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
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
0.70000
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 -----
-1.2884 -1.3383 1.6712 -2.3379 2.2214 2.3629 -0.3550 -0.7639
-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
-0.0000 -0.0000 -0.0000 -0.0001 -0.5822 -1.5988 -2.3588 0.8251
0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0001 0.7792 -2.0518
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19 -----
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20 -----
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21 -----
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22 -----
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23 -----
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24 -----
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25 -----
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26 -----
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27 -----
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28 -----
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29 -----
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30 -----
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31 -----
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32 -----
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33 -----
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34 -----
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35 -----
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36 -----
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37 -----
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38 -----
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39 -----
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40 -----
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41 -----
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42 -----
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43 -----
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44 -----
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45 -----
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46 -----
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47 -----
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48 -----
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49 -----
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50 -----
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51 -----
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52 -----
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53 -----
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54 -----
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55 -----
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56 -----
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57 -----
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58 -----
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59 -----
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60 -----
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61 -----
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62 -----
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63 -----
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64 -----
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65 -----
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66 -----
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67 -----
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68 -----
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0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 1.7782 1.2727
69 -----
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70 -----
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71 -----
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72 -----
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73 -----
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1.2491 2.8218 0.9287 2.3370 -0.4093 1.0789 1.0887 -0.8304
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74 -----
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0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.1698 0.5342
75 -----
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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
Content source: atcemgil/notes
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