%Laplace matrix (see Pages 115-116)

C = [
25/6 -2/3 0 0 -7/6 -1/2 0 0 0 0;
-2/3 23/6 -1/2 -1/2 0 -1 0 0 0 0;
0 -1/2 25/6 -7/6 0 -2/3 -2/3 0 0 0;
0 -1/2 -7/6 23/6 0 0 0 0 0 -1;
-7/6 0 0 0 23/6 -1/2 0 -1 0 0;
-1/2 -1 -2/3 0 -1/2 31/6 -2/3 -2/3 -2/3 0;
0 0 -2/3 0 0 -2/3 8/3 0 -2/3 -2/3;
0 0 0 0 -1 -2/3 0 10/3 -2/3 0;
0 0 0 0 0 -2/3 -2/3 -2/3 11/3 -2/3;
0 0 0 -1 0 0 -2/3 0 -2/3 10/3;
]

%Fixed pin vectors (See Page 116)
dx = [ -1 0 -2/3 -2/3 -1 -1 0 -3 -4 -4];

%solve for top optimization level (l=0)
%NOTE: if you did not specify "options", and directly run x = quadprog(C,dx), there will be a warning. But it will not change the results.

options=optimset('Algorithm', 'interior-point-convex')
x = quadprog(C,dx,[],[],[],[],[],[],[],options)

%the solution from matlab is as follows. The same to the results in Page 117, X^T
%x =
%
%    0.9485
%    0.9154
%    1.2134
%    1.3171
%    1.3167
%    1.6115
%    1.9805
%    2.1350
%    2.5884
%    2.5089

%for optimization level l=1,
$A1, ux1 in page 118	
A1 = [
1/5 1/5 1/5 1/5 1/5 0 0 0 0 0;
0 0 0 0 0 1/5 1/5 1/5 1/5 1/5;
]

ux1 = [ 1; 3;]

%solve the problem
%NOTE: if you did not specify options, but directly run x = quadprog(C,dx,[],[],A1,ux1), you will obtain the same results. But there will be a message like "Optimization terminated: relative (projected) residual of PCG iteration <= OPTIONS.TolFun."

x = quadprog(C,dx,[],[],A1,ux1,[],[],[],options)

%the solution from matlab, same as the solution in page 118
% x =
%
%    0.6954
%    0.7149
%    1.1670
%    1.2075
%    1.2151
%    2.1720
%    3.0964
%    2.8431
%    3.5628
%    3.3257

%for optimization level l=2,
%A2 and ux2 in page 120,

A2 = [
0 0 1/2 1/2 0 0 0 0 0 0;
1/3 1/3 0 0 1/3 0 0 0 0 0;
0 0 0 0 0 0 1/2 0 0 1/2;
0 0 0 0 0 1/3 0 1/3 1/3 0;
]

ux2 = [ 1; 1; 3; 3;]

x = quadprog(C,dx,[],[],A2,ux2,[],[],[],options)

%the solution from matlab, same as the solution in page 121
%x =
%
%    0.8275
%    0.7823
%    1.0006
%    0.9994
%    1.3901
%    2.2850
%    2.8897
%    3.0586
%    3.6564
%    3.1103