josdejong/mathjs

Schur result not quasi upper triangular

Open

#3600 opened on Nov 22, 2025

View on GitHub
 (3 comments) (0 reactions) (0 assignees)JavaScript (13,832 stars) (1,298 forks)batch import
bugcategory:numericalhelp wanted

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

Tech stack
javascript
Domain
data
Issue type
bug
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-2 days
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
active
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
clear
Prerequisites
Numerical linear algebramathjs code structure
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
65
Research direction
Investigate the Schur decomposition implementation in mathjs, likely in the linear algebra module (e.g., src/function/algebra/schur.js or similar). Check if the QR algorithm used includes a shift strategy (e.g., Wilkinson shift or Francis double shift). The issue author suggests that the absence of such shift may cause the result to not be quasi upper triangular. Consider implementing the shift or verifying the existing code. The linked issue comments may provide additional clues.