FDLA and FMMC solutions for a 64-node, 95-edge cut-grid graph
[A,xy] = cut_grid_data;
[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(0.425,1.05,'FDLA optimal weights')
figure(2), clf
plotgraph(A,xy,w_fmmc);
text(0.425,1.05,'FMMC optimal weights')
figure(3), clf
plotgraph(A,xy,w_md);
text(0.375,1.05,'Max degree optimal weights')
figure(4), clf
plotgraph(A,xy,w_bc);
text(0.375,1.05,'Best constant optimal weights')
figure(5), clf
plotgraph(A,xy,w_mh);
text(0.3,1.05,'Metropolis-Hastings optimal weights')
Calling sedumi: 4184 variables, 120 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
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
eqs m = 120, order n = 131, dim = 8218, blocks = 4
nnz(A) = 699 + 0, nnz(ADA) = 14400, nnz(L) = 7260
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.32E+02 0.000
1 : -5.40E+00 8.97E+00 0.000 0.0680 0.9900 0.9900 -0.65 1 1 5.1E+01
2 : -3.09E+00 3.82E+00 0.000 0.4260 0.9000 0.9000 2.14 1 1 1.2E+01
3 : -1.05E+00 1.67E+00 0.000 0.4369 0.9000 0.9000 4.41 1 1 1.8E+00
4 : -9.93E-01 5.92E-01 0.000 0.3547 0.9000 0.9000 1.30 1 1 5.9E-01
5 : -9.98E-01 1.74E-01 0.000 0.2935 0.9000 0.9000 1.03 1 1 1.7E-01
6 : -9.91E-01 3.55E-02 0.000 0.2044 0.9000 0.8709 1.02 1 1 3.6E-02
7 : -9.89E-01 8.25E-03 0.000 0.2322 0.9056 0.9000 1.01 1 1 8.1E-03
8 : -9.88E-01 2.44E-03 0.000 0.2955 0.9129 0.9000 1.00 1 1 2.3E-03
9 : -9.88E-01 7.84E-04 0.000 0.3217 0.9038 0.9000 1.00 1 1 7.5E-04
10 : -9.88E-01 1.90E-04 0.000 0.2417 0.9023 0.9000 1.00 1 1 1.8E-04
11 : -9.88E-01 1.82E-05 0.078 0.0959 0.9900 0.9902 1.00 1 1 1.7E-05
12 : -9.88E-01 4.45E-06 0.000 0.2447 0.9000 0.9124 1.00 2 2 4.3E-06
13 : -9.88E-01 8.04E-07 0.000 0.1806 0.9000 0.9063 1.00 2 2 7.7E-07
14 : -9.88E-01 1.47E-07 0.000 0.1826 0.9000 0.9077 1.00 7 7 1.4E-07
15 : -9.88E-01 1.53E-08 0.425 0.1041 0.9900 0.9900 1.00 48 46 1.5E-08
iter seconds digits c*x b*y
15 1.4 9.1 -9.8829188306e-01 -9.8829188380e-01
|Ax-b| = 1.4e-08, [Ay-c]_+ = 4.6E-11, |x|= 1.8e+00, |y|= 6.8e+00
Detailed timing (sec)
Pre IPM Post
2.000E-02 1.430E+00 1.000E-02
Max-norms: ||b||=1, ||c|| = 9.843750e-01,
Cholesky |add|=0, |skip| = 22, ||L.L|| = 57279.1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.988292
Calling sedumi: 4368 variables, 145 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
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
eqs m = 145, order n = 290, dim = 8402, blocks = 4
nnz(A) = 910 + 0, nnz(ADA) = 21025, nnz(L) = 10585
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.33E+02 0.000
1 : -6.90E-01 5.51E+01 0.000 0.4155 0.9000 0.9000 2.46 1 1 7.3E+01
2 : -9.46E-01 1.35E+01 0.000 0.2459 0.9000 0.9000 1.80 1 1 1.3E+01
3 : -1.00E+00 1.01E+00 0.000 0.0742 0.9900 0.9900 1.25 1 1 8.4E-01
4 : -9.93E-01 3.60E-01 0.000 0.3577 0.9000 0.9000 1.05 1 1 3.0E-01
5 : -9.93E-01 7.88E-02 0.000 0.2192 0.9000 0.9000 1.01 1 1 6.5E-02
6 : -9.91E-01 2.34E-02 0.000 0.2968 0.9029 0.9000 1.02 1 1 1.9E-02
7 : -9.90E-01 1.11E-02 0.000 0.4749 0.9000 0.9068 1.03 1 1 8.9E-03
8 : -9.89E-01 5.97E-03 0.000 0.5369 0.9000 0.9393 1.03 1 1 4.9E-03
9 : -9.89E-01 2.88E-03 0.000 0.4822 0.9000 0.9233 1.01 1 1 2.4E-03
10 : -9.89E-01 1.60E-03 0.000 0.5557 0.9000 0.9000 1.01 1 1 1.3E-03
11 : -9.89E-01 4.66E-04 0.000 0.2918 0.9161 0.9000 1.01 1 1 3.7E-04
12 : -9.89E-01 2.10E-04 0.000 0.4499 0.9000 0.8811 1.01 1 1 1.7E-04
13 : -9.89E-01 9.92E-05 0.000 0.4727 0.9000 0.5906 1.01 2 2 8.1E-05
14 : -9.89E-01 2.73E-05 0.000 0.2748 0.9155 0.9000 1.00 2 2 2.1E-05
15 : -9.89E-01 1.11E-05 0.000 0.4079 0.9000 0.9063 1.00 2 2 8.8E-06
16 : -9.89E-01 5.03E-06 0.000 0.4523 0.9000 0.7132 1.00 8 8 4.1E-06
17 : -9.89E-01 1.55E-06 0.000 0.3080 0.9079 0.9000 1.00 11 11 1.2E-06
18 : -9.89E-01 6.37E-07 0.000 0.4111 0.9000 0.8005 1.00 16 16 5.2E-07
19 : -9.89E-01 2.32E-07 0.000 0.3648 0.9000 0.8496 1.00 27 27 1.9E-07
20 : -9.89E-01 8.77E-08 0.000 0.3776 0.9000 0.9000 1.01 75 77 7.1E-08
Run into numerical problems.
iter seconds digits c*x b*y
20 3.0 Inf -9.8882616673e-01 -9.8882616654e-01
|Ax-b| = 7.1e-08, [Ay-c]_+ = 2.5E-10, |x|= 2.3e+00, |y|= 8.2e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 3.010E+00 1.000E-02
Max-norms: ||b||=1, ||c|| = 1.015625e+00,
Cholesky |add|=0, |skip| = 31, ||L.L|| = 12696.9.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +0.988826
Results:
FDLA weights: rho = 0.9883 tau = 84.9099
FMMC weights: rho = 0.9888 tau = 88.9939
M-H weights: rho = 0.9917 tau = 120.2442
MAX_DEG weights: rho = 0.9927 tau = 136.7523
BEST_CONST weights: rho = 0.9921 tau = 126.3450