Improve static analysis: type stability and JET tests

[ChrisRackauckas-Claude]

Summary

• Add type parameters to POD struct (POD{S, T <: AbstractFloat}) for improved type stability
• Add type parameters to SVD and TSVD structs for proper kwargs typing (using NamedTuple)
• Add return type annotations to key functions for better static analysis
• Add JET.jl tests to verify type stability of core functions

Changes Made

Type Parameter Improvements

• POD struct: Changed from Any typed fields to properly parameterized types
  • snapshots::S (parameterized by snapshot type)
  • min_renergy::T, renergy::T (parameterized by element type)
  • rbasis::Union{Missing, Matrix{T}}, spectrum::Union{Missing, Vector{T}}
• SVD/TSVD structs: Changed kwargs::Any to kwargs::K where K <: NamedTuple

Return Type Annotations

• matricize(VoV::Vector{Vector{T}})::Matrix{T}
• determine_truncation(...)::Tuple{Int, T}
• reduce!(...)::Nothing
• only_dvs(...)::Bool
• Base.show(::IO, ::POD)::Nothing

JET.jl Tests

Added new test file test/jet.jl that verifies type stability of:

• deim_interpolation_indices
• matricize
• POD constructors (Matrix and Vector{Vector})
• reduce! with SVD algorithm

Type Stability Before/After

Before (@code_warntype reduce!(pod, TSVD())):

u::ANY
s::ANY
v::ANY
n_max::ANY

After:

u::Matrix{Float64}
s::Vector{Float64}
v::Matrix{Float64}
n_max::Int64

Test plan

• Run Pkg.test() - all tests pass
• Runic formatting check passes
• JET.jl analysis passes for core functions

CC: @ChrisRackauckas

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