Implement ConcatenatedVectorNormMap + develop projects/OceanBoundaryLayerParameterizations

[adelinehillier]

1. Implements missing functionality for ConcatenatedVectorNormMap and modifies it so that it produces the square root of the norm rather than the norm.
2. Adds a property objective_values to IterationSummary, a vector of NamedTuples (Φ1 , Φ2) indicating, for each ensemble member, the data misfit Φ1 = || Γy^(-¹/₂) * (y .- G) ||² and prior misfit Φ2 = || Γθ^(-¹/₂) * (θ .- μθ) ||², so that the magnitudes of these values can be compared. This is provides a rough sense of how strongly regularized the loss function is given the observation noise covariance.
3. Deletes projects directory.
4. Updates EKI API to include several adaptive time stepping options. The current scheme is renamed Default()

[navidcy]

Suggested change

	Given forward map `G` and *unconstrained* parameters `θ`, return a
	tuple `(Φ1, Φ2)` of terms in the EKI regularized objective function, where
	Φ = (1/2)*(Φ1 + Φ2). Φ1 measures output misfit `|| Γy^(-¹/₂) * (y .- G(θ)) ||²` and
	Φ2 measures prior misfit `|| Γθ^(-¹/₂) * (θ .- μθ) ||²`, where `y` is the observation
	map, `G(θ)` is the forward map, `Γy` is the observation noise covariance, `Γθ` is
	the prior covariance, and `μθ` represents the prior means. Note that `Γ^(-1/2) =
	inv(sqrt(Γ))`.
	Given forward map `G` and *unconstrained* parameters `θ`, return a
	tuple `(Φ₁, Φ₂)` of terms in the EKI regularized objective function, where
	`Φ = ½(Φ₁ + Φ₂)`. `Φ₁` measures output misfit `|| Γy^(-½) * (y - G(θ)) ||²` and
	`Φ₂` measures prior misfit `|| Γθ^(-½) * (θ - μθ) ||²`, where `y` is the observation
	map, `G(θ)` is the forward map, `Γy` is the observation noise covariance, `Γθ` is
	the prior covariance, and `μθ` represents the prior means. Note that `Γ^(-½) =
	inv(√Γ)`.

[navidcy]

mostly aesthetic
do we need LaTeXStrings as main package dep?

[adelinehillier]

All tests pass and the changes in this PR are fairly minimal. @glwagner would you mind re-reviewing?

[glwagner]

Should we have two properties, output_misfit and prior_misfit?

[glwagner]

I didn't quite grasp the logic here. This implements a feature that allows users to pass a function adaptive_step_parameters that overrides the adaptive_step_parameters in the source?

Should we use multiple dispatch to control the behavior of adaptive_step_parameters instead? This would mean generalizing the convergence_rate parameter (which is now either nothing or Float64) to something more general (eg adaptivity...)

If we stick with this design, then I guess we will find ourselves providing alternative adaptive_step_parameters functions that users can import into their scripts, and pass into iterate. But those new functions will ignore the property convergence_rate (and may require closing any additional parameters of those alternative functions... ?) That might get a little tricky.

As is, without any alternatives, only advanced users who are ready to rewrite functions like

ParameterEstimocean.jl/src/EnsembleKalmanInversions.jl

Line 285 in 3dd370b

function adaptive_step_parameters(convergence_rate, Xⁿ, Gⁿ, y, Γy, process)

can use this.

[adelinehillier]

Yes, this was intended to be a temporary hack. I'm all for implementing a good time-stepping API in the next PR. I'll go ahead and merge.

[glwagner]

We can merge this, though it looks like we will need to implement an API for utilizing different adaptive time-stepping methods in the future.