Fix indefinite GradientGrassmann preconditioner on nearly rank-deficient bonds - #532
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…ent bonds The regularized inverse of `ρ = C * C'` was formed explicitly as `U * inv(S² + δ²) * U'`. Once the gradient is small, its condition number exceeds `1 / eps` on nearly rank-deficient bonds, and the explicit matrix is no longer numerically positive definite. The preconditioned gradient then need not be a descent direction, the line search returns a zero step, and the Hager-Zhang β in the next CG iteration evaluates to 0/0, feeding a NaN tangent into the Grassmann retraction. Apply the inverse in factored form instead, scaling before mixing back with U'. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This was referenced Oct 1, 2026
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Fixes the intermittent
ArgumentError: invalid argument #4 to LAPACK callin the finiteGradientGrassmanntest for the long-range Ising model (12 of 20 seeds failed onmain).Cause
The long-range model's bonds are nearly rank-deficient (Schmidt values
[1.0, 0.062, ~1e-10, …]). Once the gradient is small, the regularizedinv(S² + δ²)has a condition number above1 / eps, so the explicitU * inv(S² + δ²) * U'is not numerically positive definite (⟨g, P g⟩ = -1.2e-17). The linesearch then returns a zero step, the next CG β is0/0 = NaN, and the NaN reaches the SVD inGrassmann.retract. This affects infinite MPS as well and does not depend on the mixed scalartype.Fix
Apply the inverse in factored form,
((Δ.Z * U) * inv(S² + δ²)) * U', so the sign of⟨g, P g⟩stays reliable. The outdated test comment about "overshooting" is removed.Tests
groundstate/groundstatepasses (109/109).Related hardening in OptimKit: Jutho/OptimKit.jl#48.
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