[General] Improve import and export

[ocots]

The import and export functions have been written quickly. They need to be checked.

[ocots]

Export/Import Verification Planning

Issue: #217 - Improve import and export
Date: 2025-12-16
Status: Planning Complete ✅

TL;DR

Existing JSON tests are comprehensive. JLD2 tests are minimal.
Goal: Verify "idempotency" (numerical stability) and data integrity.
Plan: Enhance JLD2 tests to match JSON coverage. Add a "Stability Test" (Export → Import → Export → Compare Files).

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1. Analysis of Current State

JSON (ext/CTModelsJSON.jl)

• Method: Manual serialization of discretized data + metadata. Reconstructs solution via build_solution + interpolation.
• Tests: Comprehensive (test/io/test_export_import.jl). Checks scalars, vectors, all duals, infos. Verifies numerical closeness (≈) of trajectories.

JLD2 (ext/CTModelsJLD.jl)

• Method: Direct Julia object serialization (save_object/load_object).
• Tests: Minimal (only checks objective and iterations).
• Risk: Serialization of function objects (interpolations) can be fragile.

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2. Verification Plan

T1: Enhance JLD2 Tests

Update test/io/test_export_import.jl to include a full test suite for JLD2, mirroring the JSON tests:

• Check all scalar fields.
• Check trajectories (state, control, costate) numerically at grid points.
• Check duals.
• Check infos.

T2: Stability / Idempotency Test

Add a test case for both formats:

1. export(sol) → file1
2. sol2 = import(file1)
3. export(sol2) → file2
4. Verify: file1 == file2 (content equality) or sol ≈ sol2 (numerical equality).

Note: For JSON, file1 == file2 might effectively hold if floating point printing is deterministic. For JLD2, binary equality is expected if the object structure is preserved.

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3. Implementation Tasks

Task	Description
T1	Add "JLD comprehensive round-trip" test set in test/io/test_export_import.jl.
T2	Add "Stability test" (double export) for JSON and JLD2.

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4. Test Commands

# Run IO tests
julia --project=. -e 'using Pkg; Pkg.test("CTModels"; test_args=["io"]);'

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5. GitHub Workflow

PR to verify and close #217.