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makispaiktis

Decomposition

Jan 21st, 2022
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  1. clc
  2. clear all
  3.  
  4. %% Estw oti brhkame ta PANTA SWSTA
  5. l_max = 3;
  6. r_max = 6;
  7. l_optimum = [0.3, 0.5, 0.2];
  8. r_optimum = [0.2, 0.2 0.1, 0.1, 0.3, 0.1];
  9. % Codewords length
  10. n = 200;
  11.  
  12.  
  13. %% Create Pi dia i and Lamda i dia i
  14. r_i_dia_i_list = zeros(1, r_max);
  15. l_i_dia_i_list = zeros(1, l_max);
  16. for index = 1:r_max
  17.     r_i_dia_i_list(index) = r_optimum(index) / (index + 1);     % Epeidi arxizei apo to 2 enw emeis apo to 1
  18. end
  19.  
  20. for index = 1:l_max
  21.     l_i_dia_i_list(index) = l_optimum(index) / (index + 1);
  22. end
  23. SUM = sum(l_i_dia_i_list);
  24.  
  25. r_i_dia_i_list;
  26. l_i_dia_i_list;
  27.  
  28. %% Create LAMDA AND RHO LISTS
  29. RHO = r_i_dia_i_list / SUM * n;
  30. LAMDA = l_i_dia_i_list / SUM * n;
  31. RHO_HAT = floor(RHO);
  32. LAMDA_HAT = floor(LAMDA);
  33. % Calculate A
  34. A_condition = sum(RHO - RHO_HAT);
  35.  
  36.  
  37. %% GENERAL CONSTRAINTS
  38. % Declare 2 sum constant variables
  39. constant_19 = n - sum(LAMDA_HAT);
  40. i_r = 2:r_max+1;
  41. i_l = 2:l_max+1;
  42. constant_20 = sum(i_r .* RHO_HAT) - sum(i_l .* LAMDA_HAT);
  43.  
  44. % Prwta stoixeia ta "l", kai meta ta "r"
  45. Aeq = zeros(2, l_max + r_max);
  46. Beq = zeros(2, 1);
  47.  
  48. % Constraint 19
  49. Aeq(1, 1:l_max) = 1;
  50. Beq(1, 1) = constant_19;
  51. % Constraint 20
  52. Aeq(2, 1:l_max) = i_l;
  53. Aeq(2, l_max+1 : l_max+r_max) = - i_r;
  54. Beq(2, 1) = constant_20;
  55. % Constraint 21
  56.  
  57.  
  58. %% CASE CONSTRAINTS
  59. % CASE 1 -  ANISOTIKOS - MATRIX A1
  60. A1 = zeros(1, l_max + r_max);
  61. A1(1, l_max+1 : l_max+r_max) = -1;
  62. B1 = -ceil(A_condition);
  63.  
  64. % CASE 2
  65. A2 = zeros(1, l_max + r_max);
  66. A2(1, l_max+1 : l_max+r_max) = 1;
  67. B2 = floor(A_condition);
  68.  
  69. % OBJECTIVE FUNCTIONS
  70. % CASE 1
  71. f1 = zeros(1, l_max + r_max);
  72. f1(1, l_max+1 : l_max+r_max) = 1;
  73.  
  74. % CASE 2
  75. f2 = -f1;
  76.  
  77.  
  78. %% SIMULATIONS
  79. lb = zeros(1, l_max + r_max);
  80. ub = ones(1, l_max + r_max);
  81. % CASE 1
  82. result1 = linprog(f1, A1, B1 , Aeq, Beq, lb, ub);
  83. % CASE 2
  84. result2 = linprog(f2, A2, B2 , Aeq, Beq, lb, ub);
  85.  
  86. %% FIND THE BEST
  87. error1 = (sum(result1(l_max+1 : l_max+r_max)) - A_condition) ^ 2;
  88. error2 = (sum(result2(l_max+1 : l_max+r_max)) - A_condition) ^ 2;
  89. if error1 >= error2
  90.     result = result2;
  91. else
  92.     result = result1;
  93. end
  94. % result = [xl1, xl2, xl3, xr1, ..., xr6] ---> length = 9
  95.  
  96.  
  97. %% FIND THE NEW LAMDA AND RHO - UPDATE
  98. n;
  99. result = result';
  100. LAMDA_HAT;
  101. RHO_HAT;
  102. LAMDA_LIST = LAMDA_HAT + result(1 : l_max);
  103. RHO_LIST = RHO_HAT + result(l_max + 1 : l_max + r_max);
  104.  
  105.  
  106. %% DISPLAY AKMES
  107. % !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  108. % MPOREI KAPOIA NOUMERA NA MIN EINAI INTEGERS, ENW ANAPARISTOUN # AKMWN !
  109. num_variable_edges = sum(LAMDA_LIST .* i_l);
  110. num_check_edges = sum(RHO_LIST .* i_r);
  111. num_variables = sum(LAMDA_LIST);
  112. num_checks = sum(RHO_LIST);
  113. %   Above: L'(1) = P'(1)  (sxesh 2 kai 3)
  114.  
  115. pretty_display("n = ", n);
  116. pretty_display("Variable degrees = ", LAMDA_LIST);
  117. pretty_display("Check degrees = ", RHO_LIST);
  118. pretty_display("Num of variable edges = ", num_variable_edges);
  119. pretty_display("Num of check edges = ", num_check_edges);
  120. pretty_display("Num of VARIABLES = ", num_variables);
  121. pretty_display("Num of CHECKS = ", num_checks);
  122.  
  123.  
  124.  
  125. %% MATRIX 545 x 545 (about sockets)
  126. sockets = num_check_edges;
  127. checks = num_checks;
  128. vars = num_variables;
  129.  
  130. % Socket Matrix is 545 x 545
  131. socket_matrix = zeros(sockets);
  132. comb1 = 1:sockets;
  133. comb2 = comb1(randperm(length(comb1)));
  134.  
  135. for i = 1:sockets
  136.     ch = comb1(i);
  137.     var = comb2(i);
  138.     socket_matrix(ch, var) = 1;
  139. end
  140.  
  141.  
  142. %% Create a vector with 82 2's and 91 3's and 27 4's (n=200)
  143. var_temp = zeros(1, vars);
  144. counter = 1;
  145. for i = 1:length(LAMDA_LIST)
  146.     var_temp(counter : counter + LAMDA_LIST(i) - 1) = ...
  147.     (i+1) * ones(1, LAMDA_LIST(i));
  148.     counter = LAMDA_LIST(i) + counter;
  149. end
  150. var_temp;
  151.  
  152.  
  153. check_temp = zeros(1, checks);
  154. counter = 1;
  155. for i = 1:length(RHO_LIST)
  156.     check_temp(counter : counter + RHO_LIST(i) - 1) = ...
  157.     (i+1) * ones(1, RHO_LIST(i));
  158.     counter = RHO_LIST(i) + counter;
  159. end
  160. check_temp;
  161.  
  162.  
  163. %% H is a decomposition of socket matrix
  164. H = zeros(checks, vars);
  165. % for i = 1:vars
  166. %     for j = 1:checks
  167. %         MAT = sockets( : , :);
  168. %         H(i, j) = sum(MAT);
  169. %     end
  170. % end
  171.  
  172.  
  173.  
  174.  
  175. %% ACCUMULATIVE RANGES
  176. var_ranges = zeros(1, length(var_temp));
  177. var_ranges = [0 var_ranges];
  178.  
  179. for i = 1:length(var_temp)
  180.     S = var_ranges(i) + var_temp(i);
  181.     var_ranges(i+1) = S;
  182. end
  183. var_ranges;
  184.  
  185.  
  186. check_ranges = zeros(1, length(check_temp));
  187. check_ranges = [0 check_ranges];
  188.  
  189. for i = 1:length(check_temp)
  190.     S = check_ranges(i) + check_temp(i);
  191.     check_ranges(i+1) = S;
  192. end
  193. check_ranges;
  194.  
  195.  
  196. %% Decomposition onto submatrices
  197. % var_ranges and check-ranges have 1 more element (0 in the beginning)
  198. socket_matrix = randi([0 1], 6, 9)
  199. check_ranges = [0, 1, 3, 6]
  200. var_ranges = [0, 2, 4, 6, 9]
  201. H = zeros(3, 4);
  202.  
  203. for i = 1:length(check_ranges) - 1
  204.     for j = 1:length(var_ranges) - 1
  205.         i
  206.         j
  207.         rows_range = check_ranges(i)+1 : + check_ranges(i+1)
  208.         cols_range = var_ranges(j)+1 : + var_ranges(j+1)
  209.         submatrix = socket_matrix(rows_range, cols_range)
  210.         SUM = sum(sum(submatrix))
  211.         H(i, j) = mod(SUM, 2)
  212.     end
  213. end
  214.  
  215. H
  216.  
  217.  
  218.  
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