clear all
N=10000;
ERROLD = zeros(N,1);
ERRNEW = zeros(N,1);
for i=1:N

   [T,X,P] = planar_mov_randconf(2,3);
   
   Q=  observe_plucker( T,X,P);
   a = T{2}(1,1);
   b = T{2}(1,2);
   ROT = [a b 0; -b a 0; 0 0 1]; 
   t1 = [0;0;0];
   t2 = -ROT'*T{2}(1:3,4);
   c = t2(1);
   d = t2(2);
   [SOLS] = solve_23grevlex( Q ) ;
   true_sols=[a;b;c;d] ;
   terr = SOLS - true_sols*ones(1,4);
   err = min( sum(abs( terr)));
   
   
   l = observe_plucker_as_cell( T,X,P ) ;
   d2  =solve_23lex_mex( l  ) ;
   d2 = transpose( d2 ) ;
   
   SOLS;
   
   terr1 = d2(1:2,:)-[a;b] *ones(1,3);
   terr2 = SOLS(1:2,:) -  [a;b]*ones(1,4);
   
   errold = min(sum(abs(terr1)));
   errnew = min(sum(abs(terr2)));
   
   ERROLD(i) = errold;
   ERRNEW(i) = errnew;
   if not( mod(i,1000))
      disp( i )
   end
   
end


[h1,x1] = hist( log10(ERRNEW+eps), -20:0.25:2);

[h2,x2] = hist( log10(ERROLD+eps), -20:0.25:2);
 
mm =  1.1*max([h1 h2] ) ;
 
figure(2)
clf
p1 = plot( x1, h1,'-.' ,   x2, h2,'--' ) ;
hold on
%plot( x1(1:20:end), h1(1:20:end),'+' ) 

%plot( x2(10:20:end), h2(10:20:end),'>' ) 


l1 = legend( {'GrevLex','Lex' } ) ;

xlim( [-17 -7] ) 
ylim([0 mm])
set( gca , 'ytickmode', 'manual', 'yticklabel','', 'fontsize',20)
set( p1, 'linewidth',6 )

set( l1, 'fontsize',20 , 'linewidth', 4  )

xlabel('log_{10} of error')
ylabel('frequency')

set( gca, 'linewidth', 4  )