function babydecouple3
global m n
m=2;n=3;
keyboard
return


function fc = phicoeffL(xind)
global n
a=sym('a','real');
b=sym('b','real');
A=[[a b];[1-a,1-b]];
x = i2c(xind)+1;
p = 1;
for i=1:n-1
  p = p * A(x(i+1),x(i));
end
fc = p/2;
return

function fc = phicoeffR(xind)
global n
a=sym('a','real');
b=sym('b','real');
A=[[a b];[1-a,1-b]];
x = i2c(xind)+1;
p0 = [1/2;1/2];
p = 1;
for i=0:n-1
  Aip = (A^i)*p0;
  p = p * Aip(x(i+1));
end
fc = p;
return



function lhs = symlhs
global n
lhs = '';
for xind=1:2^n
  fc = phicoeffL(xind);
  fcs = char(fc);
  xs = i2cs(xind);
  lhs = [lhs fcs '*x' xs '+'];
end
lhs = lhs(1:end-1);
return

function rhs = symrhs
global n
a=sym('a','real');
b=sym('b','real');
rhs = '';
for xind=1:2^n
  fc = phicoeffR(xind);
  fcs = char(fc);
  xs = i2cs(xind);
  rhs = [rhs fcs '*x' xs '+'];
end
rhs = rhs(1:end-1);
H = 0;
for i=0:n-1
  H = H + (a-b)^i;
end
rhs = ['(' char(H) ')(' rhs ')'];
return



function i=c2i(c)
global m n
dims = repmat(m,[1 n]);
i = coord2ind(c+1,dims);
return

function c=i2c(i)
global m n
dims = repmat(m,[1 n]);
c = ind2coord(i,dims)-1;
return

function cs = i2cs(i)
global m n
dims = repmat(m,[1 n]);
c = ind2coord(i,dims)-1;
cs = num2str(c);
cs = strrep(cs,' ','');
return