[0,1,-r-R;1,-r-R,r*R],2*abs(R));
       figure(gcf), pause(auto);end;
end;

%% Alex Barnett's Taylor pix
%% % show identity function
if n==-9
	clear opt
	opt.slice = 0.3;
	figure; set(gcf,'Units','normalized','Position',[.3 .1 .4 .8]);
	opt.func = 'z';                
	show_zser([], opt);
    pause; close all;
end;

%%  show exp function
if n==-8
	clear opt
	opt.slice = 0.3;
	figure; set(gcf,'Units','normalized','Position',[.3 .1 .4 .8]);
	opt.func = 'exp(z)';           %
	show_zser([], opt);
    pause; close all;
end;

%% exponential convergence: converges everywhere 
if n==-7
	clear opt
	opt.slice = 0.3;
	figure; set(gcf,'Units','normalized','Position',[.3 .1 .4 .8]);
	opt.func = 'exp(z)';           
	for n=1:20; show_zser([1 1./cumprod(1:n)], opt); drawnow; pause(auto); end;
    pause; close all;
end;

%% pole on real axis at 1
if n==-6
	clear opt
	opt.slice = 0.3;
	opt.func = '1./(1-z)';         
	opt.win = 1.4;
	for n=1:20; show_zser(ones(1,n+1), opt); drawnow; pause(0.2); end;
    pause; close all;
end;

%% rational two simple poles 
if n==-5
	clear opt
	opt.slice = 0.3;
	opt.func = '1./(1+z.^2)';      
	opt.win = 1.4;
	for n=1:50; show_zser([1 cos((1:n)*pi/2)], opt); drawnow; end;
    pause; close all;
end;

% log singularity at 0, expanded about 1 
if n==-4
	clear opt
	opt.slice = 0.3;
	opt.func = 'log(z)';          
	opt.z0 = 1;
	opt.win = 2.2;
	for n=1:20; show_zser([0 -cos(pi*(1:n))./(1:n)], opt); drawnow; end;
    pause; close all;
end;

return;