FEDVR.jl

THIS LIBRARY HAS BEEN DEPRECATED

a more structured library, with support for finite-differences and B-splines as well can be found at

https://github.com/JuliaApproximation/CompactBases.jl

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This is a Julia package for the Finite-Element Discrete Variable Representation method, used in the solution of partial differential equations. The main purpose for the package is for numerical solution of the Time-Dependent Schrödinger Equation ([i∂ₜ-Ĥ]|ψ⟩ = 0), however, its usefulness is not limited to this equation.

Usage

Grid setup

using FEDVR

We set up the basis for the calculations like so:

basis = FEDVR.Basis(range(0,stop=1,length=11),10)

FEDVR Basis(FEDVR Grid with 10 elements of order 10 [dirichlet0,dirichlet0])

By default, Dirichlet0 boundary conditions at both boundaries are assumed (by passing any other symbol than :dirichlet0, Dirichlet1 boundary conditions are applied; Neumann boundary conditions not yet supported).

We can then plot the grid point locations:

plot(basis.grid)

as well as the basis functions:

plot(basis)

Expansion of scalar functions

A scalar function can be expanded by

f = x -> x*(x-1)^2
ϕ = project(f, basis)[2:end-1]

Note that the function expanded has to vanish at the boundaries of the grid, since :dirichlet0 was chosen above. For non-vanishing functions, pass :dirichlet1 to the Basis constructor.

Kinetic operator

The 1D kinetic operator is given by T̂ = -∂ₓ²/2, and can be retrieved by

T = kinop(basis)

89×89 BlockBandedMatrices.BlockBandedMatrix{Float64}:
  38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455    -118.267  │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222     145.455  │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
   2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205    -204.825  │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
   -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409     339.899  │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
    339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19     -703.111  │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
   -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71     2051.09   │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
    145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7    -12242.1    │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
   -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1     38845.7    │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
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     76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88   -43683.7    │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
     -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0        -0.0    │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
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       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │        ⋅      │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7       4144.88    -1037.72     405.94    -208.298    129.491     -93.5532      76.7633  │     -50.0     │        ⋅           ⋅          ⋅          ⋅          ⋅          ⋅           ⋅            ⋅    
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7     -12242.1      2051.09    -703.111    339.899   -204.825     145.455     -118.267   │      76.7633  │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1      13209.7     -5878.71    1216.19    -489.409    270.205    -183.222      145.455   │     -93.5532  │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09     -5878.71     7776.17   -4092.18     966.858   -437.805     270.205     -204.825   │     129.491   │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111     1216.19    -4092.18    6168.51   -3660.71     966.858    -489.409      339.899   │    -208.298   │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899     -489.409     966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111   │     405.94    │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825      270.205    -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09    │   -1037.72    │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455     -183.222     270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1     │    4144.88    │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267      145.455    -204.825    339.899   -703.111   2051.09   -12242.1      38845.7     │  -43683.7     │      -0.0        -0.0       -0.0       -0.0       -0.0       -0.0        -0.0         -0.0   
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │     -50.0     │      76.7633     -93.5532    129.491   -208.298    405.94   -1037.72     4144.88    -43683.7     │  136500.0     │  -43683.7      4144.88   -1037.72     405.94    -208.298    129.491     -93.5532      76.7633
 ──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │  -43683.7     │   38845.7    -12242.1     2051.09    -703.111    339.899   -204.825     145.455     -118.267 
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    4144.88    │  -12242.1     13209.7    -5878.71    1216.19    -489.409    270.205    -183.222      145.455 
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │   -1037.72    │    2051.09    -5878.71    7776.17   -4092.18     966.858   -437.805     270.205     -204.825 
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     405.94    │    -703.111    1216.19   -4092.18    6168.51   -3660.71     966.858    -489.409      339.899 
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │    -208.298   │     339.899    -489.409    966.858  -3660.71    6168.51   -4092.18     1216.19      -703.111 
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     129.491   │    -204.825     270.205   -437.805    966.858  -4092.18    7776.17    -5878.71      2051.09  
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │     -93.5532  │     145.455    -183.222    270.205   -489.409   1216.19   -5878.71    13209.7     -12242.1   
       ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅           ⋅     │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │        ⋅            ⋅           ⋅          ⋅          ⋅          ⋅           ⋅            ⋅      │        ⋅      │      -0.0         -0.0        -0.0       -0.0       -0.0       -0.0        -0.0         -0.0     │      76.7633  │    -118.267     145.455   -204.825    339.899   -703.111   2051.09   -12242.1      38845.7

which returns a BlockBandedMatrix.

In the special case of bases of polynomial order 2, the derivative operators reduce to tridiagonal matrices

derop(FEDVR.Basis(0.0:10, 2), 2)

9×9 LinearAlgebra.Tridiagonal{Float64,Array{Float64,1}}:
 -2.0   1.0    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ 
  1.0  -2.0   1.0    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ 
   ⋅    1.0  -2.0   1.0    ⋅     ⋅     ⋅     ⋅     ⋅ 
   ⋅     ⋅    1.0  -2.0   1.0    ⋅     ⋅     ⋅     ⋅ 
   ⋅     ⋅     ⋅    1.0  -2.0   1.0    ⋅     ⋅     ⋅ 
   ⋅     ⋅     ⋅     ⋅    1.0  -2.0   1.0    ⋅     ⋅ 
   ⋅     ⋅     ⋅     ⋅     ⋅    1.0  -2.0   1.0    ⋅ 
   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    1.0  -2.0   1.0
   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    1.0  -2.0

which we recognize as the three-point stencil of the second derivative, arising from a finite-difference treatment.

Its eigenstates (also known as the eigenstates of a particle-in-a-box) can be computed using Julia’s builtin sparse diagonalization routine:

λ,ϕ = eigs(T,which=:SR)

If we plot the eigenvalues, we see the typical quadratic behaviour initially, but due to the division into finite elements, a series of steps occurs towards higher energies.

Wishes

Efficiently calculate matrix elements for
- Local operators
- Derivative operators
- Two-body operators
Allow different polynomial orders n in different finite elements
Helper routines for different types of grids
- Cartesian Nd grids
- Spherical coordinates
  - Radial grid
  - Angular? [c.f. Schneider2016]
Tensor product bases (multi-body problems)
Laplacian operators
Exterior Complex Scaling [c.f. Rescigno2000]
Support for different quadratures [c.f. Baye2015]

References

<<Rescigno2000>>Rescigno, T. N., & McCurdy, C. W. (2000). Numerical grid methods for quantum-mechanical scattering problems. Physical Review A, 62(3), 032706. DOI: 10.1103/physreva.62.032706
<<McCurdy2001>>McCurdy, C. W., Horner, D. A., & Rescigno, T. N. (2001). Practical calculation of amplitudes for electron-impact ionization. Physical Review A, 63(2), 022711. DOI: 10.1103/physreva.63.022711
<<McCurdy2004>>McCurdy, C. W., Baertschy, M., & Rescigno, T. N. (2004). Solving the three-body coulomb breakup problem using exterior complex scaling. Journal of Physics B: Atomic, Molecular and Optical Physics, 37(17), 137–187. DOI: 10.1088/0953-4075/37/17/r01
<<Balzer2010>>Balzer, K., Bauch, S., & Bonitz, M. (2010). Finite elements and the discrete variable representation in nonequilibrium green’s function calculations. atomic and molecular models. Journal of Physics: Conference Series, 220(1), 012020. DOI: 10.1088/1742-6596/220/1/012020
<<Baye2015>>Baye, D. (2015). The Lagrange-mesh method. Physics Reports, 565, 1–107. DOI: 10.1016/j.physrep.2014.11.006
<<Schneider2016>>Schneider, B. I., Guan, X., & Bartschat, K. (2016). Time propagation of partial differential equations using the Short Iterative Lanczos method and finite-element discrete variable representation. Advances in Quantum Chemistry, 72, 95–127. DOI: 10.1016/bs.aiq.2015.12.002

Name	Name	Last commit message	Last commit date
Latest commit jagot Added deprecation notice May 17, 2020 15df79f · May 17, 2020 History 70 Commits
figures	figures	Updated README for boundary conditions	Aug 4, 2018
src	src	Added deprecation notice	May 17, 2020
test	test	Update tests broken by `21431f6`	Oct 18, 2018
.codecov.yml	.codecov.yml	FEDVR.jl generated files.	Jan 2, 2018
.gitignore	.gitignore	Switched from BlockMaps to BlockBandedMaps	Oct 24, 2018
.travis.yml	.travis.yml	Switched from BlockMaps to BlockBandedMaps	Oct 24, 2018
LICENSE.md	LICENSE.md	FEDVR.jl generated files.	Jan 2, 2018
Manifest.toml	Manifest.toml	Removed BlockMaps	Nov 11, 2018
Project.toml	Project.toml	Removed BlockMaps	Nov 11, 2018
README.org	README.org	Added deprecation notice	May 17, 2020
appveyor.yml	appveyor.yml	Switched from BlockMaps to BlockBandedMaps	Oct 24, 2018

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