Test Script Genetic Algo solver for Marsili-Giada Model

Name: SECTORS_TEST_ANNEALING_001.M

Authors: Tim Gebbie

This test script is part of the "Sector and State" toolbox SECTOR.ZIP. The data set considered has correlated Assets with four clusters. The test script is developed to show that the algorithm picks up those clusters.

References:

1. J. D. Noh, Phys. Rev. E 61, 5981 (2000)
1. L. Giada & M. Marsili (2005) ...
2. Marsili (2002) ...

See Also: GA, GAMGCONFIG

Contents

Clear the workspace

clear all; clc;

The algorithm used to control the entire algorithm

help gamgconfig
  GAMGCONFIG GA configuration solver for the Marsili-Giada spin model
 
  Need to find a linkage object specifying which object is in which cluster
  based on the Marsili-Giada cost function. The algorithm starts with N
  distinct objects in N clusters. The algorithm iterates this chromosome
  until it finds the optimal chromosome with the integer valued i-th gene 
  giving the cluster that the i-th object occupies.
 
  [X,FVAL] = GAMGCONFIG(C) For correlation matrix C. Compute the chromosome
  X with the i-th gene giving the cluster that the i-th object occupies.
 
  See Also: SLIKELIHOOD, GA

Test 4.1: Correlated data with Four Clusters

C41 = [[ 1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0.45]; ...
   [0.4,   1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4,   1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4,   1, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4, 0.4,   1, 0.4, 0.4, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4, 0.4, 0.4,   1, 0.4, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   1, 0.4, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   1, 0.4, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   1, 0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0,-.3,0,0,0,0,0,0,0,0]; ...
   [0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,   1,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  -.4,0,0,0,0,0,0,0,0,0]; ...

   [0,0,0,0,0,0,0,0,0,0,     1, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,  -0.1,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5,   1, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,  -0.2,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5,   1, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,  -0.3,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5,   1, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,  -0.4,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5, 0.5,   1, 0.5, 0.5, 0.5, 0.5, 0.5,  -0.6,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5, 0.5, 0.5,   1, 0.5, 0.5, 0.5, 0.5,  -0.5,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5, 0.5, 0.5, 0.5,   1, 0.5, 0.5, 0.5,  -0.4,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,   1, 0.5, 0.5,  -0.3,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,   1, 0.5,  -0.2,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,   1,  -0.1,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0]; ...

   [0,0,0,0,0,0,0,0,0,0,   -.1,-.2,-.3,-.4,-.6,-.5,-.4,-.3,-.2,-0.1,   1, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...

   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3,   1, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3,   1, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3,   1, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3, 0.3,   1, 0.3, 0.3, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3, 0.3, 0.3,   1, 0.3, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3, 0.3, 0.3, 0.3,   1, 0.3, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,   1, 0.3, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,   1, 0.3,  0,0,0,0,0,0,0,0,0,0]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,   1,  0,0,0,0,0,0,0,0,0,0]; ...

   [0,0,0,0,0,0,0,0,0,-0.4,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,    1, 0.1, 0.1, 0.1,-0.1,-0.2, 0.1, 0.3, 0.4, 0.5]; ...
   [0,0,0,0,0,0,0,0,-.3,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.1,   1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.4]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.1, 0.1,   1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.3]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.1, 0.1, 0.1,   1, 0.1, 0.1, 0.1, 0.1, 0.1,-0.1]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.1, 0.1, 0.1, 0.1,   1, 0.1, 0.1, 0.1, 0.1,-0.2]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0, -0.2, 0.1, 0.1, 0.1, 0.1,   1, 0.1, 0.1, 0.1, 0.1]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0, -0.1, 0.1, 0.1, 0.1, 0.1, 0.1,   1, 0.1, 0.1, 0.1]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.3, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,   1, 0.1, 0.1]; ...
   [0,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.4, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,   1, 0.1]; ...
   [0.45,0,0,0,0,0,0,0,0,0,   0,0,0,0,0,0,0,0,0,0,  0,0,0,0,0,0,0,0,0,0,  0.5, 0.4, 0.3,-0.1,-0.2, 0.1, 0.1, 0.1, 0.1,  1]];

Test 4.1.1: Use ANNEALING to generate clusters from the correlations

[x,fval]=gamgconfig(C41);
                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
    1           600         -0.7773         -0.4261        0
    2           900         -0.8309         -0.5613        0
    3          1200          -1.084         -0.5994        0
    4          1500          -1.084         -0.5966        1
    5          1800          -1.084         -0.6465        2
    6          2100          -1.089         -0.6661        0
    7          2400          -1.089         -0.6515        1
    8          2700          -1.089         -0.6575        2
    9          3000          -1.089         -0.6553        3
   10          3300          -1.089          -0.642        4
   11          3600          -1.089         -0.6238        5
   12          3900          -1.089         -0.6205        6
   13          4200          -1.089         -0.6148        7
   14          4500          -1.089          -0.629        8
   15          4800          -1.089         -0.6277        9
   16          5100          -1.112         -0.6208        0
   17          5400          -1.112          -0.623        1
   18          5700          -1.178         -0.6188        0
   19          6000          -1.304         -0.6476        0
   20          6300          -1.392         -0.7034        0
   21          6600          -1.392          -0.701        1
   22          6900          -1.447         -0.7078        0
   23          7200          -1.491         -0.7008        0
   24          7500          -1.491          -0.746        1
   25          7800          -1.491         -0.7512        2
   26          8100          -1.491          -0.746        3
   27          8400          -1.491         -0.7498        4
   28          8700          -1.491         -0.7425        5
   29          9000          -1.491         -0.7504        6
   30          9300          -1.491         -0.7332        7

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
   31          9600          -1.491         -0.7635        8
   32          9900          -1.491         -0.7581        9
   33         10200          -1.491          -0.721       10
   34         10500          -1.491         -0.7541       11
   35         10800          -1.491         -0.7681       12
   36         11100          -1.491          -0.782       13
   37         11400          -1.491         -0.7664       14
   38         11700          -1.512         -0.7821        0
   39         12000          -1.512         -0.7754        1
   40         12300          -1.682         -0.7679        0
   41         12600          -1.689         -0.7947        0
   42         12900          -1.689         -0.8139        1
   43         13200          -1.689         -0.7896        2
   44         13500          -1.728         -0.8505        0
   45         13800          -1.728         -0.8158        1
   46         14100          -1.728         -0.8468        2
   47         14400          -1.835         -0.8262        0
   48         14700          -1.887         -0.8958        0
   49         15000          -1.888         -0.8718        0
   50         15300          -1.889         -0.9177        0
   51         15600          -1.903         -0.8573        0
   52         15900           -1.92         -0.8936        0
   53         16200          -1.923         -0.9041        0
   54         16500          -1.923         -0.8505        1
   55         16800          -1.923         -0.8977        2
   56         17100          -1.923         -0.8919        3
   57         17400          -1.923          -0.884        4
   58         17700          -1.923         -0.9368        5
   59         18000          -1.923         -0.9088        6
   60         18300          -1.923         -0.9412        7

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
   61         18600          -1.923         -0.8756        8
   62         18900          -1.923         -0.8859        9
   63         19200          -1.923         -0.9001       10
   64         19500          -1.923         -0.8533       11
   65         19800          -1.923         -0.8053       12
   66         20100          -1.923         -0.8336       13
   67         20400          -1.923          -0.847       14
   68         20700          -1.923         -0.8941       15
   69         21000          -1.923         -0.9045       16
   70         21300          -1.923         -0.8238       17
   71         21600          -1.923         -0.9083       18
   72         21900          -1.923         -0.8834       19
   73         22200          -1.923         -0.8882       20
   74         22500          -1.923         -0.9112       21
   75         22800          -1.923         -0.8913       22
   76         23100          -1.923         -0.9585       23
   77         23400          -1.923         -0.9191       24
   78         23700          -1.923         -0.9067       25
   79         24000          -1.923         -0.9752       26
   80         24300          -1.923         -0.9456       27
   81         24600          -1.923         -0.9433       28
   82         24900          -1.923         -0.9401       29
   83         25200          -1.923         -0.9554       30
   84         25500          -1.923         -0.9614       31
   85         25800          -1.923         -0.9338       32
   86         26100          -1.923         -0.9546       33
   87         26400          -1.923         -0.9523       34
   88         26700          -1.923          -0.908       35
   89         27000          -1.923         -0.9668       36
   90         27300          -1.923         -0.9089       37

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
   91         27600          -1.923         -0.9291       38
   92         27900          -2.401           -0.95        0
   93         28200          -2.908         -0.9524        0
   94         28500          -2.908          -1.031        1
   95         28800          -2.908          -1.046        2
   96         29100          -2.908         -0.9336        3
   97         29400          -2.908         -0.9768        4
   98         29700          -2.908          -1.034        5
   99         30000          -2.954          -1.089        0
  100         30300          -3.029          -1.078        0
  101         30600          -3.029          -1.142        1
  102         30900          -3.029          -1.204        2
  103         31200          -3.029          -1.132        3
  104         31500          -3.029          -1.116        4
  105         31800          -3.029          -1.078        5
  106         32100          -3.029          -1.035        6
  107         32400          -3.029          -1.085        7
  108         32700          -3.029          -1.159        8
  109         33000          -3.029          -1.133        9
  110         33300          -3.029          -1.197       10
  111         33600          -3.029          -1.038       11
  112         33900          -3.029          -1.101       12
  113         34200          -3.029           -1.07       13
  114         34500          -3.029          -1.059       14
  115         34800          -3.029          -1.014       15
  116         35100          -3.029          -1.144       16
  117         35400          -3.029          -1.051       17
  118         35700          -3.029          -1.083       18
  119         36000          -3.029          -1.098       19
  120         36300          -3.029          -1.063       20

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  121         36600          -3.029          -1.206       21
  122         36900          -3.029          -1.103       22
  123         37200          -3.029         -0.9924       23
  124         37500          -3.029          -1.088       24
  125         37800          -3.029          -1.083       25
  126         38100          -3.029          -1.081       26
  127         38400          -3.029          -1.017       27
  128         38700          -3.029          -1.071       28
  129         39000          -3.029         -0.9418       29
  130         39300          -3.029          -1.005       30
  131         39600          -3.029           -1.13       31
  132         39900          -3.029          -1.076       32
  133         40200          -3.029          -1.019       33
  134         40500          -3.029          -1.016       34
  135         40800          -3.029          -1.154       35
  136         41100          -3.029          -1.069       36
  137         41400          -3.029           -1.12       37
  138         41700          -3.029          -1.122       38
  139         42000          -3.029          -1.073       39
  140         42300          -3.029          -1.123       40
  141         42600          -3.029          -1.081       41
  142         42900          -3.029          -1.088       42
  143         43200          -3.029          -1.111       43
  144         43500          -3.029          -1.121       44
  145         43800          -3.029           -1.09       45
  146         44100          -3.029          -1.061       46
  147         44400          -3.029          -1.075       47
  148         44700          -3.029         -0.9515       48
  149         45000          -3.029         -0.9136       49
  150         45300          -3.029          -1.082       50

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  151         45600          -3.029          -1.042       51
  152         45900          -3.029         -0.9562       52
  153         46200          -3.029         -0.9448       53
  154         46500          -3.029          -0.956       54
  155         46800          -3.029          -1.026       55
  156         47100          -3.029          -1.032       56
  157         47400          -3.029         -0.9963       57
  158         47700          -3.029          -1.032       58
  159         48000          -3.029          -1.102       59
  160         48300          -3.029          -1.076       60
  161         48600          -3.029         -0.9077       61
  162         48900          -3.029          -1.127       62
  163         49200          -3.029          -1.034       63
  164         49500          -3.029          -1.032       64
  165         49800          -3.029          -1.091       65
  166         50100          -3.029          -1.148       66
  167         50400           -3.15          -1.125        0
  168         50700           -3.15          -1.023        1
  169         51000           -3.15          -1.185        2
  170         51300           -3.15           -1.12        3
  171         51600           -3.15          -1.092        4
  172         51900           -3.15          -1.045        5
  173         52200           -3.15          -1.113        6
  174         52500           -3.15          -1.123        7
  175         52800           -3.15          -1.066        8
  176         53100           -3.15          -1.116        9
  177         53400           -3.15          -1.049       10
  178         53700           -3.15          -1.152       11
  179         54000           -3.15           -1.04       12
  180         54300           -3.15          -1.045       13

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  181         54600           -3.15          -1.081       14
  182         54900           -3.15          -1.093       15
  183         55200           -3.15          -1.163       16
  184         55500           -3.15          -1.102       17
  185         55800           -3.15          -1.106       18
  186         56100           -3.15          -1.158       19
  187         56400           -3.15          -1.254       20
  188         56700           -3.15          -1.089       21
  189         57000           -3.15          -1.152       22
  190         57300           -3.15          -1.107       23
  191         57600           -3.15          -1.096       24
  192         57900           -3.15          -1.002       25
  193         58200           -3.15          -1.083       26
  194         58500           -3.15          -1.156       27
  195         58800           -3.15           -1.15       28
  196         59100           -3.15          -1.056       29
  197         59400           -3.15           -1.11       30
  198         59700           -3.15          -1.047       31
  199         60000           -3.15          -1.095       32
  200         60300           -3.15          -1.106       33
  201         60600           -3.15          -1.156       34
  202         60900           -3.15          -1.073       35
  203         61200           -3.15          -1.112       36
  204         61500           -3.15          -1.123       37
  205         61800           -3.15          -1.009       38
  206         62100           -3.15          -1.049       39
  207         62400           -3.15          -1.095       40
  208         62700           -3.15          -1.094       41
  209         63000          -3.157          -1.075        0
  210         63300          -3.157          -1.126        1

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  211         63600          -3.157          -1.163        2
  212         63900          -3.157           -1.08        3
  213         64200          -3.157          -1.078        4
  214         64500          -3.157          -1.062        5
  215         64800          -3.157           -1.09        6
  216         65100          -3.157          -1.034        7
  217         65400          -3.157           -1.12        8
  218         65700          -3.157          -1.083        9
  219         66000          -3.157          -1.078       10
  220         66300          -3.157          -1.044       11
  221         66600          -3.157          -1.144       12
  222         66900          -3.157          -1.035       13
  223         67200          -3.157          -1.117       14
  224         67500          -3.157          -1.001       15
  225         67800          -3.157          -1.081       16
  226         68100          -3.157          -1.099       17
  227         68400          -3.157          -1.027       18
  228         68700          -3.157          -1.133       19
  229         69000          -3.157           -1.08       20
  230         69300          -3.157          -1.064       21
  231         69600          -3.157          -1.115       22
  232         69900          -3.157          -1.056       23
  233         70200          -3.157           -1.13       24
  234         70500          -3.157           -1.02       25
  235         70800          -3.157          -1.091       26
  236         71100          -3.157          -1.049       27
  237         71400          -3.157          -1.105       28
  238         71700          -3.157          -1.084       29
  239         72000          -3.157         -0.9767       30
  240         72300          -3.157          -1.079       31

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  241         72600          -3.157         -0.9667       32
  242         72900          -3.157          -1.104       33
  243         73200          -3.157          -1.059       34
  244         73500          -3.157          -1.042       35
  245         73800          -3.157          -1.008       36
  246         74100          -3.157          -1.033       37
  247         74400          -3.157          -1.079       38
  248         74700          -3.157          -1.049       39
  249         75000          -3.157          -1.017       40
  250         75300          -3.157          -1.058       41
  251         75600          -3.157           -1.03       42
  252         75900          -3.157          -1.056       43
  253         76200          -3.157           -1.01       44
  254         76500          -3.157          -1.171       45
  255         76800          -3.157          -1.149       46
  256         77100          -3.157          -1.131       47
  257         77400          -3.157          -1.143       48
  258         77700          -3.157          -1.127       49
  259         78000          -3.157          -1.079       50
  260         78300          -3.157          -1.024       51
  261         78600          -3.157         -0.9681       52
  262         78900          -3.157         -0.9466       53
  263         79200          -3.157          -1.002       54
  264         79500          -3.157         -0.9918       55
  265         79800          -3.157         -0.9402       56
  266         80100          -3.157          -1.052       57
  267         80400          -3.157           -1.05       58
  268         80700          -3.157          -1.044       59
  269         81000          -3.157          -1.012       60
  270         81300          -3.157         -0.9505       61

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  271         81600          -3.157         -0.9255       62
  272         81900          -3.157          -1.003       63
  273         82200          -3.157         -0.9484       64
  274         82500          -3.157         -0.9812       65
  275         82800          -3.157         -0.8808       66
  276         83100          -3.157         -0.8568       67
  277         83400          -3.157         -0.9572       68
  278         83700          -3.157          -1.082       69
  279         84000          -3.157         -0.9719       70
  280         84300          -3.157          -0.953       71
  281         84600          -3.157         -0.9659       72
  282         84900          -3.157          -0.951       73
  283         85200          -3.157          -0.907       74
  284         85500          -3.157         -0.8794       75
  285         85800          -3.157          -1.085       76
  286         86100          -3.157          -1.004       77
  287         86400          -3.157          -1.023       78
  288         86700          -3.157          -1.024       79
  289         87000          -3.157          -1.011       80
  290         87300          -3.157          -1.014       81
  291         87600          -3.157         -0.9956       82
  292         87900          -3.157          -1.035       83
  293         88200          -3.157         -0.8842       84
  294         88500          -3.157         -0.9754       85
  295         88800          -3.157         -0.9335       86
  296         89100          -3.157         -0.9526       87
  297         89400          -3.157          -1.058       88
  298         89700          -3.157         -0.9684       89
  299         90000          -3.157         -0.9224       90
  300         90300          -3.157         -0.9161       91

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  301         90600          -3.157         -0.9092       92
  302         90900          -3.157         -0.9623       93
  303         91200          -3.157         -0.9741       94
  304         91500          -3.157           -1.02       95
  305         91800          -3.157         -0.9511       96
  306         92100          -3.157          -1.034       97
  307         92400          -3.157         -0.9393       98
  308         92700          -3.157          -1.019       99
  309         93000          -3.157           -0.97      100
  310         93300          -3.157         -0.9705      101
  311         93600          -3.157          -1.006      102
  312         93900          -3.157          -0.963      103
  313         94200          -3.157         -0.9646      104
  314         94500          -3.157         -0.9862      105
  315         94800          -3.157         -0.9872      106
  316         95100          -3.157         -0.9489      107
  317         95400          -3.157         -0.8871      108
  318         95700          -3.157         -0.9722      109
  319         96000          -3.157         -0.9217      110
  320         96300          -3.157          -1.045      111
  321         96600          -3.157         -0.9612      112
  322         96900          -3.157         -0.9944      113
  323         97200          -3.157         -0.9504      114
  324         97500          -3.157          -0.998      115
  325         97800          -3.157         -0.9587      116
  326         98100          -3.157          -1.008      117
  327         98400          -3.157         -0.9601      118
  328         98700          -3.157         -0.9857      119
  329         99000          -3.157         -0.9594      120
  330         99300          -3.157          -1.009      121

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  331         99600          -3.157          -1.005      122
  332         99900          -3.157          -1.055      123
  333         100200          -3.157          -1.031      124
  334         100500          -3.157          -1.005      125
  335         100800          -3.157         -0.9773      126
  336         101100          -3.157          -1.057      127
  337         101400          -3.157          -1.053      128
  338         101700          -3.157          -1.037      129
  339         102000          -3.157          -1.018      130
  340         102300          -3.157          -1.005      131
  341         102600          -3.157          -1.113      132
  342         102900          -3.157          -1.012      133
  343         103200          -3.157          -1.002      134
  344         103500          -3.157          -1.061      135
  345         103800          -3.157          -1.067      136
  346         104100          -3.157          -1.092      137
  347         104400          -3.157         -0.9721      138
  348         104700          -3.157          -1.099      139
  349         105000          -3.157          -1.058      140
  350         105300          -3.157         -0.9923      141
  351         105600          -3.157         -0.9643      142
  352         105900          -3.157          -1.117      143
  353         106200          -3.157          -1.079      144
  354         106500          -3.157          -1.067      145
  355         106800          -3.157          -1.032      146
  356         107100          -3.157          -1.075      147
  357         107400          -3.157          -1.052      148
  358         107700          -3.157          -1.006      149
  359         108000          -3.157          -1.047      150
  360         108300          -3.157          -1.018      151

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  361         108600          -3.157          -1.095      152
  362         108900          -3.157          -1.027      153
  363         109200          -3.157          -1.167      154
  364         109500          -3.157           -1.01      155
  365         109800          -3.157         -0.9932      156
  366         110100          -3.157         -0.9869      157
  367         110400          -3.157          -0.977      158
  368         110700          -3.157          -1.063      159
  369         111000          -3.157          -0.979      160
  370         111300          -3.157          -1.025      161
  371         111600          -3.157         -0.9434      162
  372         111900          -3.157         -0.8726      163
  373         112200          -3.157         -0.9857      164
  374         112500          -3.198         -0.9902        0
  375         112800          -3.198         -0.9891        1
  376         113100          -3.285          -1.046        0
  377         113400          -3.318         -0.9976        0
  378         113700          -3.318          -1.023        1
  379         114000          -3.318          -1.021        2
  380         114300          -3.318          -1.105        3
  381         114600          -3.318          -1.024        4
  382         114900          -3.318           -1.01        5
  383         115200          -3.318          -1.037        6
  384         115500          -3.318              -1        7
  385         115800          -3.318         -0.9602        8
  386         116100          -3.318         -0.9915        9
  387         116400          -3.318          -1.037       10
  388         116700          -3.318          -1.014       11
  389         117000          -3.318          -1.048       12
  390         117300          -3.318          -1.102       13

                               Best           Mean      Stall
Generation      f-count        f(x)           f(x)    Generations
  391         117600          -3.318         -0.9611       14
  392         117900          -3.318          -1.036       15
  393         118200          -3.318          -1.075       16
  394         118500          -3.318          -1.006       17
  395         118800          -3.318          -1.133       18
  396         119100          -3.318          -1.051       19
  397         119400          -3.318          -1.005       20
  398         119700          -3.318          -1.093       21
  399         120000          -3.318         -0.9834       22
  400         120300          -3.318          -1.076       23
Optimization terminated: maximum number of generations exceeded.

Display covariance

figure;
subplot(2,1,1);
imagesc(C41);
colorbar;
subplot(2,1,2);
scatter(1:length(x),x,150,x,'filled','s');
set(gca,'XLim',[0.5 40.5]);
ylabel('cluster #');
xlabel('object #');
grid minor;