%VENICE_TRANS transforms the Venice coordinate data

clear('X0','L0','X1','L1');

clear('V','x','y','z','L','X','XX','U','a','m') ;


V = venice ;
z = V(:,4); %1973 data

%Transform Sample Locations

x = V(:,1);
y = V(:,2);

L = V(:,1:2);

X(:,1:2) = L;
X(:,3) = x.*y;
X(:,4:5) = L.^2;
X(:,6) = x.*(y.^2);
X(:,7) = y.*(x.^2);
X(:,8:9) = L.^3;

U = ones(length(X),1);

m = mean(X) ;

XX = X - U*m;

a = max(abs(XX));

XX = XX./(U*a);

X0 = XX;
L0 = L;

%Now start with grid locations

clear('V','x','y','L','X','XX','U','a','m','s1','u1',...
      'U1','s2','u2','U2','S'); 

s1 = [150:25:900]';
u1 = length(s1);
U1 = ones(u1,1);

s2 = [200:25:650]';
u2 = length(s2);
U2 = ones(u2,1);

S(:,1) = kron(s1,U2);
S(:,2) = kron(U1,s2);

V = S;

x = V(:,1);
y = V(:,2);

L = V(:,1:2);

X(:,1:2) = L;
X(:,3) = x.*y;
X(:,4:5) = L.^2;
X(:,6) = x.*(y.^2);
X(:,7) = y.*(x.^2);
X(:,8:9) = L.^3;

U = ones(length(X),1);

m = mean(X) ;

XX = X - U*m;

a = max(abs(XX));

XX = XX./(U*a);

X1 = XX;
L1 = L;