function [decimal_space]=decoding(min_confines,max_confines,binary_space,bits)

%Decoding 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 AAPP dat)
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%Decoding is the second step in SGA(Simple Genetic Algorithm )
%this decoding function is deconding the binary value which coded by coding
%function ,that is to say you should use coding function first
%it can transfer binary value to decimal value 
%~
%Usage:
%decimal_space=decoding(min_confines,max_confines,binary_space,bits,bits_No)
% in the method of 'X=Decimal*decimal_step+min_confines'
%~~
%decimal_space is the decimal number which from binary_space
%min_confines is the minimum of input value in decimal-space
%max_confines is the maximum of input value in decimal-space
%~~~
%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]=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])
% [decimal_space]=decoding([1,2,3,4],[7,8,9,10],binary_space,bits)

%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%  See Also CODING ,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_confines<max_confines)~=1  % min_confines & max_confines check
        disp(':( Warning!! One of The Min=Min! Check your Data!')
        break;
else   
   [population,bits_sum]=size(binary_space);
   confines_deta=(max_confines-min_confines);
   coded_step=confines_deta./(2.^bits-1);
   [line,parameter_numbers]=size(min_confines);
   %~~~~~~~~bits_No is important to all the sga
%bits_No is important
bits_No=[0,bits];
% to find out which is the binary parameter

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

% important ,matrix of matlab begins from 1 ,not 0

       for i=parameter_numbers:-1:1
           for j=population:-1:1                      
               for k=bits_No(i+1):-1:(bits_No(i)+1)
                   twos(j,k)=pow2(bits_No(i+1)-k)*binary_space(j,k);
                end 
                   twos_sum(j,i)=sum(twos(j,:),2);
                   decimal_space(j,i)=twos_sum(j,i)*coded_step(i)+min_confines(i);
           end  
           twos=zeros(population,bits_sum);%clear twos at present i 
           % X=Decimal*coded_step+min_confines
        end   
      
%~~~~~~~~~~~~~~~~~~plot~~~~~~~~~~~~~~`     
% figure(2)
%    i=population:-1:1;
%    plot(decimal_space(i,:),i,'*');
%    xlabel('initialized decimal-space');
%    ylabel('population');
%    title('the corresponding deciaml-space of binary-space');
%    grid on;      
end

%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% end of decoding