Refactor MPS to account for canonical form

[jofrevalles]

This is still a draft, but it aims to have an MPS class that has the center of ortogonality, and the λ singular values.
CC @starsfordummies

Example:

julia> using Tenet

julia> mps = rand(MPS, Open; n=10, χ=10, center=Site(5))
[isleftcanonical(mps, Site(i)) for i = 1:n] = Bool[1, 1, 1, 1, 0, 0, 0, 0, 0, 0]
[isrightcanonical(mps, Site(i)) for i = 1:n] = Bool[0, 0, 0, 0, 1, 1, 1, 1, 1, 1]
Matrix{Float64}(I, size(𝟙ₗ, 1), size(𝟙ₗ, 1)) = [1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0]
MPS (inputs=0, outputs=10)

julia> Tenet.convert_left_to_right(mps, 4)
8×8 Tensor{Float64, 2, Matrix{Float64}}:
  1.0          -4.22748e-16  -3.25933e-16  -1.8408e-16   -8.42906e-17  -2.32961e-16  -1.12601e-16   2.9837e-17
 -4.22748e-16   1.0           1.57864e-16  -1.65245e-16   1.41122e-17   1.21602e-16  -1.21454e-17  -9.31933e-17
 -3.25933e-16   1.57864e-16   1.0          -7.27056e-16   5.47332e-16  -7.70478e-16  -2.2881e-16   -3.68635e-16
 -1.8408e-16   -1.65245e-16  -7.27056e-16   1.0          -2.16267e-16  -6.30313e-16   1.46576e-16  -1.76226e-16
 -8.42906e-17   1.41122e-17   5.47332e-16  -2.16267e-16   1.0          -4.14662e-17  -4.36183e-16   6.74531e-17
 -2.32961e-16   1.21602e-16  -7.70478e-16  -6.30313e-16  -4.14662e-17   1.0          -1.03779e-16   8.96328e-17
 -1.12601e-16  -1.21454e-17  -2.2881e-16    1.46576e-16  -4.36183e-16  -1.03779e-16   1.0          -2.83137e-17
  2.9837e-17   -9.31933e-17  -3.68635e-16  -1.76226e-16   6.74531e-17   8.96328e-17  -2.83137e-17   1.0

julia> Tenet.convert_right_to_left(mps, 5)
10×10 Tensor{Float64, 2, Matrix{Float64}}:
  1.0           8.33546e-16   8.18263e-16  -9.26519e-16   9.9221e-16    8.83287e-17  -2.34717e-17   1.84523e-15   8.09384e-16  -4.23474e-16
  8.33546e-16   1.0          -1.48931e-15  -5.00768e-16  -6.41938e-16   5.54066e-16   1.47982e-15   2.98344e-16   1.03615e-16   5.77647e-16
  8.18263e-16  -1.48931e-15   1.0          -3.44524e-16   9.62516e-16  -3.97036e-16   1.01287e-15   1.23511e-16  -7.11506e-16   8.35282e-16
 -9.26519e-16  -5.00768e-16  -3.44524e-16   1.0           9.53429e-16  -3.19678e-16  -7.66375e-16  -3.38745e-16   6.41531e-16   2.26201e-16
  9.9221e-16   -6.41938e-16   9.62516e-16   9.53429e-16   1.0          -4.40842e-16   7.34784e-16  -1.04615e-15  -5.79741e-16   5.26484e-16
  8.83287e-17   5.54066e-16  -3.97036e-16  -3.19678e-16  -4.40842e-16   1.0          -4.45837e-16  -1.79542e-16  -8.49437e-16   1.31244e-15
 -2.34717e-17   1.47982e-15   1.01287e-15  -7.66375e-16   7.34784e-16  -4.45837e-16   1.0          -5.97942e-16   3.53225e-16  -3.2382e-16
  1.84523e-15   2.98344e-16   1.23511e-16  -3.38745e-16  -1.04615e-15  -1.79542e-16  -5.97942e-16   1.0           5.72744e-16   8.43409e-16
  8.09384e-16   1.03615e-16  -7.11506e-16   6.41531e-16  -5.79741e-16  -8.49437e-16   3.53225e-16   5.72744e-16   1.0           8.09661e-16
 -4.23474e-16   5.77647e-16   8.35282e-16   2.26201e-16   5.26484e-16   1.31244e-15  -3.2382e-16    8.43409e-16   8.09661e-16   1.0

julia> mps.λ
9-element Vector{Union{Nothing, Tensor}}:
 [0.796327747399762, 0.604865372393908]
 [0.6017504036070982, 0.5484516246936645, 0.44685610016419625, 0.3706978457930666]
 [0.5414969213553932, 0.49786829596905524, 0.37558092737959625, 0.36639832798659755, 0.2749512698915463, 0.2427195738260526, 0.18556681511691353, 0.1210513984342991]
 [0.5552915300977606, 0.5343145750143071, 0.3762404775497805, 0.316949458463826, 0.249028862689978, 0.21981731436696372, 0.14640247352835156, 0.1448821392800681, 0.08537861213945974, 0.06400268170124704]
 [0.7047734556421628, 0.39900158234406774, 0.3684963163753138, 0.2779876717429905, 0.2510062779512473, 0.21105878212014392, 0.11120836539756873, 0.08103912134469375, 0.06023690988575784, 0.030205075228998186]
 [0.7717046483573069, 0.4461096507664728, 0.3441545649848504, 0.25687653233098595, 0.10168385386238375, 0.07726344847170057, 0.045719183231821676, 0.03890962603869955, 0.030372722876442743, 0.013937220655711948]
 [0.8315127733559501, 0.5023424866874187, 0.179337296419813, 0.12965805498849664, 0.0813152000523422, 0.02267645424101963, 0.011665235358199537, 0.001730795068626314]
 [0.9532682205612897, 0.2648208726347147, 0.1446245813163982, 0.015275325330649814]
 [0.978825377509097, 0.2046970452746542]

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 391 lines in your changes missing coverage. Please review.

Project coverage is 0.83%. Comparing base (882049b) to head (5c6bd48).
Report is 50 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Ansatz/MPS.jl	0.00%	391 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #202       +/-   ##
==========================================
- Coverage   72.73%   0.83%   -71.90%     
==========================================
  Files          27      32        +5     
  Lines        1944    2382      +438     
==========================================
- Hits         1414      20     -1394     
- Misses        530    2362     +1832     

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[jofrevalles]

Closing this, some of the code will be added as a new kind of Form trait with the changes from PR #232.