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function [binary_space,bits_sum,bits]=coding(min_confines,max_confines,population,decimal_step) 
 
%Coding Function Of Simple Genetic Algorithm Program (Version 1.0.0.1 ) 
%Support multi-dimesion parameters 
%By chen yi ,CQU .QQ:2376635  Email:cdey@10mail.net  (April,17th,2002) 
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
%Coding is the first step in SGA(Simple Genetic Algorithm ) 
%this coding function is to code variable by binary coding method   
%~ 
%Usage: 
%[binary_space,bits_sum,bits_No,bits]=coding(min_confines,max_confines,population,decimal_step) 
% 
%in this: 
% 
%min_confines is the minimum of input value in decimal-space 
%max_confines is the maximum of input value in decimal-space 
%i.e. X belong to [min_confines,max_confines] 
% min_confines < max_confines 
%~~ 
%decimal_step is the search step in decimal-space 
%it must be smaller than (max_confines-min_confines)/2 
%~~~ 
%population is the random decimal value in  [min_confines,max_confines] 
% it is given by yourself and it must be integer and larger than 0 
% 
%binary_space is the coded space in 0 or 1 
% 
%bits_No is the genetic position pointer of binary_space 
% 
%bits_sum is the total length of the binary_space of all the parameters 
% 
%bits is the length of every parameter 
%~~~~ 
%e.g.  
% f(x)=2x  x belong to [1,7] 
% [binary_space,bits_sum,bits_No,bits]=coding(1,7,10,0.01) 
%e.g. 
% f(x)=1./a+sin(b)+exp(c)+log2(d)+10 , a,b,c,d belong to [1,7],[2,8],[3,9],[4,10] 
% [binary_space,bits_sum,bits]=coding([1,2,3,4],[7,8,9,10],10,[0.01,0.01,0.01,0.01]) 
% 
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
%  See Also DECODING ,SELECTION ,CROSSOVER,MUTATION,FITNESS, 
%           FITNESS_FUNCTION, SGA	 
% 
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
 
 
if      size(min_confines)~=size(max_confines) % min_confines & max_confines check 
        disp(':( Warning !! The size of min_confines&max_confines do not match !') 
        break;%Reinforce the robust of this function  
elseif (min_confines0)~=1 % population check 
       disp('Warning!! every population members must be even Integer and larger than 0') 
       break; 
elseif mod(population,2)~=0 % population check 
       disp('Warning!! the population must be even integer and larger than 0') 
       break;                      
elseif (decimal_step>=0)~=1 
       disp('Warning!! the decimal_step must be >= 0 ') 
       break; 
else 
   %add all the binary parameters into a long-chromosome   
   % count the sum bits 
confines_deta=(max_confines-min_confines); 
bits=ceil(log2(confines_deta./decimal_step)); 
   if min(bits>=1)~=1 
      disp('the bits must be > 0 ,please chose the min_confines and max_confines again.') 
   break; 
   end 
bits_sum=sum(bits,2); 
[line,parameter_numbers]=size(bits); 
%next->Use sparse matrix to store binary_space 
binary_space=(randint(population,bits_sum));  
 
%~~~~~~~~~~~~~plot~~~~~~~~~~~~~~~ 
%figure(1) 
%plot binary_space in sparse model 
%binary_space_sparse=sparse(binary_space);  
%spy(binary_space_sparse); 
%hold on; 
%ini bits_No 
 
%bits_No is important 
bits_No=[0,bits]; 
% to find out which is the binary parameter 
%i=0:0.1:population; 
for i=1:1:parameter_numbers 
   %to avoid that Index exceeds matrix dimensions 
    bits_No(i+1)=bits_No(i+1)+bits_No(i); 
end 
 
%title('the Initialization of the coded binary-space in sparsity pattern'); 
%xlabel('Non-Zero bits'); 
%ylabel('Population'); 
   
end 
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
%  end of coding