perf: speed up SVD (~4.7x) and symmetric EVD (~1.7x) via transposed internal storage

[lpatiny]

Summary

The decomposition algorithms iterate their hot inner loops down columns (the row index varies), but Matrix stores data row-major (data[row][col]). Those column walks thrash the CPU cache. This PR makes the hot loops scan memory sequentially by storing the worked-on matrices transposed internally and transposing them back before returning — so the public API and the numerical results are unchanged.

This supersedes the original exploratory commit (which globally swapped get/set). A global swap is the wrong fix: it speeds SVD/EVD but makes LU ~1.6× slower, and breaks non-square matrices and every consumer that assumes row-major data. The win is captured per-algorithm instead.

What was done

• SVD (src/dc/svd.js): work on at = value.transpose() and accumulate the U/V singular vectors in transposed storage, then transpose back. The Householder and QR-rotation inner loops become sequential.
• Symmetric EVD (src/dc/evd.js, tred2/tql2): accumulate the eigenvectors V transposed, then transpose back.
• Non-symmetric EVD (orthes/hqr2): left row-major on purpose. Its two O(n³) phases (the QR sweep vs. the eigenvector back-transform Σ V(i,k)·H(k,j)) have opposite layout preferences, so a single static transpose cancels out — not worth the large, fragile rewrite of the complex-eigenvector code.
• LU: untouched. Its only O(n³) loop is already a sequential row scan, so it is cache-optimal as-is.
• Tests: the EVD only had a single 2×2 example. Added a reconstruction oracle (A·V = V·D, eigenvector orthonormality, complex eigenvalue pairs) for symmetric (4×4, 12×12) and non-symmetric matrices.
• Benchmark: scripts/benchmark.js is now deterministic (seeded inputs), warmed up, and reports both EVD paths.

Speed (1000×1000 unless noted, deterministic, warmed up)

Decomposition	before	after	speedup
SVD	17764 ms	3804 ms	~4.7×
EVD, symmetric (600×600)	666 ms	386 ms	~1.7×
EVD, symmetric (300×300)	78 ms	51 ms	~1.5×
LU	232 ms	238 ms	unchanged (intentional)
EVD, non-symmetric	—	—	left row-major (see above)

(Numbers from an M-series laptop; ratios are what matter.)

Results are bit-identical, not just close

Because only storage location changes and never the order of arithmetic, every IEEE-754 operation sees the same operands in the same sequence. Verified by dumping full outputs (singular/eigen values + complete vector matrices, full float precision) from this branch and from main, then byte-comparing with cmp:

• SVD: byte-for-byte identical across square / tall / wide shapes × autoTranspose on/off.
• EVD: byte-for-byte identical across n = 3, 5, 10, 25, 40, 80 × {symmetric, symmetric auto-detected, general}.

Zero differing bytes in both.

Follow-up

The non-symmetric EVD path could still be sped up (~1.5×) with a phase-split transpose (transpose V between the QR and back-transform phases). Left out of this PR to keep it low-risk; the new test oracle is in place to support it later.

[codecov]

Codecov Report

❌ Patch coverage is 64.97175% with 62 lines in your changes missing coverage. Please review.
✅ Project coverage is 68.46%. Comparing base (67cda77) to head (93bdb7e).

Files with missing lines	Patch %	Lines
scripts/benchmark.js	0.00%	56 Missing and 1 partial ⚠️
src/dc/svd.js	95.38%	3 Missing ⚠️
src/dc/evd.js	94.28%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #167      +/-   ##
==========================================
+ Coverage   64.83%   68.46%   +3.62%     
==========================================
  Files          47       48       +1     
  Lines        5625     5727     +102     
  Branches      954     1013      +59     
==========================================
+ Hits         3647     3921     +274     
+ Misses       1967     1794     -173     
- Partials       11       12       +1     

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