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Nov 24th, 2011
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  1. %% Create Matrices
  2.  
  3. % Create y (solution) vector
  4. y(1)        = 80;
  5. y(2:6)      = 40;
  6. y(7:10)     =  0;
  7. y(11)       = 40;
  8. y(12:15)    =  0;
  9. y(16)       = 40;
  10. y(17:20)    =  0;
  11. y(21)       = 30;
  12. y(22:25)    = 10;
  13.  
  14. % Create diagonal vector for 4
  15.  
  16. for i = 1:25
  17.     v(i) = 4;
  18. end
  19.  
  20. % Create diagonal vector for -1 dependant on the sizes needed
  21.  
  22. for i = 1:24
  23.     w(i) = -1;
  24. end
  25.  
  26. for i = 1:20
  27.     k(i) = -1;
  28. end
  29.  
  30. % Create vector A with the diagonals
  31.  
  32. A = diag(v) + diag(w,1) + diag(w,-1) + diag(k,5) + diag(k,-5);
  33.  
  34. % Remove undependant variables from A (edges of the roster)
  35.  
  36. for i=5:5:19;
  37.     j= i+1;
  38.     A(j,i) = 0;
  39.     i+5;
  40. end
  41.  
  42. % Solve for 'x'
  43.  
  44. x = A\y';
  45.  
  46. %% Plot the solution
  47.  
  48. % Create matrix X to correspond to the grid
  49. s = 1
  50. for i = 1:5
  51.     for j = 1:5
  52.         X(i,j) = x(s);
  53.         s = s+1;
  54.     end
  55. end
  56.  
  57. % Plot X with surf
  58.  
  59. surf(X);
  60.  
  61.  
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