optimal interpolation examples

[anthony-meza]

I'd like to add the following examples to the code:

• Optimal interpolation of a time series (used in the tests)
• Optimal interpolation of a 2D field

transfer pedagogical example from Dynamical-Insights-From-Data.jl

• Optimal interpolation of a 1D field

All of can use AlgebraicArrays.jl

[ggebbie]

It would be great to add a 2D objective mapping test to BLUEs! 1D is already handled in the tests, as you note above.

Also note that the term "objective mapping" better represents what you want to do, as this algorithm is not always optimal and it is not interpolation.

If you would like to make an example or tutorial rather than a test, then it is better to do it in a new environment that uses BLUEs.jl as a dependency.

[ggebbie]

Three objective mapping notebooks now exist in the notebooks branch.

2.9_objectivemapping.jl - pedagogical example from Dynamical Insights From Data class

objectivemapping_blues.jl - objective mapping that uses BLUEs to solve the Gauss-Markov problem

objectivemapping_BLUES_AlgebraicArrays.jl - full featured notebook using whole ecosystem, including BLUEs for the Gauss-Markov problem, AlgebraicArrays.jl to handle conversion from a 2D grid to matrices and vectors, and DimensionalData.jl for labeling the variables.

Take a look. If there are no problems, we can close this issue as completed.