josdejong/mathjs

Schur result not quasi upper triangular

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#3,600 opened on Nov 22, 2025

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bugcategory:numericalhelp wanted

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Description

Describe the bug A clear and concise description of what the bug is.

I think sometimes Schur returns a matrix that isn't quasi upper triangular.

To Reproduce Generic orthonormal matrices seem to create a problem. For example:

math.matrix([
      [-0.03591206220229135, -0.09100469507870354, 0.9952027277203429],
      [-0.3802068171617618, -0.9197139315803332, -0.09782157349362577],
      [0.9242040358990549, -0.38189583596928406, -0.0015717815434243287]
    ])

Possibly mathjs is running QR without a Wilkinson/Francis shift strategy?

Happy to contribute a PR on this if I'm not hallucinating the problem :).

Contributor guide

Research direction
Investigate the QR algorithm implementation in mathjs's Schur decomposition. Examine whether a shift strategy (e.g., Wilkinson or Francis shift) is applied during the QR iteration to ensure the resulting matrix is quasi upper triangular. Check the source code in the 'src/function/matrix/schur.js' file and its dependencies.
Tech stack
javascript
Domain
backend
Issue type
Bug
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
4
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
Over 1 week
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Active
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Clear
Prerequisites
JavaScriptLinear algebra
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
25