% Testroutine 
% Achtung, die Laufzeit betraegt ca 1 min
%
% Das Programm StdApproxMat hat die Syntax
% 
% A = StdApproxMat(U,V,I,J,h);

h = .12;
TstNearestInner
s = linspace(0,1,17);
[U,V] = ndgrid(s,s);
f = find(U.^2+V.^2<1);
U = U(f);
V = V(f);
G = exp(1-(U.^2+V.^2));

A = StdApproxMat(U,V,I,J,h);

F = A\G;

r = linspace(0.9,1,5);
w = linspace(0,pi/2,20);

[R,W] = ndgrid(r,w);
f = 0*R;

K = [I,J];
nK = length(K);
mK = max(real(K));
T = (-3:mK+4)*h;
m = length(T) - 4;
P = zeros(m,m);

for r = 1:length(R(:))
  u = R(r)*cos(W(r));
  v = R(r)*sin(W(r));
  for k = 1:nK
    P(:) = 0;
    P(real(K(k))+4,imag(K(k))+4) = 1;
    f(r) = f(r) + F(k)*seval(P,T,T,u,v);
  end
end

Ae = A*E;
Fe = Ae\G;
F = E*Fe;
fe = 0*R;

for r = 1:length(R(:))
  u = R(r)*cos(W(r));
  v = R(r)*sin(W(r));
  for k = 1:nK
    P(:) = 0;
    P(real(K(k))+4,imag(K(k))+4) = 1;
    fe(r) = fe(r) + F(k)*seval(P,T,T,u,v);
  end
end

figure(1)
clf reset
mesh(R.*cos(W), R.*sin(W), f - exp(1-R.^2))
title('Fehler Standard')

figure(2)
clf reset
mesh(R.*cos(W), R.*sin(W), fe - exp(1-R.^2))

title('Fehler erweitert')