Added `get_u` and `get_s` functions

[dlcole3]

Added functions to query the solution. Functions take an input of the solver reference and the model. They return $s$ and $u$ solution values for all sparse cases. They return $u$ solution only for the condensed case with no K matrix. Additional functionalities to query the $s$ and $u$ variables in the condensed case will be addressed later.

[codecov-commenter]

Codecov Report

Merging #24 (1a58b9b) into main (f8547b4) will decrease coverage by 0.09%. The diff coverage is 94.73%.

@@            Coverage Diff             @@
##             main      #24      +/-   ##
==========================================
- Coverage   96.32%   96.23%   -0.10%     
==========================================
  Files           1        1              
  Lines         599      637      +38     
==========================================
+ Hits          577      613      +36     
- Misses         22       24       +2     

Impacted Files	Coverage Δ
src/DynamicNLPModels.jl	96.23% <94.73%> (-0.10%)	:arrow_down:

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[sshin23]

@frapac agreed that it would be good to define separate data structure for dense/sparse case. In terms of the naming, I'd call them

SparseLQDynamicModel <: AbstractLQDynamicModel
DenseLQDynamicModel <: AbstractLQDynamicModel

[frapac]

@sshin23 I agree with the naming you just proposed:

SparseLQDynamicModel <: AbstractLQDynamicModel
DenseLQDynamicModel <: AbstractLQDynamicModel

Just: which one is supposed to implement the condensed model?

[sshin23]

@frapac DenseLQDynamicModel implements the dense form (states are eliminated), and condensing (eliminating the inequality block) is done internally in MadNLP

[dlcole3]

@sshin23, do you want me to go ahead and make the change to

SparseLQDynamicModel <: AbstractLQDynamicModel
DenseLQDynamicModel <: AbstractLQDynamicModel

now, or should I do this later? Over Slack, it sounded like you suggested doing this later, but I can address it now if desired

[dlcole3]

Also, I have been mixed up on condensed and dense. I think I will rename some of my functions to be dense to reflect the proper terminology

[sshin23]

@dlcole3 You can work on the new data structure in a separate PR

[dlcole3]

It is not exact. It is very close (<1e-10).