feat: bound the number of sweeps the SVD spends on one singular value

[tayal-sarthak]

Closes #70.

Summary

The issue reports a dataset that hangs, with the observation that p never drops below 93. That p is the counter driving the sweep in the singular value decomposition:

let iter = 0;
...
while (p > 0) {
  ...
  iter = iter + 1;

iter is raised on every sweep along with being reset once a singular value settles, yet nothing ever reads it. There is no ceiling anywhere in the loop, so an input the sweep cannot settle keeps it going with no way out. The caller gets no error, no result, and no thread back.

LAPACK bounds the same loop, dbdsqr allowing 6 sweeps per singular value before it reports failure.

The ceiling

A maxIterations option, 100 by default, caps how many sweeps any one singular value gets. Passing it means the sweep is stuck, which is reported:

Error: SVD did not converge after 100 iterations on a single singular value

Choosing the default

Measuring how many sweeps a decomposition that converges takes per singular value, across random matrices:

ceiling	40x25, out of 40	200x150, out of 10
1	40 reported	10 reported
2	40 reported	10 reported
3	37 reported	10 reported
5	none	none
10	none	none
100	none	none

Four sweeps covers every case measured, and the figure does not grow with the size of the input, since the count is spent per singular value rather than over the whole run. A default of 100 therefore sits at roughly 25 times what a decomposition needs, wide enough that a converging input cannot reach it, while a stuck one stops in bounded time instead of running on.

Compatibility

Every decomposition that converges today behaves exactly as before. The only inputs affected are the ones that never finish.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 68.94%. Comparing base (1a4a05a) to head (52c9aec).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #220      +/-   ##
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+ Coverage   68.88%   68.94%   +0.06%     
==========================================
  Files          49       49              
  Lines        5904     5916      +12     
  Branches     1060     1064       +4     
==========================================
+ Hits         4067     4079      +12     
  Misses       1824     1824              
  Partials       13       13              

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