Enhance relationship matrices and BLUP workflow

[meibujun]

Summary

• wire up the AnimalBreeding module so the core, data, relationship, and BLUP components load automatically and are exported for public use
• harden pedigree ingestion and relationship-matrix builders with robust topological sorting, Henderson-style A⁻¹ assembly, and improved genomic/H-inverse calculations
• refresh BLUP helpers and tests to honor the new animal index mapping, provide richer design matrices, and validate sparse solver integration

Testing

• julia --project=AnimalBreeding.jl -e 'using Pkg; Pkg.test()' (fails: julia executable not available in container)

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https://chatgpt.com/codex/tasks/task_e_68de0a88d0dc8321a45602074af76510

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Slice random-effect coefficients when forming residuals

The residual term in the EM loop subtracts sum(Z * solutions[n_fixed+1:end] for (name, Z) in Z_dict), i.e. every random-effect design matrix is multiplied by the entire concatenated random-effect solution vector. As soon as the model contains more than one random effect, each Z expects only its own coefficient slice, so this call either raises a dimension-mismatch error or reuses the same coefficients for all effects. The code should accumulate residuals by iterating over the random effects with a running offset, mirroring the logic used later in the loop.

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[chatgpt-codex-connector]

Trace term addresses wrong submatrix for subsequent random effects

When updating a random effect’s variance, the trace term is computed as tr(C_inv[current_pos+1:end, current_pos+1:end] * dm.A_inv_matrix). For any model with more than one random effect, this expression takes the entire remaining lower-right block of C_inv and multiplies it with the full A⁻¹, producing a dimension mismatch or an incorrect trace for all but the first random effect. The slice should be limited to the current effect’s block (current_pos+1:current_pos+dim) and use the corresponding covariance structure for that effect only.

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