function [P]= pdecmpo(A,C)
%
% Author: Nasser M. Abbasi, Northeastern University
%
% functionality:
%                        -1
% contruct the P   , or Q  , a constant nonsingular matrix which
% transforms  a nonobservable state equation into an observable
% one and nonobservable parts.
% The algorithm used is that of lemma 3.6 , page 74 of book
% computer aided analysis and design of Linear control systems
% by Jamshidi,Tarokh,Shafai
%
% arguments:
% A: IN, the A matrix of the state equation
% C: IN, the C matrix of the state equation
% P: OUT, the P transformation matrix 
%

if(nargin ~=2)
  error('Number of input arguments must be 2, the A and C matrix');
end

[row,col]= size(A);
if(row ~= col)
  error('Matrix A supplied must be SQUARE matrix');
end

%
% first find the observability matrix
%
ro= ltiro(A,C);
[original_row,original_col]= size(ro);

%
% t is the temp matrix we use to build P from
%
t(1,1:original_col) = ro(1,1:original_col);

old_ro_row= 2;
new_ro_row= 1;

%
% Now loop over all rows of Ro, select those that are
% Linearly independent with each others, ignore the rest
%
for i=2:original_row
    temp= t;
    temp(new_ro_row+1,1:original_col)= ro(i,1:original_col);
    %
    % rotate by 90 the matrix, because i want to see if rows
    % are L.I. to each others not the columns 
    % you have to be carfull here, make sure we check the
    % column number in the rot matrix with the row number of
    % the Ro matrix, if you draw a picture you'll see it
    %
    rot= rot90(temp);
    [row,col]= size(orth(rot));
    if (col==new_ro_row+1)
       t=temp;
       new_ro_row= new_ro_row+1;
    end
end

%
% now see if the matrix t build has rank same as A
% if not, we need to come up with arbitrary rows
% that are linearly independent with those allready
% extracted from Ro from above
%
[arow,acol]= size(A);
[row,col]= size(t);
if(row == arow)
  P=t;   
else
  dif= arow-row;
  for i=1:dif
      temp=t;
      more=1;
      while (more==1)
            % 
            % The trick i use to find arbitrary row that is L.I. with
            % those allready in Q, is by random generation, using the
            % built in magic function, I keep looping, generating random
            % rows untill i find one that is L.I., then i use it
            %
            temp1= magic(original_row);
            temp(new_ro_row+i,1:original_col)= temp1(1:1,1:original_col);
            [row,col]= size(orth(temp));
            if(row == new_ro_row+i)
               more=0;
               t=temp;
            end
       end
   end
   P=t;
end