A = [ 1 0 0 1 0 0 0 0 0 0 0 0 0;
-1 1 0 0 1 1 0 0 0 0 0 0 1;
0 -1 1 0 0 0 0 0 -1 0 0 0 0;
0 0 -1 0 0 -1 0 0 0 -1 0 0 0;
0 0 0 -1 0 0 -1 1 0 0 0 0 0;
0 0 0 0 0 0 1 0 0 0 1 0 0;
0 0 0 0 0 0 0 -1 1 0 -1 1 -1;
0 0 0 0 -1 0 0 0 0 1 0 -1 0];
xy = [ 1 2 3 3 1 1 2 3 ; ...
3 2.5 3 2 2 1 1.5 1 ]';
[n,m] = size(A);
[ w_fdla, rho_fdla ] = fdla(A);
[ w_fmmc, rho_fmmc ] = fmmc(A);
[ w_md, rho_md ] = max_deg(A);
[ w_bc, rho_bc ] = best_const(A);
[ w_mh, rho_mh ] = mh(A);
tau_fdla = 1/log(1/rho_fdla);
tau_fmmc = 1/log(1/rho_fmmc);
tau_md = 1/log(1/rho_md);
tau_bc = 1/log(1/rho_bc);
tau_mh = 1/log(1/rho_mh);
fprintf(1,'\nResults:\n');
fprintf(1,'FDLA weights:\t\t rho = %5.4f \t tau = %5.4f\n',rho_fdla,tau_fdla);
fprintf(1,'FMMC weights:\t\t rho = %5.4f \t tau = %5.4f\n',rho_fmmc,tau_fmmc);
fprintf(1,'M-H weights:\t\t rho = %5.4f \t tau = %5.4f\n',rho_mh,tau_mh);
fprintf(1,'MAX_DEG weights:\t rho = %5.4f \t tau = %5.4f\n',rho_md,tau_md);
fprintf(1,'BEST_CONST weights:\t rho = %5.4f \t tau = %5.4f\n',rho_bc,tau_bc);
figure(1), clf
plotgraph(A,xy,w_fdla);
text(0.55,1.05,'FDLA optimal weights')
figure(2), clf
plotgraph(A,xy,w_fmmc);
text(0.55,1.05,'FMMC optimal weights')
figure(3), clf
plotgraph(A,xy,w_md);
text(0.5,1.05,'Max degree optimal weights')
figure(4), clf
plotgraph(A,xy,w_bc);
text(0.5,1.05,'Best constant optimal weights')
figure(5), clf
plotgraph(A,xy,w_mh);
text(0.46,1.05,'Metropolis-Hastings optimal weights')
Calling sedumi: 73 variables, 59 equality constraints
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 1 free variables
eqs m = 59, order n = 19, dim = 131, blocks = 3
nnz(A) = 145 + 0, nnz(ADA) = 2791, nnz(L) = 1425
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.70E+00 0.000
1 : 6.61E-01 4.22E-01 0.000 0.2482 0.9000 0.9000 0.59 1 1 2.1E+00
2 : 6.11E-01 1.41E-01 0.000 0.3331 0.9000 0.9000 2.38 1 1 3.7E-01
3 : 6.60E-01 2.95E-02 0.000 0.2094 0.9000 0.9000 1.20 1 1 7.1E-02
4 : 6.46E-01 5.39E-03 0.000 0.1829 0.9000 0.9000 1.10 1 1 1.3E-02
5 : 6.44E-01 2.24E-04 0.000 0.0416 0.9900 0.9900 1.02 1 1 5.2E-04
6 : 6.43E-01 3.51E-06 0.000 0.0157 0.9900 0.9317 1.00 1 1 2.0E-05
7 : 6.43E-01 2.99E-07 0.201 0.0853 0.9458 0.9450 1.00 1 1 1.8E-06
8 : 6.43E-01 5.40E-08 0.248 0.1805 0.9156 0.9000 1.00 1 1 3.7E-07
9 : 6.43E-01 9.46E-09 0.000 0.1754 0.9099 0.9000 1.00 1 1 6.5E-08
10 : 6.43E-01 2.88E-10 0.156 0.0304 0.9900 0.9901 1.00 2 2 2.0E-09
iter seconds digits c*x b*y
10 0.1 Inf 6.4333140650e-01 6.4333140760e-01
|Ax-b| = 3.5e-10, [Ay-c]_+ = 1.2E-09, |x|= 3.5e+00, |y|= 9.5e-01
Detailed timing (sec)
Pre IPM Post
1.000E-02 7.000E-02 1.000E-02
Max-norms: ||b||=6.250000e-01, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 99.2911.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.643331
Calling sedumi: 94 variables, 80 equality constraints
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 1 free variables
eqs m = 80, order n = 40, dim = 152, blocks = 3
nnz(A) = 180 + 0, nnz(ADA) = 4438, nnz(L) = 2296
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 7.51E-01 0.000
1 : 2.31E-01 2.60E-01 0.000 0.3466 0.9000 0.9000 3.03 1 1 1.2E+00
2 : 6.39E-01 8.43E-02 0.000 0.3238 0.9000 0.9000 1.54 1 1 2.9E-01
3 : 6.99E-01 2.04E-02 0.000 0.2420 0.9000 0.9000 1.32 1 1 6.0E-02
4 : 6.82E-01 4.67E-03 0.000 0.2291 0.9000 0.9000 1.14 1 1 1.3E-02
5 : 6.81E-01 1.18E-03 0.000 0.2530 0.9000 0.9000 1.02 1 1 3.3E-03
6 : 6.81E-01 2.49E-04 0.000 0.2102 0.9000 0.8437 1.00 1 1 7.6E-04
7 : 6.81E-01 7.95E-06 0.000 0.0320 0.9900 0.9900 1.00 1 1 2.4E-05
8 : 6.81E-01 8.85E-07 0.193 0.1114 0.9450 0.9118 1.00 1 1 2.9E-06
9 : 6.81E-01 1.35E-07 0.041 0.1520 0.9021 0.9000 1.00 1 1 4.6E-07
10 : 6.81E-01 1.75E-08 0.052 0.1304 0.9070 0.9000 1.00 1 1 7.1E-08
11 : 6.81E-01 1.34E-09 0.472 0.0762 0.9900 0.9900 1.00 1 1 5.4E-09
iter seconds digits c*x b*y
11 0.1 8.9 6.8096067815e-01 6.8096067720e-01
|Ax-b| = 6.2e-09, [Ay-c]_+ = 2.1E-09, |x|= 3.7e+00, |y|= 1.2e+00
Detailed timing (sec)
Pre IPM Post
0.000E+00 8.000E-02 1.000E-02
Max-norms: ||b||=8.750000e-01, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 40.1861.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.680961
Results:
FDLA weights: rho = 0.6433 tau = 2.2671
FMMC weights: rho = 0.6810 tau = 2.6025
M-H weights: rho = 0.7743 tau = 3.9094
MAX_DEG weights: rho = 0.7793 tau = 4.0093
BEST_CONST weights: rho = 0.7119 tau = 2.9422