perf: C++ backend performance improvements (Phase 2)#13
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Three targeted changes to the single-group fast EM path: 1. Save a 1-based copy of mloc before the decrement so uP2() is called with the pre-saved matrix instead of creating a J×L temporary via `mloc+1` on every EM iteration. 2. Hoist the missing-data mask (mX0 / mX1 / mXMissing) and the `has_nan()` check out of the while-loop. The data matrix mX never changes during estimation, so the mask only needs to be built once. 3. Precompute per-item, per-category column-index vectors from mloc before the loop. Previously arma::find(mloc.row(j)==k) was called twice per (j,k) pair per EM iteration; now each lookup is O(1). Also replace the J×N ones-matrix multiply used to compute expN in the no-missing case with arma::repmat(arma::sum(msdPost,0),J,1), reducing cost from O(J·N·L) to O(N·L + J·L). Numerical results are identical; only wall-clock time changes.
In the no-missing-data branch of both LikNR and LikNR_LC, expN was computed as ones(J,N) * msdPost — an O(J·N·L) matrix multiplication whose result has identical rows equal to sum(msdPost, 0). Replace with arma::repmat(arma::sum(msdPost,0), J, 1) which costs O(N·L + J·L) and produces the same result exactly.
Mord() computes ordinal moment matrices (Xi11, Xi21, Xi22) used for fit statistics. The Xi21 loop is O(nitem^3) and Xi22 is O(nitem^4); both previously called LCprob.rows(arma::find(item_no==(x+1))) inside their innermost iterations, re-scanning the full item_no vector on every visit. Extract a one-time precomputation step that builds lc[i] for each item before any loop runs. All inner-loop variables (lci, lcj, lck, lcl) become const references into this cache, so no matrix data is copied and no find() call is repeated. Numerical output is identical; the saving grows as O(nitem^4) for large tests with many items.
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Summary
mX0/mX1/mXMissing) out of thefast_GDINA_EMwhile-loop inLik2.cpp. The data matrix never changes during estimation, so the mask andhas_nan()check were being redundantly rebuilt every EM iteration.mlocbefore decrement infast_GDINA_EM, eliminating aJ x Ltemporary matrix created viamloc+1on every iteration.mlocbefore the EM loop infast_GDINA_EM. Previouslyarma::find(mloc.row(j)==k)was called twice per(j,k)pair per iteration; now each lookup is O(1).ones(J,N) * msdPostwithrepmat(sum(msdPost,0), J, 1)inLikNR,LikNR_LC, andfast_GDINA_EM. In the no-missing-data case every row ofexpNis identical, so the J x N ones-matrix multiply (O(J x N x L)) is wasteful; the replacement costs O(N x L + J x L).LCprobrow slices into astd::vector<arma::mat>inMord(). The Xi21 loop is O(nitem^3) and Xi22 is O(nitem^4); without caching, each iteration re-ranrows(find(...))over the full category index vector.Benchmark
Measured on the built-in
sim30GDINAdataset (N=1000, J=30, K=5, L=32):LikNRfast_GDINA_EM(30 itr)MordGains scale with larger J, N, or K.
Mordbenefits most because the savings compound across its O(nitem^4) Xi22 loop.Verification
:::in test files, unrelated to this PR).R CMD INSTALL.