Power Iteration


In [51]:
A = randn(4);

A = A + A';

In [52]:
[V, lam] = eig(A)


V =

   0.483346   0.544800  -0.218761  -0.649395
  -0.614515   0.502559  -0.586221   0.161710
  -0.010575   0.665975   0.671561   0.324611
  -0.623407  -0.084289   0.396856  -0.668404

lam =

Diagonal Matrix

  -2.869506          0          0          0
          0   0.064090          0          0
          0          0   1.181904          0
          0          0          0   3.755084


In [53]:
V*lam*V'

A


ans =

   0.98877   0.62709  -0.92729   2.38902
   0.62709  -0.56306  -0.26538  -1.78285
  -0.92729  -0.26538   0.95682  -0.52227
   2.38902  -1.78285  -0.52227   0.74904

A =

   0.98877   0.62709  -0.92729   2.38902
   0.62709  -0.56306  -0.26538  -1.78285
  -0.92729  -0.26538   0.95682  -0.52227
   2.38902  -1.78285  -0.52227   0.74904


In [76]:
eig(A)


ans =

  -2.00000
   0.70000
   2.99900
   3.00000


In [75]:
v = randn(size(A,1),1);
v = v/norm(v);

for e=1:500,
    w = A\v;
    v = w/norm(w);    
    l = v'*(A*v);
    if rem(e,3)==1
        disp(l)
    end
end


-0.23878
 0.68832
 0.69998
 0.70000
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 0.70000

In [68]:
A = rand(4);

inv(A)

A\eye(4)


ans =

   3.1115  -5.9877  -4.4688   5.9874
  -4.6204   9.3109   4.0799  -6.7412
   2.5641  -1.7461   1.3553  -1.2396
  -3.1700   3.9247   2.8360  -1.9369

ans =

   3.1115  -5.9877  -4.4688   5.9874
  -4.6204   9.3109   4.0799  -6.7412
   2.5641  -1.7461   1.3553  -1.2396
  -3.1700   3.9247   2.8360  -1.9369


In [71]:
[Q, R] = qr(randn(4));

L = diag([3,2.999,0.7,-2]);

A = Q*L*Q'


A =

   1.227637   0.085145   0.263379   2.237816
   0.085145   0.827294   0.640538  -0.903183
   0.263379   0.640538   2.764004  -0.093422
   2.237816  -0.903183  -0.093422  -0.119935

Inverse Iteration


In [86]:
N = size(A,1);
v = randn(N,1);
v = v/norm(v);

mu = 0

for e=1:100,
    w = (A-mu*eye(N))\v;
    v = w/norm(w);    
    l = v'*A*v
    %mu = l;
end


mu = 0
l =  1.1558
l =  0.71672
l =  0.69832
l =  0.69959
l =  0.69994
l =  0.69999
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000
l =  0.70000

In [110]:
format none
N = 8;
A = randn(N);
X = A;
%X = A*A';
for e=1:100,
    [Q, R] = qr(X);
    X = R*Q;
fprintf('%d -----\n',e)
for i=1:N,
    fprintf(1,'%2.4f ',X(i,:))
    fprintf(1,'\n')
end


end


1 -----
0.1857 0.6897 -0.6947 1.7320 -3.1186 0.7912 -0.7055 -2.2570 
-0.4407 1.5317 0.5521 -2.0524 -3.5983 0.4486 0.2148 1.0496 
0.5891 1.8038 -2.2275 -0.2639 0.1598 0.0555 -0.2636 -0.5362 
0.3660 -0.0979 0.0378 -1.1567 0.5630 0.0394 -1.3977 0.0362 
1.0448 -0.7749 1.8732 -0.6074 -0.0165 -2.4529 -0.8404 2.3071 
0.6652 0.4374 1.4846 0.1471 0.9814 1.6331 -0.8225 1.7787 
-0.0632 0.1843 -0.1663 -0.0588 -0.1366 0.0903 -0.1130 0.3534 
0.5821 -0.6041 0.4236 0.1825 0.3108 0.2214 0.4999 -0.8861 
2 -----
1.6168 0.1875 0.9445 -0.3271 -1.9438 -0.1711 -0.4655 1.1406 
-2.7405 1.1978 -2.4501 -0.7952 0.5643 1.6730 -0.4948 0.4090 
-0.8981 -1.8161 -1.8910 0.3230 -0.5078 -1.1542 3.3230 -0.0236 
0.0069 -0.7312 0.3230 -0.5825 -1.1566 -1.4208 -2.6550 -0.2675 
3.2464 -0.8512 -1.5249 0.2664 -0.8729 -0.9027 -0.5938 -0.3869 
0.3349 0.6575 -1.1420 -0.7981 1.4725 -0.2556 1.0935 0.4022 
0.1413 -0.1429 0.0082 -0.0006 -0.0796 0.1525 -0.3006 1.5086 
-0.1317 0.0696 -0.0312 -0.0169 0.0845 -0.2008 0.2450 0.0390 
3 -----
0.8010 -0.5013 -2.2879 1.4754 -3.3317 -0.4261 -2.9243 0.5192 
-0.7411 0.8038 3.1501 0.3553 -0.0371 -1.5590 -0.7673 0.6899 
1.2109 2.9847 -0.5199 -0.2981 0.2432 0.8982 1.5949 -0.8908 
-0.7125 0.2079 -0.7207 -1.2612 -0.5433 -1.5623 -0.6009 0.6349 
1.4628 -0.4642 1.0129 -0.4674 -0.6088 1.1433 0.9984 -0.3941 
-0.0046 0.1617 0.1897 0.1872 0.2981 -0.8176 -0.2425 -0.9359 
-0.0736 0.1402 0.0095 -0.1340 -0.0905 -1.9330 -0.2214 2.6534 
0.0283 -0.0190 -0.0049 0.0089 -0.0063 0.6271 0.0602 0.7751 
4 -----
-1.0203 -0.7291 1.0230 -2.1501 -1.2961 2.0433 -1.3187 0.6948 
0.2721 1.3486 -2.5985 -0.9661 -1.5436 0.9130 1.0616 -0.1148 
-2.8370 -2.8883 0.1484 -0.5162 0.1947 -1.0316 -0.4833 0.2425 
1.4061 -0.5724 -1.3135 -0.5652 0.7114 2.0628 0.9066 -0.6038 
1.4253 -0.5228 -1.2743 0.8088 -0.6103 3.0090 -0.4843 0.5911 
0.0332 -0.1406 0.0641 0.2179 -0.2563 -1.7021 1.3465 -1.3096 
0.0113 0.0004 -0.0021 0.0145 -0.0197 -0.2385 -0.1580 -1.7070 
-0.0197 0.0148 0.0072 0.0006 -0.0097 0.4566 0.2743 1.5098 
5 -----
0.8744 -0.7783 -0.7179 -4.0165 -1.8872 -2.3708 -0.2128 0.6743 
0.2622 1.7973 2.0822 0.6818 -0.5656 -1.3263 0.6896 -0.3791 
-1.7131 2.1024 -1.4363 0.3371 0.1946 1.3584 0.2583 -0.8669 
1.2824 1.6345 -0.8065 -0.9825 1.2835 2.1314 -1.0476 0.3204 
0.6091 0.7446 -0.3642 0.1652 -0.6991 1.3798 -1.3258 0.4499 
0.0037 0.1066 0.0568 0.1645 -0.5361 -1.3085 2.9509 -0.3873 
-0.0067 -0.0151 -0.0004 0.0096 -0.0174 0.2951 1.0843 1.4272 
0.0044 0.0082 0.0006 -0.0031 0.0022 -0.1870 -0.6873 -0.3788 
6 -----
-0.7313 -1.7828 0.4994 -2.4364 0.8227 -0.2521 -1.6505 -0.3497 
0.9416 2.5027 -2.1475 -0.7733 1.0851 1.4658 0.4334 0.5847 
0.9389 -2.4376 -1.8631 0.4822 1.6203 1.6436 -0.7939 0.3280 
2.0061 2.2205 1.3639 1.0943 1.1295 2.5327 0.2401 0.3499 
-0.4217 -0.4587 -0.2749 -0.5086 -1.5790 -0.2023 0.3300 -0.4025 
-0.0105 -0.0566 0.0263 -0.0393 -0.4522 -1.8758 2.1365 -0.6610 
-0.0035 -0.0068 -0.0005 0.0043 0.0224 -0.2981 1.0303 -2.1358 
-0.0008 -0.0012 -0.0000 0.0002 0.0005 -0.0645 0.2267 0.3728 
7 -----
0.8318 -0.7677 -0.4217 -3.7466 -2.6601 -2.5837 -0.2660 0.6598 
-1.9019 1.0814 2.9035 1.3894 -1.2490 0.1660 1.2934 0.1657 
1.6943 2.5736 -0.7163 0.1766 0.3452 0.2621 0.2512 -0.3188 
2.0269 -0.2471 1.4024 -0.3560 0.8567 0.2522 -1.1633 -0.1634 
-0.2523 0.0301 -0.1671 -0.1289 -1.5412 0.2958 0.9508 0.6901 
-0.0052 0.0211 0.0201 -0.0365 -0.6172 -1.4730 2.0889 1.2622 
0.0004 -0.0005 0.0001 -0.0015 -0.0117 0.0545 0.3220 2.0196 
-0.0003 0.0001 -0.0000 0.0002 0.0007 -0.0277 -0.1730 0.8021 
8 -----
-1.1503 -1.5812 0.9049 -3.4943 0.1597 -0.5958 -1.1795 0.9068 
-0.2054 1.4767 -3.1256 -0.5101 0.9111 0.6160 1.1270 -0.2161 
-1.8550 -2.4411 -0.1739 0.2860 0.0329 -0.1721 0.1368 -0.0749 
1.5546 -0.3902 -1.9340 0.3442 4.1098 0.7461 -0.1099 0.9049 
0.1027 -0.0279 -0.1218 0.1200 -1.2899 0.3628 0.8657 -1.7137 
0.0025 -0.0115 0.0067 0.0278 -0.6032 -1.4122 0.9166 -1.4670 
-0.0001 -0.0000 0.0000 -0.0001 0.0026 0.0104 -0.3091 -1.4451 
0.0001 -0.0001 -0.0001 -0.0000 0.0008 -0.0310 0.7988 1.4654 
9 -----
0.4625 0.0248 -1.8436 -3.3688 -2.3077 0.0509 0.0221 0.3275 
-0.5896 1.9120 1.6558 1.0433 -1.6833 0.8398 1.1501 -0.6394 
-2.5428 1.2496 -1.2357 1.5168 2.9846 -0.2739 0.1371 -0.9288 
1.8150 1.8890 -1.6792 -0.4040 0.8844 -0.5477 -1.2021 0.4945 
0.0632 0.0681 -0.0555 0.0392 -1.6140 0.3321 2.4246 -0.2700 
0.0014 0.0074 0.0011 0.0125 -0.5257 -1.3459 0.8021 -0.2783 
0.0001 0.0001 -0.0000 -0.0001 0.0019 -0.0355 1.4724 1.4718 
-0.0000 -0.0001 0.0000 0.0000 -0.0003 0.0180 -0.7687 -0.2963 
10 -----
-0.2867 -1.7921 1.0431 -3.3587 -1.7534 0.2867 -1.3930 -0.6017 
0.4107 2.2490 -1.8258 -1.1070 0.4910 -0.0884 0.1880 0.3415 
1.4126 -2.4132 -2.0399 -1.1820 1.1808 -1.2068 -0.9683 0.1898 
1.4495 1.7745 0.7865 0.9081 2.9635 -1.6225 -0.6615 0.3802 
-0.0353 -0.0447 -0.0172 -0.0578 -1.7314 0.5552 2.4599 -0.8867 
-0.0006 -0.0035 0.0013 -0.0054 -0.4173 -1.3237 0.1647 0.0883 
0.0000 0.0000 0.0000 -0.0000 -0.0017 0.0239 0.8052 -2.0509 
0.0000 0.0000 0.0000 -0.0000 -0.0001 0.0054 0.1930 0.3702 
11 -----
-1.1378 -0.1124 1.0439 -1.9885 -2.6171 2.7210 0.8224 0.7605 
-2.2495 2.7991 1.4417 2.4208 1.3745 -0.3932 1.0966 -0.2168 
2.1921 1.5186 -0.7154 0.1103 -0.3809 0.4827 0.7121 -0.0807 
2.2610 -1.2355 1.9756 -0.1996 -1.0880 0.4574 -1.0452 0.0595 
-0.0287 0.0162 -0.0239 -0.0157 -1.6013 0.5467 2.1733 1.3711 
-0.0004 0.0012 0.0005 -0.0017 -0.3442 -1.3608 -0.3839 -0.4290 
-0.0000 0.0000 -0.0000 0.0000 0.0007 -0.0065 0.3509 2.0398 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0032 -0.1961 0.8158 
12 -----
-1.0307 1.7161 0.1319 -3.8700 0.8639 -0.1428 0.8698 -0.6143 
0.6512 1.6996 -3.0365 -1.0591 1.1104 -0.6509 1.2580 -0.3224 
1.6356 -1.9515 -0.2572 -0.9740 0.8134 -1.2166 0.2778 0.0858 
1.2462 0.3231 1.7791 0.3292 -2.0498 3.1078 0.4471 -1.0537 
-0.0116 -0.0032 -0.0159 -0.0164 -1.5449 0.5754 1.1590 -2.0714 
-0.0001 -0.0005 0.0003 -0.0016 -0.3025 -1.4147 -0.3746 1.0125 
-0.0000 0.0000 -0.0000 -0.0000 -0.0002 -0.0013 -0.3204 -1.4118 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0038 0.8296 1.4901 
13 -----
-1.0503 -0.2450 2.0358 -1.8155 0.4362 -0.7661 -0.4200 0.2500 
1.2183 1.8776 2.7276 -0.9068 0.2972 1.0479 1.3468 -0.9448 
2.3592 0.9975 -0.4419 -1.9047 1.5885 -3.3079 -0.5671 -0.5386 
1.8725 -1.3959 2.7030 0.3780 1.0201 -1.3361 0.5445 -0.5538 
-0.0077 0.0058 -0.0109 -0.0074 -1.5059 0.6315 2.1090 -0.3300 
-0.0001 0.0003 -0.0000 -0.0008 -0.2854 -1.4802 -1.4997 0.0522 
0.0000 -0.0000 0.0000 -0.0000 -0.0001 0.0040 1.4546 1.5137 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0020 -0.7272 -0.2810 
14 -----
-0.2415 -1.3502 1.5722 -3.2977 -1.1417 2.6737 -0.9371 -0.7454 
-0.0196 2.4834 -0.9848 -0.7648 -0.0213 0.9668 0.5148 0.1397 
2.3821 -1.4627 -1.7741 -2.5287 -0.4261 -0.6749 -1.0331 0.0365 
1.2159 1.5847 0.9170 0.2933 0.4992 -2.8136 -1.1280 0.2977 
-0.0034 -0.0045 -0.0025 -0.0047 -1.4397 0.6204 1.7514 -0.5203 
-0.0000 -0.0002 0.0000 -0.0005 -0.2933 -1.5392 -1.7276 0.7396 
-0.0000 -0.0000 -0.0000 0.0000 0.0001 -0.0023 0.7879 -2.0485 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0005 0.1904 0.3807 
15 -----
-2.2032 1.9396 -0.7793 1.7757 0.4772 2.0693 1.2534 0.5440 
-0.4394 3.4232 0.1247 -1.8296 0.4824 -1.7470 0.5742 -0.4124 
-1.8283 -1.0191 -1.1580 -0.5641 -0.2652 -0.5467 -1.1982 -0.0193 
-1.5357 1.7334 2.3778 0.6971 0.4124 -3.1474 0.4218 -0.4200 
-0.0019 0.0021 0.0029 0.0025 -1.3795 0.5780 1.2442 0.6715 
-0.0000 0.0001 0.0000 0.0002 -0.3257 -1.6000 -1.7878 -1.2820 
0.0000 -0.0000 -0.0000 0.0000 -0.0001 0.0005 0.3439 2.0409 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0003 -0.1999 0.8273 
16 -----
-1.5061 1.3294 -1.4300 3.1007 0.2765 -0.7046 0.3364 -0.3150 
0.7841 2.4104 2.0349 2.5859 0.3417 -1.5465 1.3585 -0.4165 
-1.7014 1.2527 -0.0165 -1.5296 0.5547 2.7661 -0.2146 -0.3738 
-1.0927 -0.4704 2.0024 -0.1278 -0.7969 -2.5617 -0.7297 1.0996 
-0.0008 -0.0003 0.0015 0.0009 -1.3349 0.5172 0.5104 -0.7120 
-0.0000 -0.0000 -0.0000 0.0001 -0.3885 -1.6451 -1.0473 2.2305 
0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0001 -0.3342 -1.3652 
-0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0003 0.8748 1.5051 
17 -----
-2.1041 -0.4313 1.3631 -1.1372 0.2985 0.7254 -0.3800 0.5524 
0.8171 2.1241 3.4813 0.6596 0.6592 -0.3682 1.2887 -1.0196 
1.7122 0.9846 -0.3231 -2.3451 -1.2071 -1.9551 -0.8836 -0.0842 
1.3212 -0.7917 2.5868 1.0621 -1.3926 -3.1354 -0.2843 -0.3732 
-0.0004 0.0003 -0.0008 -0.0008 -1.3231 0.4264 0.1276 -0.1629 
-0.0000 0.0000 -0.0000 -0.0001 -0.4821 -1.6555 -2.5970 0.2370 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0003 1.4339 1.5504 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0001 -0.6896 -0.2634 
18 -----
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-1.1801 2.4498 -0.2538 0.6587 1.4315 0.6897 1.1458 0.0854 
2.8094 -0.0979 -0.2215 -3.3342 0.7894 1.4384 -0.6470 -0.2421 
1.0793 1.3848 1.8456 -0.1806 -1.3573 -0.8125 -1.2799 0.1141 
-0.0002 -0.0002 -0.0003 -0.0002 -1.3804 0.3253 -0.6617 0.3983 
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0001 0.7792 -2.0518 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1883 0.3916 
19 -----
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0.6468 3.1469 0.9141 -0.9958 -0.7564 -0.6334 0.6024 -0.3202 
-1.5510 -0.7637 -1.2853 -1.9926 0.4618 0.6060 -1.3406 0.0784 
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-0.0001 0.0001 0.0002 0.0002 -1.5060 0.2859 -1.3221 -1.0270 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2027 0.8386 
20 -----
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0.1673 3.1592 0.0865 3.1468 -1.5098 -0.6053 1.2695 -0.4422 
-1.4669 0.5549 0.2182 -1.7388 3.8232 -0.2508 0.0515 -0.7865 
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-0.0000 -0.0000 0.0001 0.0001 -1.6193 0.3461 -0.9025 2.1273 
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0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.9258 1.5170 
21 -----
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0.4604 2.4663 2.9633 2.0863 -0.8560 -0.4697 1.1990 -1.0520 
1.4502 0.6709 0.0130 -2.9149 -0.1953 0.3795 -0.7266 0.1771 
0.8045 -0.5215 2.1299 0.8593 -3.4546 1.3864 -0.8678 -0.1138 
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0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 1.4158 1.5849 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.6552 -0.2451 
22 -----
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-1.7924 2.3526 -1.4658 1.5808 0.1487 -0.9525 1.4972 0.2394 
1.7763 -0.0118 0.9911 -2.6334 2.5730 -1.6920 0.2987 -0.4022 
0.8438 0.9058 3.0065 -0.0754 0.7033 -0.0386 -1.0778 -0.1656 
-0.0000 -0.0000 -0.0001 -0.0000 -1.6364 0.5365 -2.4335 0.8964 
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-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.1862 0.4023 
23 -----
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1.2118 2.9000 1.2621 0.1667 -0.5916 0.0714 0.9137 -0.2223 
-1.3318 -0.3167 -0.6323 -3.1066 1.6057 -1.2350 -1.1312 0.2426 
-0.5272 0.7637 2.0128 0.5557 -2.2548 2.8436 -0.8210 -0.6727 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.3207 2.0342 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.2059 0.8500 
24 -----
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-0.6961 3.2843 1.7629 -2.1300 -1.0508 0.5710 1.0958 -0.4801 
0.9539 -0.3079 -0.2000 -1.8276 -1.5069 3.2946 -0.5125 1.1805 
0.6725 0.6761 3.4160 0.2818 -1.1490 1.2659 0.7771 -0.3965 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5262 0.6182 -0.9499 2.0341 
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0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3560 -1.2598 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.9803 1.5267 
25 -----
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0.5736 2.7833 -1.8682 -2.8041 -1.0258 0.8396 1.0717 -1.0655 
-1.1782 -0.2773 0.5595 -3.1519 -0.7329 1.3241 0.3662 -0.3119 
-0.4986 0.4055 2.0615 0.2978 0.7946 -3.0309 1.1822 -0.1256 
-0.0000 0.0000 0.0000 0.0000 -1.4635 0.6202 -1.9473 0.2056 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.6232 -0.2263 
26 -----
-2.9274 -0.8167 0.2366 -1.1584 0.1150 -2.0166 0.2058 -0.5185 
-1.5193 2.5724 -2.7691 0.5581 -0.7228 -0.0166 1.5125 0.3589 
0.8871 -0.2081 0.3830 -2.1981 0.1521 -2.3261 1.0092 -0.2577 
0.5356 0.5004 3.2823 0.7315 0.6497 -2.7886 -0.3934 -0.4359 
-0.0000 -0.0000 -0.0000 -0.0000 -1.4025 0.5979 -1.5237 0.4548 
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.7579 -2.0559 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1842 0.4128 
27 -----
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1.4857 2.7133 -0.9141 -1.4062 -0.4646 0.4703 1.1970 -0.1794 
0.9763 0.0410 0.3216 -3.4146 -0.0523 3.1710 0.6605 -0.4306 
0.3551 -0.4756 2.2140 0.0090 -0.5145 -2.6221 1.1355 0.5908 
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0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.2094 0.8615 
28 -----
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-1.2247 3.0997 -2.4527 0.3642 -0.4300 0.6505 1.0163 -0.5849 
-0.6358 0.2583 -0.7018 -2.6460 -1.0435 -1.5374 0.8439 -1.1895 
-0.3963 -0.4535 3.0299 1.0238 -1.0000 -3.3285 -0.3602 -0.3335 
-0.0000 -0.0000 0.0000 0.0000 -1.3216 0.4658 -0.3033 0.3697 
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0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 1.0384 1.5335 
29 -----
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0.8879 2.9112 -0.5795 -2.9283 0.3203 1.4410 0.9498 -1.0337 
-0.7842 -0.0502 1.0089 -2.9266 1.6988 2.4296 -0.1520 -0.3227 
-0.3283 0.3259 2.4547 -0.2002 -1.4126 -1.2305 1.2712 -0.3488 
-0.0000 0.0000 0.0000 0.0000 -1.3480 0.3624 0.3888 0.1352 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 1.3780 1.6466 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.5935 -0.2073 
30 -----
-2.9676 -0.6747 0.3760 -1.2029 -1.4726 -0.6554 0.1469 -0.4607 
-1.2639 2.7516 -2.8243 -1.0307 0.0143 0.8336 1.4576 0.4002 
0.5449 -0.1993 -0.0432 -2.7549 -0.4859 0.0800 1.1019 0.0161 
0.2934 0.2666 2.6484 1.0187 -3.2970 -1.9567 0.3832 -0.5269 
-0.0000 -0.0000 -0.0000 -0.0000 -1.4513 0.2896 1.1869 -0.6010 
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-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.1823 0.4233 
31 -----
-2.5293 1.6103 1.3908 -1.5083 -0.9170 0.2709 0.4113 0.3246 
1.5098 2.6550 0.1920 -2.1361 0.5371 0.6394 1.3490 -0.1712 
0.5879 -0.0108 0.9186 -2.9343 3.9011 0.5911 -0.0153 -0.6233 
0.2569 -0.3141 2.8322 -0.2848 -0.9889 0.2784 1.2289 0.3672 
-0.0000 0.0000 -0.0000 -0.0000 -1.5814 0.3124 1.6696 1.2767 
-0.0000 0.0000 -0.0000 -0.0000 -0.5951 -1.3979 1.3417 0.7904 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.2975 2.0271 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.2130 0.8732 
32 -----
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-1.4579 2.9344 -2.1696 -1.0972 0.3227 0.5810 1.0227 -0.7074 
-0.4907 0.1484 -0.3513 -3.4575 0.3747 0.3973 0.8762 -0.8623 
-0.2178 -0.2537 2.3717 0.8918 -3.6880 0.9482 0.0620 -0.8417 
-0.0000 -0.0000 0.0000 0.0000 -1.6518 0.4079 0.7970 -2.3826 
-0.0000 -0.0000 0.0000 0.0000 -0.4996 -1.3275 0.3740 -0.6246 
0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.3661 -1.1397 
-0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 1.1004 1.5368 
33 -----
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1.1316 2.9044 0.8598 -2.5165 1.4011 -0.1420 0.8947 -0.9860 
-0.4304 -0.0141 0.9098 -2.2977 3.1031 -1.8870 -0.7999 -0.1496 
-0.2248 0.2514 3.2073 -0.1592 0.4393 0.2088 1.0210 -0.5352 
-0.0000 0.0000 0.0000 0.0000 -1.6500 0.5054 2.6106 -0.0496 
-0.0000 0.0000 0.0000 0.0000 -0.4020 -1.3293 -0.0470 -0.1498 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.5658 -0.1882 
34 -----
-2.9413 -0.7502 0.6652 -0.9819 -0.9470 1.1137 0.0395 -0.4505 
-1.1873 2.8626 -2.1030 -2.1333 0.8743 0.1327 1.4025 0.3999 
0.3921 -0.1142 0.2152 -3.2391 1.2167 -0.7365 0.8388 0.2454 
0.1643 0.1546 2.2029 0.6229 -2.5113 2.6432 0.9158 -0.4729 
-0.0000 -0.0000 -0.0000 -0.0000 -1.6083 0.5734 2.3634 -0.8934 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3340 -1.3710 -0.5612 0.3786 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.7370 -2.0595 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1806 0.4337 
35 -----
-2.6948 1.4738 -1.5943 0.5203 -0.3453 1.1210 0.3306 0.3605 
1.4216 2.6813 -1.6975 1.7549 0.9411 -0.3177 1.4003 -0.1765 
-0.3066 -0.0280 0.5594 -2.2728 -1.9347 3.1279 0.7706 0.7074 
-0.1794 0.2067 3.4760 0.2135 -1.1397 1.0230 -0.9113 0.0386 
-0.0000 0.0000 0.0000 0.0000 -1.5508 0.6107 1.9469 1.2983 
-0.0000 0.0000 0.0000 0.0000 -0.2967 -1.4285 -0.8691 -0.7816 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.2856 2.0233 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2168 0.8851 
36 -----
-2.7920 -1.4001 -0.3270 0.0412 -0.6991 1.6655 -0.5518 -0.1730 
-1.5153 2.8535 1.4203 2.0874 0.6578 0.1504 1.0493 -0.8037 
0.3556 -0.0563 0.3458 -3.6659 -1.1219 1.6313 -0.7390 0.4137 
0.1285 0.1456 2.1604 0.3522 1.0799 -3.0710 -0.3738 1.1042 
-0.0000 -0.0000 -0.0000 -0.0000 -1.4885 0.6222 0.7106 -1.9562 
-0.0000 -0.0000 -0.0000 -0.0000 -0.2852 -1.4908 -0.3595 1.5431 
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.1661 1.5359 
37 -----
-2.8165 1.7009 1.1999 0.2556 0.0627 1.4815 0.6272 0.0784 
1.2638 2.8612 2.0853 -1.3258 0.8031 -0.9968 0.9015 -0.9500 
-0.2241 -0.0447 0.0535 -2.1579 0.2922 -2.6904 -1.2664 0.1838 
-0.1407 0.1661 3.4319 0.6613 0.8512 -2.5197 0.3080 -0.5570 
-0.0000 0.0000 0.0000 0.0000 -1.4263 0.6099 1.7447 -0.1140 
-0.0000 0.0000 0.0000 0.0000 -0.2976 -1.5530 -1.9431 -0.0984 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 1.3398 1.7001 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.5400 -0.1691 
38 -----
-2.9146 -0.8958 0.8368 -0.5726 0.0886 1.4569 -0.0513 -0.4611 
-1.2131 2.9158 -1.0328 -2.7288 0.6997 -0.5113 1.3608 0.3818 
0.2674 -0.0446 0.6984 -3.2805 0.2769 -2.7635 0.4035 0.4152 
0.1021 0.1010 2.2439 0.0598 0.2620 2.7516 1.2235 -0.3357 
-0.0000 -0.0000 -0.0000 -0.0000 -1.3692 0.5715 1.2652 -0.3679 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3359 -1.6101 -2.0674 0.9120 
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-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.1789 0.4440 
39 -----
-2.7814 1.4368 -1.3695 -0.4437 0.6153 1.1756 0.3163 0.3890 
1.3370 2.7289 -2.5488 0.3295 0.3842 -1.0337 1.4020 -0.1843 
-0.1733 -0.0494 -0.1701 -2.5674 0.7754 1.7709 1.1783 0.5273 
-0.1060 0.1196 3.1368 0.9820 0.5928 3.3420 -0.1881 0.4527 
-0.0000 0.0000 0.0000 0.0000 -1.3283 0.5024 0.6814 0.3120 
-0.0000 0.0000 0.0000 0.0000 -0.4051 -1.6510 -2.0096 -1.4974 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.2736 2.0192 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.2209 0.8971 
40 -----
-2.8547 -1.2593 0.5131 0.0713 0.9325 1.5117 -0.5020 -0.2046 
-1.4821 2.8352 -0.3064 -2.6228 0.4975 -0.4957 1.0607 -0.8690 
-0.2222 0.0151 0.9410 -3.3167 -1.4094 -2.8968 0.4947 0.1179 
-0.0843 -0.0922 2.4507 -0.1621 1.3148 1.5748 0.6019 -1.1673 
-0.0000 -0.0000 0.0000 0.0000 -1.3286 0.4041 0.1379 0.0664 
-0.0000 -0.0000 0.0000 0.0000 -0.5034 -1.6507 -0.6931 2.5176 
0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.3593 -1.0046 
-0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 1.2355 1.5300 
41 -----
-2.7743 1.6925 -0.9457 -1.0332 1.2641 0.5389 0.6048 0.0791 
1.3218 2.8228 -2.3981 -0.1779 -0.4481 -1.0991 0.9371 -0.9289 
0.1437 0.0436 -0.3323 -2.8895 0.7670 0.1003 1.2138 -0.4473 
0.0771 -0.0924 2.7548 1.0432 2.8929 2.4435 0.4758 0.3807 
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-0.0000 0.0000 -0.0000 -0.0000 -0.5976 -1.5774 -2.4327 0.0185 
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0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.5160 -0.1501 
42 -----
-2.8961 -1.0191 0.8418 -0.0806 1.4756 0.3407 -0.1062 -0.4756 
-1.2672 2.9281 0.3527 -2.8136 -0.2499 -0.7862 1.3375 0.3597 
0.1589 -0.0145 1.0145 -2.8213 -3.5485 -1.1148 -0.2049 0.5223 
0.0700 0.0722 2.7797 -0.2870 1.1926 -0.0639 1.2943 -0.1084 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5327 0.2908 -1.6523 0.7903 
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.7165 -2.0626 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1775 0.4542 
43 -----
-2.8173 1.4591 -0.8439 -1.0231 1.3206 -0.4727 0.3318 0.4066 
1.2912 2.7686 -2.3821 -1.0293 -1.0499 -0.5016 1.3864 -0.1890 
-0.1225 -0.0337 -0.1140 -3.2375 -0.2259 -0.3759 1.1064 0.2126 
-0.0576 0.0653 2.4361 0.9222 3.8130 -0.4266 0.4768 0.6539 
-0.0000 0.0000 0.0000 0.0000 -1.6335 0.3660 -1.8970 -1.4586 
-0.0000 0.0000 0.0000 0.0000 -0.5414 -1.3458 -0.9274 -0.5058 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2252 0.9093 
44 -----
-2.8900 -1.1512 0.5569 0.3310 1.5355 -0.7652 -0.4749 -0.2092 
-1.4226 2.8466 1.1808 -2.4547 -0.5152 -0.5207 1.0503 -0.9156 
-0.1197 0.0092 1.0008 -2.5514 -3.4863 1.5610 0.1234 0.7277 
-0.0588 -0.0629 3.1589 -0.1979 -0.1811 -0.3616 0.7260 -0.9354 
-0.0000 -0.0000 0.0000 0.0000 -1.6574 0.4693 -0.5774 2.5353 
-0.0000 -0.0000 0.0000 0.0000 -0.4381 -1.3219 -0.2009 0.2011 
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0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 1.3083 1.5182 
45 -----
-2.7662 1.6424 -0.4091 -1.3976 0.7617 -1.0954 0.5763 0.0956 
1.3365 2.7995 -2.0064 -1.3364 -1.1300 0.1734 0.9763 -0.9160 
0.1051 0.0219 0.0436 -3.4336 -1.1681 0.4445 0.8518 -0.5528 
0.0427 -0.0512 2.2396 0.6826 2.7822 -2.4177 0.9842 0.1554 
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-0.0000 0.0000 -0.0000 -0.0000 -0.3572 -1.3515 0.4263 0.1615 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 1.3018 1.7464 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.4937 -0.1311 
46 -----
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-1.3120 2.9209 -1.9035 2.0242 -0.7809 -0.1161 1.3306 0.3409 
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47 -----
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1.2762 2.7932 1.7099 1.9239 -1.0053 0.6302 1.3699 -0.1882 
0.0880 0.0132 0.3896 -3.4944 1.1667 -1.4949 -0.7944 0.0943 
0.0334 -0.0383 2.1663 0.4025 -1.3604 3.0587 -0.9199 -0.6804 
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48 -----
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-1.3717 2.8660 2.5002 -1.1873 -0.7499 0.1025 1.0226 -0.9545 
-0.0611 0.0152 0.2158 -2.2041 -0.6141 2.9112 -0.3155 1.1736 
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0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.3289 -0.8559 
-0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 1.3842 1.4996 
49 -----
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1.3283 2.7906 -1.2325 -2.1102 -0.6745 0.9098 1.0083 -0.9056 
0.0716 0.0059 0.6284 -3.4601 -0.5479 2.5798 0.3593 -0.5537 
0.0263 -0.0313 2.2234 0.1165 -0.0033 -2.8668 1.2495 -0.0656 
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0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.4729 -0.1124 
50 -----
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-1.3365 2.9099 -2.7293 0.3471 -0.6307 0.4409 1.3337 0.3273 
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-0.0285 -0.0306 3.2118 0.9375 -0.2156 -3.2804 -0.1623 -0.4716 
-0.0000 -0.0000 0.0000 0.0000 -1.3415 0.5339 -0.9625 0.2536 
-0.0000 -0.0000 0.0000 0.0000 -0.3735 -1.6378 2.2071 -0.9900 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.6962 -2.0652 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1749 0.4745 
51 -----
-2.8230 1.5268 0.3749 -1.2558 -0.8557 -1.1282 0.3653 0.4189 
1.2751 2.8054 -0.7214 -2.4383 -0.1486 1.1770 1.3589 -0.1822 
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-0.0216 0.0251 2.4042 -0.1282 -1.1603 -1.8778 1.1773 0.5757 
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-0.0000 0.0000 0.0000 0.0000 -0.4617 -1.6580 2.0636 1.5719 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2347 0.9343 
52 -----
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-1.3388 2.8836 -2.7328 -0.5269 -0.2764 0.7196 0.9832 -0.9922 
0.0379 -0.0144 -0.2647 -2.8325 -0.9126 -0.4291 0.5770 -1.1374 
0.0210 0.0222 2.8278 1.0501 -2.4393 -2.8297 -0.3300 -0.4688 
-0.0000 -0.0000 -0.0000 -0.0000 -1.3629 0.3427 -0.0629 -0.5869 
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.4625 1.4733 
53 -----
-2.7908 1.5544 0.7783 -1.1876 -1.3277 -0.2347 0.5391 0.1330 
1.3112 2.7915 -0.0843 -2.4752 0.6265 0.9487 1.0312 -0.8947 
0.0425 0.0005 1.0324 -2.9732 3.2310 1.6762 -0.2611 -0.4576 
0.0179 -0.0212 2.7101 -0.2736 -1.3523 -0.2157 1.2738 -0.2919 
-0.0000 0.0000 -0.0000 -0.0000 -1.4786 0.2856 1.4936 0.2119 
-0.0000 0.0000 -0.0000 -0.0000 -0.6219 -1.5007 2.1365 0.0398 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 1.2645 1.7867 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.4534 -0.0938 
54 -----
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-1.3427 2.9024 -2.4772 -1.1830 0.3088 0.6968 1.3403 0.3182 
-0.0323 0.0115 -0.2049 -3.1941 0.0428 0.4124 1.1848 0.0377 
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-0.0000 -0.0000 0.0000 0.0000 -1.6021 0.3282 2.0046 -0.9426 
-0.0000 -0.0000 0.0000 0.0000 -0.5792 -1.3772 1.3241 -0.4265 
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-0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.1737 0.4845 
55 -----
-2.8181 1.5399 1.0096 -0.8726 -1.1894 0.7412 0.3700 0.4203 
1.2769 2.8103 0.6303 -2.4384 1.1472 0.2616 1.3543 -0.1726 
-0.0310 -0.0007 1.0031 -2.5731 3.6604 -1.1293 -0.3251 -0.6299 
-0.0150 0.0177 3.0896 -0.2358 -0.0898 0.4522 1.1781 0.2994 
-0.0000 0.0000 0.0000 0.0000 -1.6564 0.4291 2.0107 1.5732 
-0.0000 0.0000 0.0000 0.0000 -0.4783 -1.3229 0.5266 0.2165 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.2236 2.0003 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.2398 0.9471 
56 -----
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-1.3211 2.8962 -2.1480 -1.7693 0.6804 0.3735 0.9363 -1.0311 
0.0276 -0.0084 0.0398 -3.3909 1.0308 -0.2189 0.6291 -0.8026 
0.0116 0.0123 2.2677 0.7340 -3.0480 2.1467 -0.0536 -0.9617 
-0.0000 -0.0000 -0.0000 -0.0000 -1.6438 0.5218 0.2679 -2.5914 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3857 -1.3355 0.1317 0.1938 
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2675 -0.6978 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 1.5423 1.4382 
57 -----
-2.8040 1.5317 -1.2888 0.5231 -0.6488 1.2007 0.5314 0.1466 
1.2934 2.7972 -1.3825 2.0818 1.1033 -0.3063 1.0473 -0.8827 
-0.0221 -0.0017 0.7196 -2.2654 -2.4710 2.7856 0.9481 0.2148 
-0.0124 0.0146 3.4141 0.0465 -0.9840 0.4768 -0.8923 0.4862 
-0.0000 0.0000 0.0000 0.0000 -1.5974 0.5832 2.4919 0.1370 
-0.0000 0.0000 0.0000 0.0000 -0.3242 -1.3819 -0.7576 -0.1995 
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0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.4353 -0.0755 
58 -----
-2.9016 -1.0954 -0.5022 0.4590 -0.8047 1.4290 -0.1225 -0.4935 
-1.3369 2.9001 1.6948 2.1648 0.7585 0.0746 1.3468 0.3116 
0.0234 -0.0055 0.3030 -3.5124 -1.2348 1.3054 -0.8159 -0.2662 
0.0089 0.0096 2.1719 0.4580 1.6417 -3.0067 -1.0167 0.4667 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5384 0.6150 2.1321 -0.8449 
-0.0000 -0.0000 -0.0000 -0.0000 -0.2924 -1.4409 -1.0954 0.6186 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.6761 -2.0674 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1727 0.4945 
59 -----
-2.8156 1.5397 1.3528 -0.0368 -0.1538 1.3809 0.3682 0.4214 
1.2762 2.8122 2.0049 -1.5027 0.9132 -0.7251 1.3542 -0.1612 
-0.0159 -0.0029 0.2676 -2.1724 0.9015 -3.0085 -0.9839 -0.6870 
-0.0098 0.0116 3.4947 0.4952 1.1067 -1.9637 0.7211 -0.1568 
-0.0000 0.0000 0.0000 0.0000 -1.4758 0.6217 1.6543 1.1601 
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-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.2107 1.9948 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2453 0.9600 
60 -----
-2.9113 -1.0550 0.6214 -0.3839 -0.2078 1.6041 -0.4862 -0.1191 
-1.3119 2.9041 -1.1960 -2.5059 0.7391 -0.2380 0.8843 -1.0717 
0.0190 -0.0034 0.5969 -3.4600 0.7335 -2.3771 0.5766 -0.3479 
0.0070 0.0075 2.2024 0.1698 -0.2596 2.9597 0.1611 -1.2236 
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-0.0000 -0.0000 -0.0000 -0.0000 -0.3031 -1.5651 -0.0060 2.0128 
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.6225 1.3936 
61 -----
-2.8137 1.5192 -1.3087 -0.4067 0.3955 1.3187 0.5276 0.1570 
1.2785 2.8044 -2.4023 0.7292 0.5596 -1.0063 1.0593 -0.8699 
-0.0120 -0.0034 -0.1172 -2.3990 0.4110 2.2067 1.3012 -0.1274 
-0.0075 0.0088 3.2765 0.8859 -0.1187 3.1561 -0.0905 0.5079 
-0.0000 0.0000 0.0000 0.0000 -1.3591 0.5602 1.2152 -0.0295 
-0.0000 0.0000 0.0000 0.0000 -0.3472 -1.6202 -2.3006 -0.2677 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 1.2282 1.8218 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.4183 -0.0575 
62 -----
-2.9083 -1.0769 0.6622 -0.2047 0.5301 1.5501 -0.1179 -0.4918 
-1.3255 2.9016 -0.5956 -2.6908 0.5609 -0.5205 1.3516 0.3061 
-0.0151 0.0019 0.8524 -3.3196 -0.6286 -3.0087 0.2990 0.4401 
-0.0057 -0.0062 2.3601 -0.0863 0.9668 2.1409 1.2651 -0.3129 
-0.0000 -0.0000 0.0000 0.0000 -1.3240 0.4845 0.6060 -0.1061 
-0.0000 -0.0000 0.0000 0.0000 -0.4229 -1.6553 -2.3135 1.0542 
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-0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.1718 0.5045 
63 -----
-2.8163 1.5317 -1.1041 -0.7989 1.0402 0.9109 0.3628 0.4230 
1.2721 2.8138 -2.5016 -0.0224 -0.0667 -1.1563 1.3564 -0.1492 
0.0097 0.0032 -0.2857 -2.7679 0.9614 0.7283 1.2157 0.4612 
0.0055 -0.0066 2.9026 1.0476 1.9622 3.1108 0.0163 0.5422 
-0.0000 0.0000 -0.0000 -0.0000 -1.3368 0.3828 -0.0679 -0.2444 
-0.0000 0.0000 -0.0000 -0.0000 -0.5247 -1.6425 -2.0536 -1.6002 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1975 1.9891 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.2510 0.9732 
64 -----
-2.9129 -1.0542 0.7170 -0.0583 1.3763 0.8546 -0.4926 -0.0928 
-1.3060 2.9089 0.0835 -2.7691 0.0897 -0.7699 0.8279 -1.1134 
0.0114 -0.0011 1.0209 -3.0243 -2.8388 -2.1366 0.4509 0.2285 
0.0047 0.0051 2.6428 -0.2574 1.4472 0.5400 0.3445 -1.2677 
-0.0000 -0.0000 -0.0000 -0.0000 -1.4259 0.2977 0.1354 1.1414 
-0.0000 -0.0000 -0.0000 -0.0000 -0.6097 -1.5534 -0.0660 2.3487 
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1679 -0.5384 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 1.7017 1.3386 
65 -----
-2.8203 1.5119 -0.8599 -1.0521 1.3813 -0.0776 0.5254 0.1653 
1.2668 2.8112 -2.4122 -0.7107 -0.8530 -0.7783 1.0695 -0.8566 
-0.0082 -0.0026 -0.2177 -3.1244 0.1988 -0.3727 1.1417 -0.3719 
-0.0040 0.0048 2.5485 0.9863 3.7713 0.7659 0.6361 0.3607 
-0.0000 0.0000 0.0000 0.0000 -1.5584 0.2999 -1.9537 -0.2917 
-0.0000 0.0000 0.0000 0.0000 -0.6076 -1.4209 -1.7138 -0.0546 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 1.2104 1.8377 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.4024 -0.0397 
66 -----
-2.9138 -1.0606 0.6861 0.1548 1.5948 -0.3555 -0.1155 -0.4898 
-1.3127 2.9054 0.8541 -2.6259 -0.4618 -0.6145 1.3547 0.3008 
-0.0084 0.0008 1.0288 -2.6600 -3.7724 0.6164 -0.3825 0.5402 
-0.0040 -0.0043 3.0156 -0.2609 0.3718 -0.4741 1.2400 -0.0525 
-0.0000 -0.0000 0.0000 0.0000 -1.6444 0.3870 -2.2260 1.0475 
-0.0000 -0.0000 0.0000 0.0000 -0.5205 -1.3349 -0.8591 0.2276 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.6563 -2.0691 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1710 0.5144 
67 -----
-2.8194 1.5206 -0.5699 -1.2399 1.0227 -0.9274 0.3560 0.4252 
1.2653 2.8161 -2.1665 -1.2538 -1.1515 -0.0693 1.3593 -0.1372 
0.0070 0.0019 -0.0204 -3.3713 -0.9024 0.0238 1.0492 0.1435 
0.0030 -0.0036 2.3011 0.7832 3.2983 -1.8177 0.6053 0.7042 
-0.0000 0.0000 -0.0000 -0.0000 -1.6546 0.4881 -2.0353 -1.6334 
-0.0000 0.0000 -0.0000 -0.0000 -0.4193 -1.3247 -0.1675 0.0588 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.1840 1.9830 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.2571 0.9866 
68 -----
-2.9155 -1.0506 0.6177 0.3542 1.1599 -1.1357 -0.4969 -0.0670 
-1.3002 2.9121 1.6358 -2.2303 -0.7248 -0.2712 0.7674 -1.1552 
0.0060 -0.0009 0.7891 -2.3054 -2.7578 2.5755 0.2238 0.8960 
0.0033 0.0036 3.3652 -0.0262 -0.8443 0.2223 0.4905 -0.9430 
-0.0000 -0.0000 -0.0000 -0.0000 -1.6183 0.5625 0.1035 2.5510 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3449 -1.3610 -0.1761 -0.5412 
-0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.1020 -0.4619 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.7782 1.2727 
69 -----
-2.8250 1.5062 -0.2902 -1.3219 0.5130 -1.2880 0.5234 0.1725 
1.2574 2.8169 -1.8390 -1.7160 -1.0653 0.4466 1.0791 -0.8434 
-0.0060 -0.0012 0.2545 -3.4913 -1.2515 1.0891 0.7414 -0.4858 
-0.0023 0.0028 2.1805 0.5130 1.9241 -2.9195 1.0790 0.1678 
-0.0000 0.0000 0.0000 0.0000 -1.5627 0.6055 -2.3745 -0.2009 
-0.0000 0.0000 0.0000 0.0000 -0.3019 -1.4166 1.0482 0.2543 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 1.1929 1.8525 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.3876 -0.0222 
70 -----
-2.9182 -1.0474 -0.4535 -0.5456 0.6269 -1.5046 -0.1149 -0.4881 
-1.3006 2.9099 -2.2967 1.5385 -0.7711 0.0281 1.3568 0.2952 
0.0043 -0.0010 0.3619 -2.1689 1.2090 -3.0583 1.0654 -0.4627 
0.0026 0.0029 3.5040 0.4058 1.1706 -1.6725 -0.7384 -0.2892 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5009 0.6218 -1.9822 0.8007 
-0.0000 -0.0000 -0.0000 -0.0000 -0.2856 -1.4784 1.3182 -0.7309 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.6464 -2.0697 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.1704 0.5243 
71 -----
-2.8237 1.5092 -0.0124 1.3618 -0.0021 -1.3813 0.3490 0.4279 
1.2568 2.8192 1.4233 2.0635 -0.8227 0.8052 1.3620 -0.1252 
-0.0049 -0.0006 0.5396 -3.4863 0.8967 -2.1840 -0.6915 0.1649 
-0.0018 0.0022 2.1868 0.2244 -0.5270 3.0249 -0.9888 -0.7063 
-0.0000 0.0000 0.0000 0.0000 -1.4384 0.6142 -1.4791 -1.0620 
-0.0000 0.0000 0.0000 0.0000 -0.2932 -1.5409 1.3893 1.2635 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1704 1.9765 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.2636 1.0003 
72 -----
-2.9189 -1.0440 0.2501 0.6631 0.0092 -1.6256 -0.4994 -0.0410 
-1.2934 2.9148 2.6798 -0.6757 -0.7026 0.3234 0.7026 -1.1959 
0.0032 -0.0011 -0.0621 -2.3355 0.1918 2.4238 -0.0685 1.2970 
0.0020 0.0022 3.3370 0.8256 -0.4081 2.9859 0.5113 -0.1849 
-0.0000 -0.0000 -0.0000 -0.0000 -1.3797 0.5814 0.0259 1.4120 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3261 -1.5996 -0.3185 -2.1786 
0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0251 -0.3900 
-0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 1.8501 1.1958 
73 -----
-2.8287 1.5002 -0.3078 1.3156 -0.5815 -1.2596 0.5208 0.1793 
1.2491 2.8218 0.9287 2.3370 -0.4093 1.0789 1.0887 -0.8304 
0.0039 0.0003 0.8082 -3.3517 -0.2761 -2.9559 -0.2146 0.5089 
0.0015 -0.0018 2.3198 -0.0418 0.7485 2.3674 -1.2933 0.0417 
-0.0000 0.0000 -0.0000 -0.0000 -1.3342 0.5186 -0.8737 0.0362 
-0.0000 0.0000 -0.0000 -0.0000 -0.3888 -1.6451 2.4404 0.3491 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 1.1758 1.8664 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.3737 -0.0051 
74 -----
-2.9219 -1.0368 0.0295 0.7116 -0.7955 -1.4196 -0.1153 -0.4867 
-1.2897 2.9145 2.7586 0.1954 -0.4521 0.6279 1.3583 0.2893 
-0.0026 0.0010 -0.2691 -2.6943 0.9445 1.0407 -1.2934 0.1942 
-0.0015 -0.0016 2.9773 1.0360 1.4859 3.2871 -0.0699 0.5129 
-0.0000 -0.0000 0.0000 0.0000 -1.3236 0.4249 -0.1888 -0.0789 
-0.0000 -0.0000 0.0000 0.0000 -0.4825 -1.6557 2.3674 -1.0935 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.6365 -2.0703 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1698 0.5342 
75 -----
-2.8284 1.4986 -0.6238 1.2054 -1.2111 -0.6684 0.3425 0.4309 
1.2477 2.8230 0.3355 2.4880 0.3052 1.1087 1.3642 -0.1132 
-0.0030 -0.0001 0.9993 -3.0937 -2.3996 -2.5105 -0.1737 0.4646 
-0.0012 0.0015 2.5794 -0.2344 1.4679 0.8854 -1.1895 -0.5656 
-0.0000 0.0000 0.0000 0.0000 -1.3811 0.3248 0.4964 0.5967 
-0.0000 0.0000 0.0000 0.0000 -0.5826 -1.5982 1.9538 1.5564 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.1565 1.9696 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2705 1.0142 
76 -----
-2.9226 -1.0356 -0.1629 0.6892 -1.5484 -0.4985 -0.5001 -0.0145 
-1.2854 2.9177 2.5965 0.9446 0.0974 0.7677 0.6334 -1.2346 
0.0022 -0.0009 -0.2474 -3.0632 0.4312 -0.2702 -0.2756 1.1948 
0.0011 0.0012 2.6099 1.0117 3.5833 1.3752 0.4171 0.5516 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5062 0.2860 -0.3901 -1.6315 
-0.0000 -0.0000 -0.0000 -0.0000 -0.6214 -1.4731 -0.2356 -1.9932 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0625 -0.3249 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.9152 1.1082 
77 -----
-2.8323 1.4932 -0.9228 0.9850 -1.3317 0.3899 -0.5177 -0.1859 
1.2413 2.8261 -0.3553 2.4894 1.0048 0.5635 -1.0982 0.8177 
0.0022 0.0001 1.0431 -2.7309 -3.7914 0.0561 -0.4514 -0.4262 
0.0010 -0.0012 2.9408 -0.2775 0.6539 -0.4210 1.2324 -0.2756 
-0.0000 0.0000 -0.0000 -0.0000 -1.6196 0.3465 -2.2818 -0.3762 
-0.0000 0.0000 -0.0000 -0.0000 -0.5610 -1.3597 -1.2219 -0.0291 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 1.1589 1.8794 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.3607 0.0118 
78 -----
-2.9253 -1.0277 -0.3269 0.6335 -1.4884 0.6541 0.1161 0.4855 
-1.2800 2.9187 2.2888 1.5522 0.5842 0.5096 -1.3597 -0.2831 
-0.0018 0.0007 -0.0633 -3.3325 -0.7394 -0.1437 1.0842 0.0839 
-0.0008 -0.0009 2.3389 0.8294 3.5206 -1.4242 0.7072 -0.5448 
-0.0000 -0.0000 0.0000 0.0000 -1.6581 0.4498 -2.3321 1.1081 
-0.0000 -0.0000 0.0000 0.0000 -0.4576 -1.3212 -0.4178 0.0299 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.6267 -2.0708 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1693 0.5440 
79 -----
-2.8331 1.4890 -1.1846 0.6526 -0.8746 1.0745 -0.3363 -0.4340 
1.2386 2.8271 -1.1065 2.2571 1.1444 -0.1031 -1.3659 0.1011 
-0.0016 -0.0001 0.8560 -2.3646 -3.0349 2.3105 -0.5109 -0.7047 
-0.0008 0.0010 3.3082 -0.0906 -0.6678 -0.0056 1.0833 0.2213 
-0.0000 0.0000 0.0000 0.0000 -1.6363 0.5368 -1.9970 -1.6541 
-0.0000 0.0000 0.0000 0.0000 -0.3706 -1.3430 0.1408 0.3135 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.1424 1.9623 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2778 1.0283 
80 -----
-2.9264 -1.0262 -0.4567 0.5423 -1.0035 1.2803 0.4992 -0.0127 
-1.2767 2.9208 1.8824 2.0226 0.7552 0.1732 -0.5600 1.2703 
0.0016 -0.0005 0.1973 -3.4793 -1.2452 0.8694 0.3864 -0.8370 
0.0006 0.0007 2.1938 0.5677 2.2073 -2.7946 -0.3068 -1.0183 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5861 0.5919 0.4999 2.4098 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3156 -1.3932 -0.3335 -0.8210 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1603 -0.2686 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.9715 1.0104 
81 -----
-2.8359 1.4854 1.3311 -0.2137 -0.3632 1.3395 0.5142 0.1925 
1.2333 2.8301 1.8019 -1.7548 1.0040 -0.5606 1.1076 -0.8054 
-0.0011 -0.0002 0.4497 -2.1707 1.5183 -3.0600 -1.1078 -0.1815 
-0.0007 0.0008 3.5012 0.3156 1.1928 -1.3766 0.7060 -0.4711 
-0.0000 0.0000 0.0000 0.0000 -1.5259 0.6183 2.2305 0.2453 
-0.0000 0.0000 0.0000 0.0000 -0.2892 -1.4534 -1.3056 -0.3199 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 1.1424 1.8917 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.3484 0.0283 
82 -----
-2.9287 -1.0192 0.5641 -0.4356 -0.4498 1.5616 -0.1169 -0.4845 
-1.2709 2.9226 -1.4024 -2.3829 0.7662 -0.1248 1.3611 0.2768 
0.0013 -0.0003 0.4861 -3.4959 1.0256 -1.9812 0.6775 0.3060 
0.0005 0.0005 2.1757 0.2795 -0.7981 3.0622 1.1018 -0.4618 
-0.0000 -0.0000 -0.0000 -0.0000 -1.4632 0.6201 1.8107 -0.7419 
-0.0000 -0.0000 -0.0000 -0.0000 -0.2873 -1.5161 -1.5192 0.8397 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.6169 -2.0712 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1689 0.5538 
83 -----
-2.8375 1.4802 -1.3243 -0.2524 0.1606 1.3781 0.3304 0.4371 
1.2297 2.8314 -2.2933 1.0350 0.7235 -0.8915 1.3673 -0.0888 
-0.0008 -0.0002 0.0086 -2.2826 -0.0524 2.6164 1.0780 0.6935 
-0.0005 0.0006 3.3899 0.7571 -0.6519 2.7783 -0.5119 0.2738 
-0.0000 0.0000 0.0000 0.0000 -1.4022 0.5978 1.2818 0.9381 
-0.0000 0.0000 0.0000 0.0000 -0.3097 -1.5771 -1.5189 -1.4184 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.1280 1.9546 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.2855 1.0427 
84 -----
-2.9301 -1.0166 -0.6437 0.3004 0.2122 1.6123 -0.4967 0.0407 
-1.2676 2.9241 0.8428 2.6317 0.6523 -0.4203 0.4825 -1.3023 
0.0010 -0.0002 0.7598 -3.3886 -0.0364 2.8596 -0.4597 0.3522 
0.0004 0.0004 2.2842 0.0057 -0.5131 -2.5586 0.1906 1.2684 
-0.0000 -0.0000 -0.0000 -0.0000 -1.3497 0.5476 -0.1788 -1.0929 
-0.0000 -0.0000 -0.0000 -0.0000 -0.3599 -1.6296 0.7288 2.2549 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.2668 -0.2233 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 2.0168 0.9039 
85 -----
-2.8397 1.4770 1.1723 0.6613 0.7766 1.1510 -0.5105 -0.1989 
1.2252 2.8339 2.5036 -0.2526 0.2325 -1.1242 -1.1168 0.7934 
-0.0007 -0.0002 -0.2500 -2.6199 -0.8743 -1.3450 1.3081 -0.1371 
-0.0004 0.0005 3.0522 1.0152 -1.0304 -3.3695 0.1309 0.4834 
-0.0000 0.0000 0.0000 0.0000 -1.3216 0.4654 -0.4690 0.0771 
-0.0000 0.0000 0.0000 0.0000 -0.4420 -1.6577 2.5375 0.4212 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 1.1261 1.9031 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.3370 0.0446 
86 -----
-2.9320 -1.0108 -0.6981 0.1428 1.0648 1.2271 0.1176 0.4835 
-1.2621 2.9262 0.1955 2.7574 0.3113 -0.7121 -1.3625 -0.2705 
-0.0008 0.0001 0.9716 -3.1518 1.9369 2.7777 0.1184 0.4791 
-0.0003 -0.0004 2.5201 -0.2063 -1.4187 -1.2293 1.2870 -0.2838 
-0.0000 -0.0000 0.0000 0.0000 -1.3483 0.3620 0.2857 -0.3013 
-0.0000 -0.0000 0.0000 0.0000 -0.5455 -1.6310 2.3405 -1.0917 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.6071 -2.0715 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1686 0.5636 
87 -----
-2.8417 1.4718 0.9368 0.9643 1.3384 0.3713 -0.3246 -0.4402 
1.2210 2.8355 2.4743 0.4665 -0.5522 -1.0054 -1.3684 0.0761 
0.0005 0.0002 -0.2658 -2.9974 -0.6368 0.0981 1.1732 0.4220 
0.0003 -0.0003 2.6750 1.0314 -3.2860 -1.9434 0.1926 0.6233 
-0.0000 0.0000 -0.0000 -0.0000 -1.4519 0.2895 0.9166 0.9694 
-0.0000 0.0000 -0.0000 -0.0000 -0.6179 -1.5274 1.7467 1.4183 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.1133 1.9464 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.2937 1.0574 
88 -----
-2.9337 -1.0071 -0.7100 -0.0467 1.6216 0.1121 0.4925 -0.0692 
-1.2584 2.9276 -0.5437 2.7096 -0.2846 -0.7232 -0.4017 1.3299 
0.0006 -0.0001 1.0506 -2.8062 3.7118 0.5325 0.5126 0.2785 
0.0003 0.0003 2.8664 -0.2850 -0.9190 0.2884 -0.0222 -1.2804 
-0.0000 -0.0000 -0.0000 -0.0000 -1.5818 0.3126 -0.8007 -1.9459 
-0.0000 -0.0000 -0.0000 -0.0000 -0.5948 -1.3975 -0.4141 -1.4976 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.3802 -0.1908 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 2.0493 0.7905 
89 -----
-2.8435 1.4685 0.6642 1.1676 1.2252 -0.6553 0.5067 0.2052 
1.2170 2.8378 2.2797 1.0690 -1.0928 -0.3464 1.1256 -0.7817 
-0.0005 -0.0002 -0.1076 -3.2907 0.5479 0.2791 -1.0595 0.3549 
-0.0002 0.0003 2.3816 0.8728 -3.6993 0.9629 -0.7796 -0.3526 
-0.0000 0.0000 0.0000 0.0000 -1.6519 0.4083 -2.4724 -0.4518 
-0.0000 0.0000 0.0000 0.0000 -0.4991 -1.3274 -0.7242 0.0267 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 1.1102 1.9139 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.3262 0.0605 
90 -----
-2.9354 -1.0022 -0.6649 -0.2561 1.3549 -0.8962 -0.1181 -0.4825 
-1.2534 2.9296 -1.3347 2.4203 -0.6672 -0.4004 1.3640 0.2642 
-0.0004 0.0001 0.9116 -2.4274 3.2867 -1.9849 0.5977 -0.5594 
-0.0002 -0.0002 3.2448 -0.1463 0.4574 0.1984 -1.1445 -0.0165 
-0.0000 -0.0000 0.0000 0.0000 -1.6499 0.5058 -2.3520 1.1338 
-0.0000 -0.0000 0.0000 0.0000 -0.4017 -1.3294 -0.0231 -0.1561 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.5973 -2.0716 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1685 0.5734 
91 -----
-2.8457 1.4636 0.3812 1.2859 0.7244 -1.1867 0.3186 0.4432 
1.2126 2.8396 1.9784 1.5601 -1.1170 0.2551 1.3694 -0.0631 
0.0004 0.0001 0.1441 -3.4604 1.2097 -0.6504 -0.9502 -0.0943 
0.0002 -0.0002 2.2118 0.6215 -2.4894 2.6279 -0.7068 -0.7543 
-0.0000 0.0000 -0.0000 -0.0000 -1.6081 0.5736 -1.9157 -1.6465 
-0.0000 0.0000 -0.0000 -0.0000 -0.3338 -1.3712 0.3999 0.5490 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0984 1.9377 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.3024 1.0723 
92 -----
-2.9372 -0.9980 0.5428 0.4615 0.8389 -1.3914 -0.4867 0.0978 
-1.2493 2.9310 2.0631 -1.8389 -0.7748 -0.0747 0.3182 -1.3526 
-0.0003 0.0001 0.5387 -2.1862 -1.8310 3.0151 0.4843 0.9640 
-0.0002 -0.0002 3.4861 0.2269 -1.1738 1.0809 0.2362 -0.8721 
-0.0000 -0.0000 0.0000 0.0000 -1.5505 0.6108 0.8720 2.1705 
-0.0000 -0.0000 0.0000 0.0000 -0.2966 -1.4288 -0.5879 -1.0124 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.4982 -0.1724 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 2.0677 0.6725 
93 -----
-2.8475 1.4600 -0.0919 -1.3372 0.2142 -1.3740 -0.5029 -0.2113 
1.2087 2.8416 -1.5935 -1.9518 -0.9334 0.6630 -1.1340 0.7704 
0.0003 0.0001 0.4302 -3.5029 -1.1268 1.7720 -0.6228 0.4663 
0.0001 -0.0002 2.1694 0.3351 1.0724 -3.0710 -1.1594 -0.1759 
-0.0000 0.0000 -0.0000 -0.0000 -1.4883 0.6222 2.0624 0.2705 
-0.0000 0.0000 -0.0000 -0.0000 -0.2852 -1.4910 -1.5368 -0.3922 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 1.0945 1.9240 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.3161 0.0762 
94 -----
-2.9388 -0.9935 -0.3546 -0.6184 0.2650 -1.6024 0.1186 0.4816 
-1.2447 2.9330 -2.5672 1.0231 -0.7479 0.2183 -1.3655 -0.2579 
-0.0002 0.0001 0.0841 -2.2380 0.3157 -2.7767 -1.1863 0.4278 
-0.0001 -0.0002 3.4343 0.6812 0.8508 -2.5410 0.5066 0.3654 
-0.0000 -0.0000 0.0000 0.0000 -1.4261 0.6098 1.6149 -0.6660 
-0.0000 -0.0000 0.0000 0.0000 -0.2977 -1.5532 -1.7020 0.9454 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.5876 -2.0717 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1684 0.5831 
95 -----
-2.8496 1.4555 -0.2028 1.3228 -0.3307 -1.3516 -0.3125 -0.4463 
1.2043 2.8436 1.1283 2.2544 -0.6066 0.9704 -1.3704 0.0497 
0.0003 0.0000 0.7102 -3.4188 0.3072 -2.7285 0.5623 -0.2297 
0.0001 -0.0001 2.2534 0.0553 0.2659 2.7165 1.0366 0.7326 
-0.0000 0.0000 -0.0000 -0.0000 -1.3689 0.5713 1.0589 0.7807 
-0.0000 0.0000 -0.0000 -0.0000 -0.3361 -1.6104 -1.6264 -1.5704 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0831 1.9284 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.3117 1.0876 
96 -----
-2.9405 -0.9890 0.1370 0.7000 -0.4535 -1.5595 0.4791 -0.1263 
-1.2403 2.9345 2.7602 -0.1369 -0.5800 0.5209 -0.2330 1.3702 
-0.0002 0.0001 -0.2195 -2.5464 0.7581 1.6371 -0.3101 -1.2809 
-0.0001 -0.0001 3.1259 0.9851 0.6084 3.3711 -0.4824 0.1040 
-0.0000 -0.0000 0.0000 0.0000 -1.3282 0.5020 -0.2057 -0.7178 
-0.0000 -0.0000 0.0000 0.0000 -0.4054 -1.6511 1.1813 2.2111 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.6182 -0.1690 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 2.0711 0.5524 
97 -----
-2.8514 1.4515 -0.5063 1.2377 -0.9755 -0.9927 0.4991 0.2172 
1.2003 2.8454 0.5717 2.4557 -0.0255 1.1432 1.1421 -0.7593 
-0.0002 -0.0000 0.9386 -3.2073 -1.4779 -2.9450 -0.0540 0.4957 
-0.0001 0.0001 2.4650 -0.1732 1.3099 1.5548 -1.3155 0.0346 
-0.0000 0.0000 0.0000 0.0000 -1.3288 0.4036 0.0030 0.1537 
-0.0000 0.0000 0.0000 0.0000 -0.5038 -1.6505 2.5676 0.4754 
-0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 1.0792 1.9335 
0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.3066 0.0915 
98 -----
-2.9421 -0.9848 -0.0693 0.7099 -1.3131 -0.9551 -0.1190 -0.4806 
-1.2359 2.9363 2.6816 0.6673 -0.1388 0.7676 1.3670 0.2516 
0.0001 -0.0001 -0.2794 -2.9288 0.7965 0.1312 -1.2582 0.1404 
0.0001 0.0001 2.7435 1.0447 2.8991 2.4359 -0.2786 0.5478 
-0.0000 -0.0000 -0.0000 -0.0000 -1.4024 0.3096 0.7930 -0.5499 
-0.0000 -0.0000 -0.0000 -0.0000 -0.5979 -1.5769 2.2019 -1.0309 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.5778 -2.0717 
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.1684 0.5929 
99 -----
-2.8534 1.4473 -0.8096 1.0620 -1.3920 -0.0407 0.3063 0.4493 
1.1960 2.8474 -0.0854 2.5210 0.7728 0.8421 1.3712 -0.0358 
0.0002 0.0000 1.0498 -2.8788 -3.5240 -1.1175 -0.0048 0.5515 
0.0001 -0.0001 2.7935 -0.2844 1.1469 -0.0789 -1.1741 -0.5455 
-0.0000 0.0000 -0.0000 -0.0000 -1.5333 0.2909 1.2747 1.3196 
-0.0000 0.0000 -0.0000 -0.0000 -0.6165 -1.4460 1.4409 1.1831 
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0676 1.9186 
0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.3215 1.1031 
100 -----
-2.9439 -0.9802 -0.2465 0.6700 -1.6036 0.2535 -0.4700 0.1541 
-1.2315 2.9378 2.4229 1.3291 0.4458 0.6408 0.1470 -1.3824 
-0.0001 0.0001 -0.1473 -3.2433 -0.3283 -0.3713 0.0833 1.1424 
-0.0001 -0.0001 2.4289 0.9128 3.8149 -0.4363 0.6089 0.5455 
-0.0000 -0.0000 0.0000 0.0000 -1.6338 0.3664 -1.2759 -2.0262 
-0.0000 -0.0000 0.0000 0.0000 -0.5410 -1.3455 -0.4152 -0.9676 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.7375 -0.1806 
0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 2.0595 0.4332 

In [54]:
help fprintf


'fprintf' is a built-in function from the file libinterp/corefcn/file-io.cc

 -- Built-in Function:  fprintf (FID, TEMPLATE, ...)
 -- Built-in Function:  fprintf (TEMPLATE, ...)
 -- Built-in Function: NUMBYTES = fprintf (...)
     This function is equivalent to `printf', except that the output is
     written to the file descriptor FID instead of `stdout'.

     If FID is omitted, the output is written to `stdout' making the
     function exactly equivalent to `printf'.

     The optional output returns the number of bytes written to the
     file.

     Implementation Note: For compatibility with MATLAB, escape
     sequences in the template string (e.g., "\n" => newline) are
     expanded even when the template string is defined with single
     quotes.

     See also: fputs, fdisp, fwrite, fscanf, printf, sprintf, fopen.


Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.

In [19]:
A = [1 0 0;0 1 0;0 0 -1]


A =

   1   0   0
   0   1   0
   0   0  -1


In [22]:
T = rand(3);

B = inv(T)*A*T

[V, L ] = eig(B)


B =

   2.258027   3.018036   1.441095
  -1.396021  -2.349088  -1.599171
   0.079493   0.190706   1.091061

V =

   0.918942   0.668839  -0.438368
  -0.393754  -0.742205  -0.231910
   0.022421   0.042263   0.868361

L =

Diagonal Matrix

   1.00000         0         0
         0  -1.00000         0
         0         0   1.00000


In [26]:
rank(rand(3))


ans =  3

In [14]:
A = 0.000000001*eye(2)

[U, S, W] = svd(A)


A =

Diagonal Matrix

   1.0000e-09            0
            0   1.0000e-09

U =

   1   0
  -0   1

S =

Diagonal Matrix

   1.0000e-09            0
            0   1.0000e-09

W =

   1   0
   0   1


In [35]:
A = [0 1/2 0 0 0;1 0 1/3 0 0;0 1/2 0 1-0.01 1;0 0 1/3 0.01 0;0 0 1/3 0 0]


A =

   0.00000   0.50000   0.00000   0.00000   0.00000
   1.00000   0.00000   0.33333   0.00000   0.00000
   0.00000   0.50000   0.00000   0.99000   1.00000
   0.00000   0.00000   0.33333   0.01000   0.00000
   0.00000   0.00000   0.33333   0.00000   0.00000


In [28]:
x = [1 0 0 0 0]'


x =

   1
   0
   0
   0
   0


In [45]:
eig(A)


ans =

  -0.9975249
  -0.5753850
   1.0000000
   0.5778850
   0.0050249


In [41]:
expm(A)


ans =

   1.264281   0.557920   0.092913   0.029449   0.029674
   1.115841   1.357194   0.411362   0.184557   0.185826
   0.278739   0.617044   1.448838   1.138935   1.145065
   0.029747   0.093211   0.383480   1.187983   0.179148
   0.029674   0.092913   0.381688   0.177357   1.178568


In [125]:
[Q, R] = qr(randn(5));
L = diag([-3,4,2.5,0.7,-2]);
A = Q*L*Q'


A =

   0.44982   0.84444  -1.95293  -1.36748  -0.22925
   0.84444  -0.10863   1.91697  -0.56667  -1.30190
  -1.95293   1.91697   1.48925  -1.20812  -1.30877
  -1.36748  -0.56667  -1.20812   1.14929  -0.61383
  -0.22925  -1.30190  -1.30877  -0.61383  -0.77973


In [126]:
eig(A)


ans =

   4.00000
   2.50000
   0.70000
  -3.00000
  -2.00000


In [123]:
format short

In [127]:
V = A

for i=1:100,
    [Q, R] = qr(V);
    V = R*Q;
end
V
diag(V)


V =

   0.44982   0.84444  -1.95293  -1.36748  -0.22925
   0.84444  -0.10863   1.91697  -0.56667  -1.30190
  -1.95293   1.91697   1.48925  -1.20812  -1.30877
  -1.36748  -0.56667  -1.20812   1.14929  -0.61383
  -0.22925  -1.30190  -1.30877  -0.61383  -0.77973

V =

   4.0000e+00  -6.3766e-12  -6.1773e-16   7.6397e-16  -1.0194e-15
  -6.3743e-12  -3.0000e+00  -1.2572e-07   7.3654e-16  -2.5528e-16
  -1.2600e-19  -1.2572e-07   2.5000e+00   5.8351e-10   9.0941e-17
  -6.4433e-30  -1.5002e-17   5.8351e-10  -2.0000e+00   1.6022e-16
  -4.2425e-76  -2.2832e-63   1.1281e-55  -9.3775e-46   7.0000e-01

ans =

   4.00000
  -3.00000
   2.50000
  -2.00000
   0.70000

Simultaneous Iteration


In [133]:
%[Q,R] = qr(randn(5,2), 0)
Q = randn(5,2);
Q = Q./repmat(sum(Q,1),[5 1]);

for i=1:10000,
    Z = A*Q;
    [Q, R] = qr(Z,0);
end

Q

R

A*Q


Q =

  -0.29350   0.53301
   0.50103  -0.27249
   0.67184   0.69975
  -0.31340   0.30626
  -0.33651   0.24125

R =

  -3.95883   0.37352
   0.00000   3.03120

ans =

  -0.51529  -1.83102
   1.60132   1.33346
   3.35321  -1.20692
  -0.84786  -1.21596
  -1.00955  -1.05936