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Bug fixes: 1. computeDirect 3x3: eigenvalues from computeRoots() are theoretically sorted via the trigonometric formula, but floating-point rounding (especially in float) can break the ordering. Add a 3-element sorting network after computeRoots() to guarantee sorted output. 2. compute(): Inf input silently returns Success with garbage results, unlike NaN which correctly returns NoConvergence. Add an isfinite() check on the scaling factor (which is maxCoeff of the matrix) to detect Inf/NaN early and return NoConvergence. 3. computeFromTridiagonal(): lacks the equilibration scaling that compute() applies, causing overflow and NoConvergence for tridiagonal matrices with large entries. Add the same scale-to-[-1,1] pattern. New tests: - Eigenvalue sorting verification (both iterative and direct solvers) - Repeated/degenerate eigenvalues (all equal, multiplicity n-1, two clusters, nearly repeated separated by O(epsilon)) - Extreme eigenvalue ranges (high condition number spanning many orders of magnitude, near-underflow, near-overflow, mixed positive/negative, rank-deficient with zero eigenvalue) - computeFromTridiagonal with large and tiny values - Diagonal matrices (eigenvalues must match sorted diagonal) - operatorInverseSqrt accuracy (sqrtA*invSqrtA=I, invSqrtA*A*invSqrtA=I, symmetry) - RowMajor storage for computeDirect (2x2, 3x3, float, double) and iterative solver (dynamic RowMajor) - Inf input detection - Tridiagonal structure verification (off-tridiagonal entries are zero) - Direct solver stress tests: 3x3 (near-planar covariance, triple eigenvalue, double eigenvalue, large off-diagonal, nearly singular) and 2x2 (equal eigenvalues, tiny off-diagonal, huge diagonal ratio, anti-diagonal dominant, negative entries) - Tightened unitary tolerance from fixed 32*test_precision to 4*n*epsilon (scales with matrix size) - Fixed typo: "expponential" -> "exponential" Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
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