%VMG_CYCLE V-Cycle algorithm.
%
%       U_OUT = VMG_CYCLE(LEVEL, B, U_IN) uses the V-cycle to recursively 
%       solve the linear system AX=B at the given level.  If the optional 
%       starting value U_IN is not passed then U_IN is set to 0's.
%
% zhiyongfinish 2008
% Department of Computer Science
% University of xiangtan in China

function u_out = vmg_cycle(level, b1, t1)
if nargin == 2,   
   t1 = zeros(size(b1));
end

C_level = coarsest;
   
   u1       = smooth(level, b1, t1, 'pre');
   r1       = residual(level, b1, u1);
   
   b2       = restrict(level, r1);  
   
   t2       = zeros(size(b2));
   u2       =smooth(level+1,b2,t2,'pre'); % 殘量方程的解:2水平上
   r2       = residual(level+1, b2, u2);
   b3       = restrict(level+1, r2);
   
   
 %  ucc      = coarse_grid_solve(level+2, b3);% 殘量方程的解:3水平上
   uc       = interpolate(level+1,ucc);  %傳遞到2水平上
   u2       = u2 + uc;
   uc       = smooth(level+1,b2,u2,'post');
   
   correct = extrapolate(level, u2,ucc);  % 3 + 2 --->1 extrapolate
   u1       = u1 + correct;               
   u_out   = smooth(level, b1, u1, 'post');