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problem2.txt
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For LU decomposition: ...
L matrix is:
[[ 1.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 4.84681368e-01 1.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 3.46305460e-01 4.79143113e-01 1.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 2.96869457e-01 3.68807539e-02 8.63272488e-01 1.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 2.73147732e-01 3.54658850e-02 -2.05040108e-02 1.04066283e-02
1.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 6.26378879e-02 2.16549486e-02 2.87634999e-01 5.98211065e-02
2.57926099e-02 1.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.31988809e-01 -6.13486990e-02 1.49788707e-01 4.94392291e-02
1.54886991e-02 4.30113710e-02 1.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.31053910e-01 -6.95498884e-02 -5.71495369e-02 1.56852361e-02
1.81494956e-03 2.09974945e-01 4.38529823e-05 1.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 7.50082880e-02 6.08870238e-02 1.20215043e-01 1.31490333e-02
-7.62948301e-03 1.62050739e-01 1.49567509e-02 2.52222782e-03
1.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 3.08648031e-02 9.35540721e-03 7.20559135e-02 7.04647182e-03
5.25621977e-03 5.00929216e-03 2.50519756e-02 3.60618494e-02
9.10045728e-02 1.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.84808392e-02 3.52620371e-02 2.69351271e-03 1.67475753e-02
1.85003150e-02 1.90348756e-02 8.52948800e-03 2.21738815e-02
1.64001975e-02 5.16007245e-01 1.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.15461074e-01 3.73354577e-03 9.89140011e-03 4.37374134e-03
1.11311264e-02 3.53991538e-02 -2.66360817e-03 6.07269257e-03
-4.34605521e-04 2.09625401e-02 2.78662890e-02 1.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.51263643e-02 4.48409282e-03 1.95106398e-02 1.21246753e-02
3.01830843e-03 3.32811624e-02 9.81919467e-03 1.61087401e-02
1.92829520e-02 1.43403560e-01 1.97946057e-02 1.87682863e-02
1.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 5.96246272e-02 1.92432404e-02 -1.97117813e-02 7.22517306e-03
4.66073351e-03 2.17840937e-03 1.03474883e-02 8.90145358e-03
7.75486929e-03 1.00532994e-01 1.07453400e-02 1.67277865e-02
1.85721308e-01 1.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 2.75414512e-02 1.07614798e-02 7.10494351e-03 1.15235848e-02
5.87824499e-03 4.46968526e-02 -3.59236123e-03 4.46045166e-03
-1.08140102e-03 6.44806400e-02 6.82418933e-03 1.36786569e-02
8.62050429e-02 3.90839912e-02 1.00000000e+00 0.00000000e+00]
[ 2.84050666e-02 1.36084948e-02 1.12585388e-02 1.23763736e-02
3.15039116e-03 4.75169457e-02 -3.20238993e-03 -1.81960943e-03
4.47277399e-03 5.13768196e-02 1.60502945e-03 5.65985404e-03
7.07940161e-02 -6.52331044e-04 4.11365293e-02 1.00000000e+00]]
U matrix is:
[[ 3.8729522e-01 3.5511550e-01 2.4105136e-01 1.2011241e-01
9.5767759e-02 5.5753987e-02 4.3184314e-02 4.8650619e-02
4.6280783e-02 4.1748010e-02 1.5442266e-02 3.4991931e-02
3.8863142e-05 3.5273787e-02 1.8746665e-02 1.4195884e-02]
[ 0.0000000e+00 6.4229566e-01 5.2636076e-02 1.1845486e-01
5.7947241e-02 -1.1274246e-02 2.0965276e-02 1.1997357e-02
2.4274621e-02 1.1364750e-02 3.6911447e-02 1.1864158e-02
8.9300219e-03 -7.1676387e-03 2.5727447e-02 1.4197157e-02]
[ 0.0000000e+00 0.0000000e+00 4.5728818e-01 -6.9314577e-02
1.4412680e-01 4.2997789e-02 5.2235853e-02 9.0307826e-03
4.4341579e-02 -1.2927374e-02 1.3020856e-02 1.6807407e-02
2.5719987e-02 1.8923694e-02 -7.8611113e-03 7.8932615e-03]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 3.0082359e+00
1.4908837e-01 8.5588507e-02 -4.2440076e-03 9.9818502e-03
-2.3786290e-02 4.3120045e-02 -1.2415510e-02 -9.0503171e-03
1.9589730e-02 2.0542830e-02 2.2282749e-02 9.3729850e-03]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
3.6154723e+00 2.1857719e-01 1.3998836e-01 -7.9651410e-03
8.6318970e-02 -1.0253605e-02 6.5092884e-02 2.8211998e-02
3.4316048e-02 3.5014611e-02 3.4908112e-02 -2.2996257e-03]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 9.2191118e-01 4.6946958e-01 2.3898284e-01
7.2151326e-02 1.1446174e-01 7.0232332e-02 1.6109798e-02
9.9658519e-03 1.2704053e-02 2.9288661e-02 4.2145029e-02]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 5.4357710e+00 9.3825758e-02
2.1317337e-01 1.4064805e-01 1.1458433e-01 5.1458035e-02
5.4152068e-02 4.6974987e-02 4.1891176e-02 2.3090668e-02]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 5.4507527e+00
3.5153979e-01 3.2936286e-02 8.7390639e-02 9.4043255e-02
6.9624089e-02 1.9796446e-02 4.6559718e-02 1.7583711e-02]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
4.5448461e+00 3.0814981e-01 1.7478195e-01 5.7888508e-02
1.8797452e-02 3.2354794e-02 1.4824679e-02 4.2381033e-02]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 8.5001129e-01 4.8166107e-02 1.8473802e-02
7.8590631e-02 1.1493106e-01 4.7482174e-02 4.2533785e-02]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 1.0541049e+01 1.8095914e-01
-3.5862379e-02 7.1174391e-02 3.2057595e-02 9.0812584e-03]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 1.1159947e+01
3.9806420e-01 1.2652490e-01 9.4277970e-02 6.1478283e-02]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
1.6329607e+00 2.1451204e-01 1.8160620e-01 1.4701302e-03]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 7.5738993e+00 4.3910307e-01 1.9497925e-01]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 3.6933832e+00 2.7487665e-01]
[ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00
0.0000000e+00 0.0000000e+00 0.0000000e+00 3.9906437e+00]]
f is: [0.00345958 0.03231731 0.08087177 0.10022925 0.13331331 0.12322342
0.13155991 0.10453997 0.08667092 0.05877324 0.04246465 0.03845601
0.01786364 0.02487733 0.01350275 0.00787694]
The sum of x is: 1.0
For LU decomposition with iterative improvements: ...
f is: [0.00345958 0.03231731 0.08087177 0.10022925 0.13331331 0.12322342
0.13155992 0.10453996 0.08667092 0.05877324 0.04246465 0.03845601
0.01786364 0.02487733 0.01350275 0.00787694]
The sum of x is: 1.0