example.m

% Example script

format long
% Computes weights and nodes of TAME with N=10 points; use a circle of radius 1 as domain
n=10; r=1;
tame_method = AAAweights(n,'Zshape','circle','r',r);
% Eliminate conjugate nodes, to use only N'=5 evaluations 
tame_method = cleanup_conjugates(tame_method)

% f(t) = exp(-t) has Laplace Transform  g(s) = 1/(s+1)
% Inverse Laplace transform of g(s), evaluated in t=1
t = 1

% exact value
fprintf('exact   = %.15f\n', exp(-t))
% ans =   0.367879441171442

fprintf('tame    = %.15f\n\n', ilt(@(s) 1/(s+1), t, tame_method))
% ans =   0.367879441171413

% Comparison with other methods
euler_method  = ILTweights(5,'euler');
fprintf('euler   = %.15f\n', ilt(@(s) 1/(s+1), t, euler_method))
gaver_method  = ILTweights(6,'gaver');
fprintf('gaver   = %.15f\n', ilt(@(s) 1/(s+1), t, gaver_method))
talbot_method = ILTweights(5,'talbot');
fprintf('talbot  = %.15f\n', ilt(@(s) 1/(s+1), t, talbot_method))
cme_method    = ILTweights(5,'cme');
fprintf('cme     = %.15f\n', ilt(@(s) 1/(s+1), t, cme_method))
zakian_method = ILTweights(4,'zakian');
fprintf('zakian  = %.15f\n', ilt(@(s) 1/(s+1), t, zakian_method))