Large cohort scaling improvements#2575
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In mean-energy mode the inverse covariance is the identity, so the gradient update is just the mean-centered points. The two correspondence functions were still building an NxN identity and multiplying by it (points_minus_mean * pinvMat) on every initialization iteration, which is an O(P*N^2) no-op. Drop the multiply in both the image/DT path (LegacyCorrespondenceFunction) and the mesh/normals path (CorrespondenceFunction). The result is identical, since multiplying by an exact identity changes nothing. OptimizeTests passes.
The optimization phase decomposes the NxN Gram matrix Y^T Y on every iteration. That matrix is symmetric positive-semidefinite, but the code ran a general vnl_svd on it and did the surrounding matrix work in single-threaded VNL. Switch to Eigen::SelfAdjointEigenSolver in both entropy paths and keep the Gram, inverse-covariance, and gradient products in Eigen. For an SPD matrix the eigenvectors and eigenvalues are the SVD's U and singular values, so the result matches to floating-point tolerance.
Reflect the mean-energy and eigensolver changes: both phases are faster and multi-core again, so the single-core-at-scale description no longer applied. Rewrite the prose, add before/after charts across the full grid to N=4096 (runtime and CPU utilization) plus end-to-end run times, and correct the per-phase core counts. Note that runtime is still cubic in the number of shapes but with a smaller constant, and that optimization utilization improves but still declines at the very high end because the eigensolve itself stays serial. Remove the pre-improvement collapse charts.
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Two changes to the per-iteration correspondence update in optimize: initialization stops multiplying by an N×N identity (an O(P·N²) no-op), and the optimization phase decomposes the symmetric Gram matrix with a symmetric eigensolver in Eigen instead of a single-threaded general SVD. Together they speed up both phases and restore multi-core use on large cohorts (about 3.5× end-to-end at N=1024, and 14× on the optimization phase at N=4096), with no change to the optimization result.