FDLA and FMMC solutions for a 64-node, 95-edge cut-grid graph
[A,xy] = cut_grid_data;
fprintf(1,'WARNING: The optimal weight computations take some time...\n');
[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')
WARNING: The optimal weight computations take some time...
Calling SeDuMi: 4166 variables (6 free), 4070 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 4070, order n = 131, dim = 8200, blocks = 4
nnz(A) = 4553 + 0, nnz(ADA) = 8884742, nnz(L) = 4444406
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 2.24E-001 0.000
1 : 1.21E+001 1.45E-002 0.000 0.0647 0.9900 0.9900 -0.68 1 1 1.3E+000
2 : 3.41E+000 6.17E-003 0.000 0.4256 0.9000 0.9000 2.14 1 1 3.1E-001
3 : 1.14E+000 2.77E-003 0.000 0.4483 0.9000 0.9000 4.54 1 1 4.6E-002
4 : 1.02E+000 9.92E-004 0.000 0.3585 0.9000 0.9000 1.30 1 1 1.6E-002
5 : 1.00E+000 2.92E-004 0.000 0.2942 0.9000 0.9000 1.04 1 1 4.6E-003
6 : 9.92E-001 1.50E-005 0.000 0.0516 0.9081 0.9000 1.02 1 1 7.4E-004
7 : 9.89E-001 4.20E-006 0.000 0.2790 0.9000 0.8584 1.00 1 1 2.0E-004
8 : 9.89E-001 1.55E-006 0.000 0.3702 0.9000 0.7890 1.00 1 1 7.5E-005
9 : 9.88E-001 4.84E-007 0.000 0.3113 0.9000 0.9000 1.00 1 1 2.3E-005
10 : 9.88E-001 1.22E-007 0.000 0.2525 0.9000 0.9000 1.00 1 1 5.9E-006
11 : 9.88E-001 8.82E-009 0.160 0.0723 0.9903 0.9900 1.00 1 1 5.0E-007
12 : 9.88E-001 1.32E-009 0.000 0.1500 0.9195 0.9000 1.00 1 1 1.0E-007
13 : 9.88E-001 5.48E-011 0.207 0.0414 0.9900 0.9900 1.00 1 1 4.2E-009
iter seconds digits c*x b*y
13 363.3 Inf 9.8829189011e-001 9.8829190041e-001
|Ax-b| = 6.3e-009, [Ay-c]_+ = 1.8E-009, |x|= 1.4e+001, |y|= 1.3e+000
Detailed timing (sec)
Pre IPM Post
8.462E+000 3.633E+002 1.001E-001
Max-norms: ||b||=9.843750e-001, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 48.5623.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.988292
Calling SeDuMi: 4320 variables (1 free), 4224 equality constraints
------------------------------------------------------------------------
SeDuMi 1.1R3 by AdvOL, 2006 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 4224, order n = 290, dim = 8354, blocks = 4
nnz(A) = 4862 + 0, nnz(ADA) = 8662492, nnz(L) = 4357082
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 2.16E-001 0.000
1 : 2.76E-001 7.40E-002 0.000 0.3426 0.9000 0.9000 2.60 1 1 2.1E+000
2 : 8.80E-001 1.77E-002 0.000 0.2397 0.9000 0.9000 1.69 1 1 3.6E-001
3 : 9.98E-001 6.10E-004 0.000 0.0344 0.9900 0.9900 1.21 1 1 1.1E-002
4 : 9.93E-001 1.60E-004 0.000 0.2618 0.9000 0.9000 1.04 1 1 2.8E-003
5 : 9.91E-001 4.36E-005 0.000 0.2729 0.9000 0.9000 1.02 1 1 7.6E-004
6 : 9.90E-001 1.63E-005 0.000 0.3734 0.9022 0.9000 1.03 1 1 3.2E-004
7 : 9.90E-001 2.31E-006 0.000 0.1421 0.9350 0.9000 1.03 1 1 1.0E-004
8 : 9.89E-001 6.65E-007 0.000 0.2881 0.9270 0.9000 1.02 1 1 3.7E-005
9 : 9.89E-001 1.31E-007 0.000 0.1967 0.9503 0.9000 1.01 1 1 1.2E-005
10 : 9.89E-001 4.32E-008 0.000 0.3303 0.9000 0.9085 1.01 1 1 3.9E-006
11 : 9.89E-001 1.95E-008 0.000 0.4516 0.9312 0.9000 1.01 1 1 1.7E-006
12 : 9.89E-001 1.03E-008 0.000 0.5274 0.9482 0.9000 1.00 1 1 9.0E-007
13 : 9.89E-001 2.11E-009 0.000 0.2045 0.9000 0.9107 1.00 2 2 1.9E-007
14 : 9.89E-001 7.02E-010 0.000 0.3336 0.9000 0.9023 1.00 2 2 6.4E-008
15 : 9.89E-001 2.60E-010 0.000 0.3707 0.0000 0.9000 1.00 2 2 2.8E-008
16 : 9.89E-001 9.54E-011 0.000 0.3665 0.9000 0.6588 1.00 2 2 1.1E-008
iter seconds digits c*x b*y
16 426.3 Inf 9.8882651338e-001 9.8882651703e-001
|Ax-b| = 1.2e-009, [Ay-c]_+ = 5.6E-009, |x|= 1.4e+001, |y|= 1.4e+000
Detailed timing (sec)
Pre IPM Post
9.243E+000 4.263E+002 1.001E-002
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 44.4774.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.988827
Results:
FDLA weights: rho = 0.9883 tau = 84.9099
FMMC weights: rho = 0.9888 tau = 88.9966
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