Replace the fixed 5x5 SVD implementation with template <uint8_t N>
building blocks over Matrix<N,N> working buffers (N = max(rows, cols)),
removing the 5x5 size limit. Public API (SVD::SVD) is unchanged and the
whole path stays heap-free: peak stack is ~11*N^2 floats, budgeted in
the SVD.hpp header doc.
Fixes found while porting/validating the templated rewrite:
- QL.Identity() was a no-op (static factory returns by value); init
the Householder accumulators with an explicit diagonal loop
- restore the QL column sign-flip in ExtractAndSortSingularValues for
negative unsolved W diagonal entries (Householder sign flips)
- T = B^T B tridiagonal formula: T[i][i] = d[i]^2 + e[i-1]^2 only
(e[i] contributes to T[i+1][i+1], not T[i][i])
- wide-matrix Vt assembly: Vt = QL^T must be filled over the full
m x m (m = columns of A), not just the top n x n
Tests:
- matrix-tests: add large-size instantiation cases beyond the old limit
(tall 7x5 N=7, square 6x6 N=6, wide 5x8 N=8 transpose path with full
orthogonal 8x8 Vt, tall 6x4 near rank-deficient N=6 deflation path),
all checked against numpy/scipy float32 references
- svd-build-blocks-tests: adapt Jacobi test to the Matrix<N,N> interface
- svd-reference-values.py: add the four new reference matrices
Cynopolis