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pkofod/gist:ce449cc8561880739954221a656fdecb

Created October 10, 2018 12:11
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gistfile1.txt
I just spent half a day wondering why my Jacobians were wrong, and didn't even think to look at `I`'s role, but is this not super weird?
```
julia> versioninfo()
Julia Version 0.6.4
Commit 9d11f62bcb (2018-07-09 19:09 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD Ryzen 3 1200 Quad-Core Processor
WORD_SIZE: 64
BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Zen MAX_THREADS=16)
LAPACK: libopenblas64_
LIBM: libopenlibm
LLVM: libLLVM-3.9.1 (ORCJIT, generic)
julia> FRE
94×94 Array{Float64,2}:
2.26954e-5 0.00129015 0.00623178 0.016232 0.0316351 0.0513055 0.0729759 … -2.34201e-8 1.9804e-8 -1.61944e-8 1.25901e-8 -8.98995e-9 5.39278e-9 -1.7974e-9
-6.76662e-6 0.000203925 0.00419142 0.0138753 0.0291195 0.0490749 0.0712448 1.77187e-7 -1.49749e-7 1.22401e-7 -9.51256e-8 6.79067e-8 -4.0728e-8 1.35733e-8
4.71671e-6 -3.60899e-5 0.000565915 0.00858543 0.0237948 0.0440718 0.0674172 -2.01177e-7 1.70043e-7 -1.39001e-7 1.08034e-7 -7.71254e-8 4.62586e-8 -1.54168e-8
-4.03045e-6 1.97552e-5 -8.95263e-5 0.00110632 0.0143481 0.0355805 0.0603676 3.16547e-7 -2.67533e-7 2.18677e-7 -1.69949e-7 1.21321e-7 -7.27643e-8 2.425e-8
3.88172e-6 -1.52292e-5 4.54385e-5 -0.000168688 0.00182339 0.0213535 0.0488525 -3.13451e-7 2.64915e-7 -2.16537e-7 1.68286e-7 -1.20134e-7 7.20521e-8 -2.40127e-8
-3.91022e-6 1.39137e-5 -3.23165e-5 8.27224e-5 -0.000273885 0.00271296 0.0294787 … 2.87735e-7 -2.43178e-7 1.98767e-7 -1.54474e-7 1.10273e-7 -6.61378e-8 2.20416e-8
4.01629e-6 -1.33314e-5 2.83776e-5 -5.58403e-5 0.000132173 -0.000405445 0.00377031 -2.85704e-7 2.41426e-7 -1.97311e-7 1.53328e-7 -1.09447e-7 6.5639e-8 -2.18748e-8
-4.24552e-6 1.37846e-5 -2.61636e-5 4.87143e-5 -8.69749e-5 0.000195391 -0.00056504 1.14952e-7 -9.71083e-8 7.93443e-8 -6.16452e-8 4.39965e-8 -2.63836e-8 8.79215e-9
4.4854e-6 -1.40695e-5 2.67471e-5 -4.25667e-5 7.5056e-5 -0.00012538 0.000271913 8.88872e-8 -7.51783e-8 6.14863e-8 -4.78082e-8 3.41409e-8 -2.04814e-8 6.82662e-9
-4.69451e-6 1.47503e-5 -2.59196e-5 4.3371e-5 -6.24067e-5 0.000107503 -0.000170993 -2.73071e-7 2.30887e-7 -1.8879e-7 1.46763e-7 -1.04791e-7 6.28592e-8 -2.09504e-8
4.9673e-6 -1.52201e-5 2.77596e-5 -4.03417e-5 6.47689e-5 -8.65576e-5 0.000147324 … 6.06827e-7 -5.12984e-7 4.19384e-7 -3.25983e-7 2.32735e-7 -1.39597e-7 4.65251e-8
-5.26671e-6 1.63167e-5 -2.75923e-5 4.43854e-5 -5.74603e-5 9.14887e-5 -0.000115256 -1.10462e-6 9.3367e-7 -7.63227e-7 5.93196e-7 -4.23484e-7 2.54e-7 -8.46514e-8
5.5373e-6 -1.67518e-5 3.00705e-5 -4.14441e-5 6.47752e-5 -7.66034e-5 0.000123053 1.63253e-6 -1.37981e-6 1.12788e-6 -8.7658e-7 6.25776e-7 -3.75325e-7 1.25085e-7
-5.75503e-6 1.7734e-5 -2.9239e-5 4.67395e-5 -5.62752e-5 8.91691e-5 -9.74758e-5 -2.16545e-6 1.8302e-6 -1.49601e-6 1.16268e-6 -8.30008e-7 4.97815e-7 -1.65907e-7
5.99397e-6 -1.79741e-5 3.22396e-5 -4.25173e-5 6.7292e-5 -7.2117e-5 0.000118356 2.81214e-6 -2.37672e-6 1.9427e-6 -1.50981e-6 1.07781e-6 -6.46434e-7 2.15436e-7
-6.24654e-6 1.92319e-5 -3.09798e-5 5.02149e-5 -5.63109e-5 9.2744e-5 -8.91289e-5 … -3.65719e-6 3.09079e-6 -2.52627e-6 1.9633e-6 -1.40151e-6 8.40565e-7 -2.80132e-7
6.52513e-6 -1.94089e-5 3.51201e-5 -4.41366e-5 7.27126e-5 -6.99684e-5 0.000123548 4.67622e-6 -3.9518e-6 3.22989e-6 -2.51003e-6 1.79175e-6 -1.0746e-6 3.58125e-7
-6.75182e-6 2.08432e-5 -3.2672e-5 5.47623e-5 -5.61849e-5 0.000100444 -8.25635e-5 -5.78571e-6 4.88918e-6 -3.99588e-6 3.1052e-6 -2.21655e-6 1.32935e-6 -4.43022e-7
6.96359e-6 -2.05149e-5 3.79137e-5 -4.45658e-5 7.94446e-5 -6.56865e-5 0.000133925 6.92792e-6 -5.85417e-6 4.7844e-6 -3.71786e-6 2.65383e-6 -1.59159e-6 5.3041e-7
-7.10472e-6 2.20931e-5 -3.32817e-5 5.94468e-5 -5.31855e-5 0.000110654 -7.14895e-5 -8.10844e-6 6.85148e-6 -5.5993e-6 4.351e-6 -3.10571e-6 1.86257e-6 -6.20715e-7
7.27295e-6 -2.1134e-5 4.05985e-5 -4.29255e-5 8.78775e-5 -5.66036e-5 0.000149904 … 9.37809e-6 -7.92402e-6 6.47562e-6 -5.03183e-6 3.59162e-6 -2.15396e-6 7.17817e-7
-7.38464e-6 2.32713e-5 -3.29367e-5 6.5427e-5 -4.65798e-5 0.000125957 -5.31317e-5 -1.07943e-5 9.12027e-6 -7.45295e-6 5.7911e-6 -4.13348e-6 2.47889e-6 -8.26095e-7
7.56724e-6 -2.15346e-5 4.40513e-5 -3.91123e-5 0.000100569 -4.10169e-5 0.000176216 1.23913e-5 -1.04691e-5 8.55485e-6 -6.64708e-6 4.74434e-6 -2.84518e-6 9.48155e-7
-7.66221e-6 2.46786e-5 -3.15689e-5 7.42587e-5 -3.48075e-5 0.000150383 -2.31258e-5 -1.41716e-5 1.19726e-5 -9.78296e-6 7.60105e-6 -5.42508e-6 3.25336e-6 -1.08417e-6
7.85522e-6 -2.16252e-5 4.88269e-5 -3.17559e-5 0.000120199 -1.44543e-5 0.000218837 1.61119e-5 -1.3611e-5 1.11212e-5 -8.64046e-6 6.16676e-6 -3.69806e-6 1.23235e-6
⋮ ⋮ ⋱ ⋮
9.70635e-6 0.000600947 0.00288671 0.00753556 0.0146676 0.0238089 0.0338416 -5.07984e-5 4.22913e-5 -3.41437e-5 2.62777e-5 -1.86233e-5 1.11162e-5 -3.69583e-6
1.15055e-5 0.000610536 0.00296323 0.00770382 0.0150307 0.0243579 0.0346672 … 4.90095e-5 -4.07473e-5 3.28616e-5 -2.52697e-5 1.78979e-5 -1.06788e-5 3.54969e-6
1.03762e-5 0.000628178 0.00302178 0.00788374 0.0153503 0.0249114 0.0354151 -4.71506e-5 3.91517e-5 -3.15417e-5 2.42346e-5 -1.71542e-5 1.02309e-5 -3.40012e-6
1.18038e-5 0.000637406 0.00308979 0.00803678 0.0156759 0.0254085 0.0361567 4.51292e-5 -3.74222e-5 3.0115e-5 -2.31184e-5 1.63535e-5 -9.74924e-6 3.23937e-6
1.09659e-5 0.000652685 0.00314309 0.0081967 0.0159637 0.0259023 0.0368288 -4.31499e-5 3.57358e-5 -2.87267e-5 2.20328e-5 -1.55751e-5 9.28095e-6 -3.08307e-6
1.20816e-5 0.000661351 0.00320279 0.00833386 0.0162517 0.026346 0.0374862 7.44368e-5 -2.9042e-5 2.76099e-5 -2.08979e-5 1.47628e-5 -8.79242e-6 2.92005e-6
1.14776e-5 0.00067442 0.00325048 0.00847394 0.0165068 0.02678 0.0380807 … 0.000497273 0.000253172 6.0538e-5 5.26277e-5 -2.01468e-6 1.33011e-5 3.59402e-6
1.23358e-5 0.000682343 0.00330206 0.00859461 0.0167574 0.027169 0.0386536 0.00235203 0.00122561 0.000691383 0.00033913 0.000187614 0.000103886 0.00032331
1.18822e-5 0.00069344 0.00334364 0.00871527 0.0169786 0.0275435 0.0391686 0.00594675 0.00365123 0.00226527 0.00128646 0.000858166 0.00034066 0.00252512
1.25113e-5 0.00070052 0.00338719 0.0088191 0.0171918 0.027877 0.0396568 0.0115379 0.00753587 0.0051437 0.0030483 0.00231754 0.000152329 0.0099176
1.21247e-5 0.000709875 0.00342217 0.0089207 0.017378 0.0281923 0.0400902 0.0184169 0.0126796 0.00920101 0.00554968 0.00460684 0.000622518 0.024376
1.33489e-5 0.000713619 0.0034617 0.00900163 0.0175607 0.0284603 0.0405031 … 0.0247171 0.0195402 0.012462 0.0107413 0.00411196 0.00583893 0.0458936
1.21856e-5 0.000723754 0.00348581 0.00908997 0.0177039 0.0287254 0.0408435 0.0319957 0.023715 0.018812 0.0118073 0.0105055 0.00170848 0.0826443
1.23062e-5 0.00072928 0.00351293 0.00916017 0.0178413 0.0289475 0.0411601 0.0362445 0.027654 0.0230449 0.0145994 0.0130651 0.00428192 0.123551
1.21705e-5 0.000734849 0.00353551 0.00922341 0.0179595 0.0291449 0.0414345 0.036975 0.0297358 0.0255881 0.0168033 0.0152291 0.0041607 0.172266
1.30609e-5 0.000736658 0.00356015 0.00927125 0.0180712 0.0293052 0.0416859 0.0330304 0.0299308 0.02515 0.0191832 0.014714 0.00392902 0.223501
1.35782e-5 0.000738957 0.00358008 0.00931409 0.018165 0.0294457 0.0418987 … 0.0249767 0.0271366 0.0224159 0.0205218 0.0114228 0.0124647 0.264673
1.26951e-5 0.000744891 0.00359046 0.00935991 0.018233 0.0295801 0.0420629 0.0147161 0.0191395 0.0205381 0.0161064 0.0142425 0.00638714 0.309604
1.36067e-5 0.000744926 0.0036075 0.00938696 0.0183053 0.0296752 0.0422231 0.000996005 0.0112324 0.0134605 0.0148889 0.00941669 0.00929307 0.341049
1.29992e-5 0.000749057 0.00361486 0.00941908 0.0183533 0.0297695 0.0423387 3.57e-5 0.000861605 0.00768324 0.0090989 0.00908457 0.00469967 0.36739
1.33036e-5 0.000750029 0.00362487 0.00943969 0.0183996 0.0298377 0.0424435 -7.75088e-5 3.73825e-5 0.000548585 0.00495234 0.00513712 0.00485126 0.381998
1.32721e-5 0.000751612 0.00363142 0.00945787 0.0184338 0.0298945 0.0425227 … -6.27775e-5 8.29281e-5 -0.000132538 0.000517753 0.00249059 0.00252816 0.390995
1.32439e-5 0.000752806 0.00363627 0.00947146 0.0184592 0.0299369 0.0425817 1.93486e-6 -4.04524e-6 9.31037e-6 -2.73214e-5 0.000205912 0.00109825 0.394388
1.32682e-5 0.00075347 0.00363972 0.00948018 0.0184765 0.0299647 0.0426215 -1.45969e-5 1.74151e-5 -2.16279e-5 2.8705e-5 -4.36665e-5 0.000119376 0.395063
1.32613e-5 0.000753859 0.00364134 0.00948468 0.018485 0.0299787 0.0426411 -1.36848e-8 1.15718e-8 -9.46267e-9 7.35662e-9 -5.25299e-9 3.1511e-9 0.394898
julia> I-FRE
94×94 Array{Float64,2}:
0.999977 -0.00129015 -0.00623178 -0.016232 -0.0316351 -0.0513055 -0.0729759 … 2.34201e-8 -1.9804e-8 1.61944e-8 -1.25901e-8 8.98995e-9 -5.39278e-9 1.7974e-9
6.76662e-6 0.999796 -0.00419142 -0.0138753 -0.0291195 -0.0490749 -0.0712448 -1.77187e-7 1.49749e-7 -1.22401e-7 9.51256e-8 -6.79067e-8 4.0728e-8 -1.35733e-8
-4.71671e-6 3.60899e-5 0.999434 -0.00858543 -0.0237948 -0.0440718 -0.0674172 2.01177e-7 -1.70043e-7 1.39001e-7 -1.08034e-7 7.71254e-8 -4.62586e-8 1.54168e-8
4.03045e-6 -1.97552e-5 8.95263e-5 0.998894 -0.0143481 -0.0355805 -0.0603676 -3.16547e-7 2.67533e-7 -2.18677e-7 1.69949e-7 -1.21321e-7 7.27643e-8 -2.425e-8
-3.88172e-6 1.52292e-5 -4.54385e-5 0.000168688 0.998177 -0.0213535 -0.0488525 3.13451e-7 -2.64915e-7 2.16537e-7 -1.68286e-7 1.20134e-7 -7.20521e-8 2.40127e-8
3.91022e-6 -1.39137e-5 3.23165e-5 -8.27224e-5 0.000273885 0.997287 -0.0294787 … -2.87735e-7 2.43178e-7 -1.98767e-7 1.54474e-7 -1.10273e-7 6.61378e-8 -2.20416e-8
-4.01629e-6 1.33314e-5 -2.83776e-5 5.58403e-5 -0.000132173 0.000405445 0.99623 2.85704e-7 -2.41426e-7 1.97311e-7 -1.53328e-7 1.09447e-7 -6.5639e-8 2.18748e-8
4.24552e-6 -1.37846e-5 2.61636e-5 -4.87143e-5 8.69749e-5 -0.000195391 0.00056504 -1.14952e-7 9.71083e-8 -7.93443e-8 6.16452e-8 -4.39965e-8 2.63836e-8 -8.79215e-9
-4.4854e-6 1.40695e-5 -2.67471e-5 4.25667e-5 -7.5056e-5 0.00012538 -0.000271913 -8.88872e-8 7.51783e-8 -6.14863e-8 4.78082e-8 -3.41409e-8 2.04814e-8 -6.82662e-9
4.69451e-6 -1.47503e-5 2.59196e-5 -4.3371e-5 6.24067e-5 -0.000107503 0.000170993 2.73071e-7 -2.30887e-7 1.8879e-7 -1.46763e-7 1.04791e-7 -6.28592e-8 2.09504e-8
-4.9673e-6 1.52201e-5 -2.77596e-5 4.03417e-5 -6.47689e-5 8.65576e-5 -0.000147324 … -6.06827e-7 5.12984e-7 -4.19384e-7 3.25983e-7 -2.32735e-7 1.39597e-7 -4.65251e-8
5.26671e-6 -1.63167e-5 2.75923e-5 -4.43854e-5 5.74603e-5 -9.14887e-5 0.000115256 1.10462e-6 -9.3367e-7 7.63227e-7 -5.93196e-7 4.23484e-7 -2.54e-7 8.46514e-8
-5.5373e-6 1.67518e-5 -3.00705e-5 4.14441e-5 -6.47752e-5 7.66034e-5 -0.000123053 -1.63253e-6 1.37981e-6 -1.12788e-6 8.7658e-7 -6.25776e-7 3.75325e-7 -1.25085e-7
5.75503e-6 -1.7734e-5 2.9239e-5 -4.67395e-5 5.62752e-5 -8.91691e-5 9.74758e-5 2.16545e-6 -1.8302e-6 1.49601e-6 -1.16268e-6 8.30008e-7 -4.97815e-7 1.65907e-7
-5.99397e-6 1.79741e-5 -3.22396e-5 4.25173e-5 -6.7292e-5 7.2117e-5 -0.000118356 -2.81214e-6 2.37672e-6 -1.9427e-6 1.50981e-6 -1.07781e-6 6.46434e-7 -2.15436e-7
6.24654e-6 -1.92319e-5 3.09798e-5 -5.02149e-5 5.63109e-5 -9.2744e-5 8.91289e-5 … 3.65719e-6 -3.09079e-6 2.52627e-6 -1.9633e-6 1.40151e-6 -8.40565e-7 2.80132e-7
-6.52513e-6 1.94089e-5 -3.51201e-5 4.41366e-5 -7.27126e-5 6.99684e-5 -0.000123548 -4.67622e-6 3.9518e-6 -3.22989e-6 2.51003e-6 -1.79175e-6 1.0746e-6 -3.58125e-7
6.75182e-6 -2.08432e-5 3.2672e-5 -5.47623e-5 5.61849e-5 -0.000100444 8.25635e-5 5.78571e-6 -4.88918e-6 3.99588e-6 -3.1052e-6 2.21655e-6 -1.32935e-6 4.43022e-7
-6.96359e-6 2.05149e-5 -3.79137e-5 4.45658e-5 -7.94446e-5 6.56865e-5 -0.000133925 -6.92792e-6 5.85417e-6 -4.7844e-6 3.71786e-6 -2.65383e-6 1.59159e-6 -5.3041e-7
7.10472e-6 -2.20931e-5 3.32817e-5 -5.94468e-5 5.31855e-5 -0.000110654 7.14895e-5 8.10844e-6 -6.85148e-6 5.5993e-6 -4.351e-6 3.10571e-6 -1.86257e-6 6.20715e-7
-7.27295e-6 2.1134e-5 -4.05985e-5 4.29255e-5 -8.78775e-5 5.66036e-5 -0.000149904 … -9.37809e-6 7.92402e-6 -6.47562e-6 5.03183e-6 -3.59162e-6 2.15396e-6 -7.17817e-7
7.38464e-6 -2.32713e-5 3.29367e-5 -6.5427e-5 4.65798e-5 -0.000125957 5.31317e-5 1.07943e-5 -9.12027e-6 7.45295e-6 -5.7911e-6 4.13348e-6 -2.47889e-6 8.26095e-7
-7.56724e-6 2.15346e-5 -4.40513e-5 3.91123e-5 -0.000100569 4.10169e-5 -0.000176216 -1.23913e-5 1.04691e-5 -8.55485e-6 6.64708e-6 -4.74434e-6 2.84518e-6 -9.48155e-7
7.66221e-6 -2.46786e-5 3.15689e-5 -7.42587e-5 3.48075e-5 -0.000150383 2.31258e-5 1.41716e-5 -1.19726e-5 9.78296e-6 -7.60105e-6 5.42508e-6 -3.25336e-6 1.08417e-6
-7.85522e-6 2.16252e-5 -4.88269e-5 3.17559e-5 -0.000120199 1.44543e-5 -0.000218837 -1.61119e-5 1.3611e-5 -1.11212e-5 8.64046e-6 -6.16676e-6 3.69806e-6 -1.23235e-6
⋮ ⋮ ⋱ ⋮
-9.70635e-6 -0.000600947 -0.00288671 -0.00753556 -0.0146676 -0.0238089 -0.0338416 5.07984e-5 -4.22913e-5 3.41437e-5 -2.62777e-5 1.86233e-5 -1.11162e-5 3.69583e-6
-1.15055e-5 -0.000610536 -0.00296323 -0.00770382 -0.0150307 -0.0243579 -0.0346672 … -4.90095e-5 4.07473e-5 -3.28616e-5 2.52697e-5 -1.78979e-5 1.06788e-5 -3.54969e-6
-1.03762e-5 -0.000628178 -0.00302178 -0.00788374 -0.0153503 -0.0249114 -0.0354151 4.71506e-5 -3.91517e-5 3.15417e-5 -2.42346e-5 1.71542e-5 -1.02309e-5 3.40012e-6
-1.18038e-5 -0.000637406 -0.00308979 -0.00803678 -0.0156759 -0.0254085 -0.0361567 -4.51292e-5 3.74222e-5 -3.0115e-5 2.31184e-5 -1.63535e-5 9.74924e-6 -3.23937e-6
-1.09659e-5 -0.000652685 -0.00314309 -0.0081967 -0.0159637 -0.0259023 -0.0368288 4.31499e-5 -3.57358e-5 2.87267e-5 -2.20328e-5 1.55751e-5 -9.28095e-6 3.08307e-6
-1.20816e-5 -0.000661351 -0.00320279 -0.00833386 -0.0162517 -0.026346 -0.0374862 -7.44368e-5 2.9042e-5 -2.76099e-5 2.08979e-5 -1.47628e-5 8.79242e-6 -2.92005e-6
-1.14776e-5 -0.00067442 -0.00325048 -0.00847394 -0.0165068 -0.02678 -0.0380807 … -0.000497273 -0.000253172 -6.0538e-5 -5.26277e-5 2.01468e-6 -1.33011e-5 -3.59402e-6
-1.23358e-5 -0.000682343 -0.00330206 -0.00859461 -0.0167574 -0.027169 -0.0386536 -0.00235203 -0.00122561 -0.000691383 -0.00033913 -0.000187614 -0.000103886 -0.00032331
-1.18822e-5 -0.00069344 -0.00334364 -0.00871527 -0.0169786 -0.0275435 -0.0391686 -0.00594675 -0.00365123 -0.00226527 -0.00128646 -0.000858166 -0.00034066 -0.00252512
-1.25113e-5 -0.00070052 -0.00338719 -0.0088191 -0.0171918 -0.027877 -0.0396568 -0.0115379 -0.00753587 -0.0051437 -0.0030483 -0.00231754 -0.000152329 -0.0099176
-1.21247e-5 -0.000709875 -0.00342217 -0.0089207 -0.017378 -0.0281923 -0.0400902 -0.0184169 -0.0126796 -0.00920101 -0.00554968 -0.00460684 -0.000622518 -0.024376
-1.33489e-5 -0.000713619 -0.0034617 -0.00900163 -0.0175607 -0.0284603 -0.0405031 … -0.0247171 -0.0195402 -0.012462 -0.0107413 -0.00411196 -0.00583893 -0.0458936
-1.21856e-5 -0.000723754 -0.00348581 -0.00908997 -0.0177039 -0.0287254 -0.0408435 -0.0319957 -0.023715 -0.018812 -0.0118073 -0.0105055 -0.00170848 -0.0826443
-1.23062e-5 -0.00072928 -0.00351293 -0.00916017 -0.0178413 -0.0289475 -0.0411601 -0.0362445 -0.027654 -0.0230449 -0.0145994 -0.0130651 -0.00428192 -0.123551
-1.21705e-5 -0.000734849 -0.00353551 -0.00922341 -0.0179595 -0.0291449 -0.0414345 -0.036975 -0.0297358 -0.0255881 -0.0168033 -0.0152291 -0.0041607 -0.172266
-1.30609e-5 -0.000736658 -0.00356015 -0.00927125 -0.0180712 -0.0293052 -0.0416859 -0.0330304 -0.0299308 -0.02515 -0.0191832 -0.014714 -0.00392902 -0.223501
-1.35782e-5 -0.000738957 -0.00358008 -0.00931409 -0.018165 -0.0294457 -0.0418987 … -0.0249767 -0.0271366 -0.0224159 -0.0205218 -0.0114228 -0.0124647 -0.264673
-1.26951e-5 -0.000744891 -0.00359046 -0.00935991 -0.018233 -0.0295801 -0.0420629 -0.0147161 -0.0191395 -0.0205381 -0.0161064 -0.0142425 -0.00638714 -0.309604
-1.36067e-5 -0.000744926 -0.0036075 -0.00938696 -0.0183053 -0.0296752 -0.0422231 0.999004 -0.0112324 -0.0134605 -0.0148889 -0.00941669 -0.00929307 -0.341049
-1.29992e-5 -0.000749057 -0.00361486 -0.00941908 -0.0183533 -0.0297695 -0.0423387 -3.57e-5 0.999138 -0.00768324 -0.0090989 -0.00908457 -0.00469967 -0.36739
-1.33036e-5 -0.000750029 -0.00362487 -0.00943969 -0.0183996 -0.0298377 -0.0424435 7.75088e-5 -3.73825e-5 0.999451 -0.00495234 -0.00513712 -0.00485126 -0.381998
-1.32721e-5 -0.000751612 -0.00363142 -0.00945787 -0.0184338 -0.0298945 -0.0425227 … 6.27775e-5 -8.29281e-5 0.000132538 0.999482 -0.00249059 -0.00252816 -0.390995
-1.32439e-5 -0.000752806 -0.00363627 -0.00947146 -0.0184592 -0.0299369 -0.0425817 -1.93486e-6 4.04524e-6 -9.31037e-6 2.73214e-5 0.999794 -0.00109825 -0.394388
-1.32682e-5 -0.00075347 -0.00363972 -0.00948018 -0.0184765 -0.0299647 -0.0426215 1.45969e-5 -1.74151e-5 2.16279e-5 -2.8705e-5 4.36665e-5 0.999881 -0.395063
-1.32613e-5 -0.000753859 -0.00364134 -0.00948468 -0.018485 -0.0299787 -0.0426411 1.36848e-8 -1.15718e-8 9.46267e-9 -7.35662e-9 5.25299e-9 -3.1511e-9 0.605102
julia> I+FRE
94×94 Array{Float64,2}:
1.00002 0.00129015 0.00623178 0.016232 0.0316351 0.0513055 0.0729759 … -2.34201e-8 1.9804e-8 -1.61944e-8 1.25901e-8 -8.98995e-9 5.39278e-9 -1.7974e-9
-6.76662e-6 1.0002 0.00419142 0.0138753 0.0291195 0.0490749 0.0712448 1.77187e-7 -1.49749e-7 1.22401e-7 -9.51256e-8 6.79067e-8 -4.0728e-8 1.35733e-8
4.71671e-6 -3.60899e-5 1.00057 0.00858543 0.0237948 0.0440718 0.0674172 -2.01177e-7 1.70043e-7 -1.39001e-7 1.08034e-7 -7.71254e-8 4.62586e-8 -1.54168e-8
-4.03045e-6 1.97552e-5 -8.95263e-5 1.00111 0.0143481 0.0355805 0.0603676 3.16547e-7 -2.67533e-7 2.18677e-7 -1.69949e-7 1.21321e-7 -7.27643e-8 2.425e-8
3.88172e-6 -1.52292e-5 4.54385e-5 -0.000168688 1.00182 0.0213535 0.0488525 -3.13451e-7 2.64915e-7 -2.16537e-7 1.68286e-7 -1.20134e-7 7.20521e-8 -2.40127e-8
-3.91022e-6 1.39137e-5 -3.23165e-5 8.27224e-5 -0.000273885 1.00271 0.0294787 … 2.87735e-7 -2.43178e-7 1.98767e-7 -1.54474e-7 1.10273e-7 -6.61378e-8 2.20416e-8
4.01629e-6 -1.33314e-5 2.83776e-5 -5.58403e-5 0.000132173 -0.000405445 1.00377 -2.85704e-7 2.41426e-7 -1.97311e-7 1.53328e-7 -1.09447e-7 6.5639e-8 -2.18748e-8
-4.24552e-6 1.37846e-5 -2.61636e-5 4.87143e-5 -8.69749e-5 0.000195391 -0.00056504 1.14952e-7 -9.71083e-8 7.93443e-8 -6.16452e-8 4.39965e-8 -2.63836e-8 8.79215e-9
4.4854e-6 -1.40695e-5 2.67471e-5 -4.25667e-5 7.5056e-5 -0.00012538 0.000271913 8.88872e-8 -7.51783e-8 6.14863e-8 -4.78082e-8 3.41409e-8 -2.04814e-8 6.82662e-9
-4.69451e-6 1.47503e-5 -2.59196e-5 4.3371e-5 -6.24067e-5 0.000107503 -0.000170993 -2.73071e-7 2.30887e-7 -1.8879e-7 1.46763e-7 -1.04791e-7 6.28592e-8 -2.09504e-8
4.9673e-6 -1.52201e-5 2.77596e-5 -4.03417e-5 6.47689e-5 -8.65576e-5 0.000147324 … 6.06827e-7 -5.12984e-7 4.19384e-7 -3.25983e-7 2.32735e-7 -1.39597e-7 4.65251e-8
-5.26671e-6 1.63167e-5 -2.75923e-5 4.43854e-5 -5.74603e-5 9.14887e-5 -0.000115256 -1.10462e-6 9.3367e-7 -7.63227e-7 5.93196e-7 -4.23484e-7 2.54e-7 -8.46514e-8
5.5373e-6 -1.67518e-5 3.00705e-5 -4.14441e-5 6.47752e-5 -7.66034e-5 0.000123053 1.63253e-6 -1.37981e-6 1.12788e-6 -8.7658e-7 6.25776e-7 -3.75325e-7 1.25085e-7
-5.75503e-6 1.7734e-5 -2.9239e-5 4.67395e-5 -5.62752e-5 8.91691e-5 -9.74758e-5 -2.16545e-6 1.8302e-6 -1.49601e-6 1.16268e-6 -8.30008e-7 4.97815e-7 -1.65907e-7
5.99397e-6 -1.79741e-5 3.22396e-5 -4.25173e-5 6.7292e-5 -7.2117e-5 0.000118356 2.81214e-6 -2.37672e-6 1.9427e-6 -1.50981e-6 1.07781e-6 -6.46434e-7 2.15436e-7
-6.24654e-6 1.92319e-5 -3.09798e-5 5.02149e-5 -5.63109e-5 9.2744e-5 -8.91289e-5 … -3.65719e-6 3.09079e-6 -2.52627e-6 1.9633e-6 -1.40151e-6 8.40565e-7 -2.80132e-7
6.52513e-6 -1.94089e-5 3.51201e-5 -4.41366e-5 7.27126e-5 -6.99684e-5 0.000123548 4.67622e-6 -3.9518e-6 3.22989e-6 -2.51003e-6 1.79175e-6 -1.0746e-6 3.58125e-7
-6.75182e-6 2.08432e-5 -3.2672e-5 5.47623e-5 -5.61849e-5 0.000100444 -8.25635e-5 -5.78571e-6 4.88918e-6 -3.99588e-6 3.1052e-6 -2.21655e-6 1.32935e-6 -4.43022e-7
6.96359e-6 -2.05149e-5 3.79137e-5 -4.45658e-5 7.94446e-5 -6.56865e-5 0.000133925 6.92792e-6 -5.85417e-6 4.7844e-6 -3.71786e-6 2.65383e-6 -1.59159e-6 5.3041e-7
-7.10472e-6 2.20931e-5 -3.32817e-5 5.94468e-5 -5.31855e-5 0.000110654 -7.14895e-5 -8.10844e-6 6.85148e-6 -5.5993e-6 4.351e-6 -3.10571e-6 1.86257e-6 -6.20715e-7
7.27295e-6 -2.1134e-5 4.05985e-5 -4.29255e-5 8.78775e-5 -5.66036e-5 0.000149904 … 9.37809e-6 -7.92402e-6 6.47562e-6 -5.03183e-6 3.59162e-6 -2.15396e-6 7.17817e-7
-7.38464e-6 2.32713e-5 -3.29367e-5 6.5427e-5 -4.65798e-5 0.000125957 -5.31317e-5 -1.07943e-5 9.12027e-6 -7.45295e-6 5.7911e-6 -4.13348e-6 2.47889e-6 -8.26095e-7
7.56724e-6 -2.15346e-5 4.40513e-5 -3.91123e-5 0.000100569 -4.10169e-5 0.000176216 1.23913e-5 -1.04691e-5 8.55485e-6 -6.64708e-6 4.74434e-6 -2.84518e-6 9.48155e-7
-7.66221e-6 2.46786e-5 -3.15689e-5 7.42587e-5 -3.48075e-5 0.000150383 -2.31258e-5 -1.41716e-5 1.19726e-5 -9.78296e-6 7.60105e-6 -5.42508e-6 3.25336e-6 -1.08417e-6
7.85522e-6 -2.16252e-5 4.88269e-5 -3.17559e-5 0.000120199 -1.44543e-5 0.000218837 1.61119e-5 -1.3611e-5 1.11212e-5 -8.64046e-6 6.16676e-6 -3.69806e-6 1.23235e-6
⋮ ⋮ ⋱ ⋮
9.70635e-6 0.000600947 0.00288671 0.00753556 0.0146676 0.0238089 0.0338416 -5.07984e-5 4.22913e-5 -3.41437e-5 2.62777e-5 -1.86233e-5 1.11162e-5 -3.69583e-6
1.15055e-5 0.000610536 0.00296323 0.00770382 0.0150307 0.0243579 0.0346672 … 4.90095e-5 -4.07473e-5 3.28616e-5 -2.52697e-5 1.78979e-5 -1.06788e-5 3.54969e-6
1.03762e-5 0.000628178 0.00302178 0.00788374 0.0153503 0.0249114 0.0354151 -4.71506e-5 3.91517e-5 -3.15417e-5 2.42346e-5 -1.71542e-5 1.02309e-5 -3.40012e-6
1.18038e-5 0.000637406 0.00308979 0.00803678 0.0156759 0.0254085 0.0361567 4.51292e-5 -3.74222e-5 3.0115e-5 -2.31184e-5 1.63535e-5 -9.74924e-6 3.23937e-6
1.09659e-5 0.000652685 0.00314309 0.0081967 0.0159637 0.0259023 0.0368288 -4.31499e-5 3.57358e-5 -2.87267e-5 2.20328e-5 -1.55751e-5 9.28095e-6 -3.08307e-6
1.20816e-5 0.000661351 0.00320279 0.00833386 0.0162517 0.026346 0.0374862 7.44368e-5 -2.9042e-5 2.76099e-5 -2.08979e-5 1.47628e-5 -8.79242e-6 2.92005e-6
1.14776e-5 0.00067442 0.00325048 0.00847394 0.0165068 0.02678 0.0380807 … 0.000497273 0.000253172 6.0538e-5 5.26277e-5 -2.01468e-6 1.33011e-5 3.59402e-6
1.23358e-5 0.000682343 0.00330206 0.00859461 0.0167574 0.027169 0.0386536 0.00235203 0.00122561 0.000691383 0.00033913 0.000187614 0.000103886 0.00032331
1.18822e-5 0.00069344 0.00334364 0.00871527 0.0169786 0.0275435 0.0391686 0.00594675 0.00365123 0.00226527 0.00128646 0.000858166 0.00034066 0.00252512
1.25113e-5 0.00070052 0.00338719 0.0088191 0.0171918 0.027877 0.0396568 0.0115379 0.00753587 0.0051437 0.0030483 0.00231754 0.000152329 0.0099176
1.21247e-5 0.000709875 0.00342217 0.0089207 0.017378 0.0281923 0.0400902 0.0184169 0.0126796 0.00920101 0.00554968 0.00460684 0.000622518 0.024376
1.33489e-5 0.000713619 0.0034617 0.00900163 0.0175607 0.0284603 0.0405031 … 0.0247171 0.0195402 0.012462 0.0107413 0.00411196 0.00583893 0.0458936
1.21856e-5 0.000723754 0.00348581 0.00908997 0.0177039 0.0287254 0.0408435 0.0319957 0.023715 0.018812 0.0118073 0.0105055 0.00170848 0.0826443
1.23062e-5 0.00072928 0.00351293 0.00916017 0.0178413 0.0289475 0.0411601 0.0362445 0.027654 0.0230449 0.0145994 0.0130651 0.00428192 0.123551
1.21705e-5 0.000734849 0.00353551 0.00922341 0.0179595 0.0291449 0.0414345 0.036975 0.0297358 0.0255881 0.0168033 0.0152291 0.0041607 0.172266
1.30609e-5 0.000736658 0.00356015 0.00927125 0.0180712 0.0293052 0.0416859 0.0330304 0.0299308 0.02515 0.0191832 0.014714 0.00392902 0.223501
1.35782e-5 0.000738957 0.00358008 0.00931409 0.018165 0.0294457 0.0418987 … 0.0249767 0.0271366 0.0224159 0.0205218 0.0114228 0.0124647 0.264673
1.26951e-5 0.000744891 0.00359046 0.00935991 0.018233 0.0295801 0.0420629 0.0147161 0.0191395 0.0205381 0.0161064 0.0142425 0.00638714 0.309604
1.36067e-5 0.000744926 0.0036075 0.00938696 0.0183053 0.0296752 0.0422231 1.001 0.0112324 0.0134605 0.0148889 0.00941669 0.00929307 0.341049
1.29992e-5 0.000749057 0.00361486 0.00941908 0.0183533 0.0297695 0.0423387 3.57e-5 1.00086 0.00768324 0.0090989 0.00908457 0.00469967 0.36739
1.33036e-5 0.000750029 0.00362487 0.00943969 0.0183996 0.0298377 0.0424435 -7.75088e-5 3.73825e-5 1.00055 0.00495234 0.00513712 0.00485126 0.381998
1.32721e-5 0.000751612 0.00363142 0.00945787 0.0184338 0.0298945 0.0425227 … -6.27775e-5 8.29281e-5 -0.000132538 1.00052 0.00249059 0.00252816 0.390995
1.32439e-5 0.000752806 0.00363627 0.00947146 0.0184592 0.0299369 0.0425817 1.93486e-6 -4.04524e-6 9.31037e-6 -2.73214e-5 1.00021 0.00109825 0.394388
1.32682e-5 0.00075347 0.00363972 0.00948018 0.0184765 0.0299647 0.0426215 -1.45969e-5 1.74151e-5 -2.16279e-5 2.8705e-5 -4.36665e-5 1.00012 0.395063
1.32613e-5 0.000753859 0.00364134 0.00948468 0.018485 0.0299787 0.0426411 -1.36848e-8 1.15718e-8 -9.46267e-9 7.35662e-9 -5.25299e-9 3.1511e-9 1.3949
julia>
julia> I
UniformScaling{Int64}
1*I
julia> I+rand(2,2)
2×2 Array{Float64,2}:
1.29909 0.210311
0.710225 1.95887
julia> r=rand(2,2)
2×2 Array{Float64,2}:
0.279161 0.372859
0.990096 0.780494
julia> I+r
2×2 Array{Float64,2}:
1.27916 0.372859
0.990096 1.78049
```
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