JQR/JRQ/JQL/JLQ factorizations
JQR/JRQ/JQL/JLQ factorizations of an array
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JQR/JRQ/JQL/JLQ computes a J-orthogonal (or J-unitary, or hyperbolic) QR/RQ/QL/LQ factorization of the matrix A. For example, the JQR factorization decomposes the matrix A = Q*R for a given signature matrix J, where R is an upper triangular matrix with positive values on the diagonal, and Q is a J-orthogonal matrix with Q'*J*Q = J. The given signature matrix J must be a diagonal matrix with 1 or -1 on the main diagonal and zeros on all the subdiagonals.
Example code:
A = randn(10);
J = blkdiag(-eye(5),eye(5));
[Q,R,Jp] = jqr(A,J);
norm(A-Q*R)
norm(Jp - Q'*J*Q)
Cite As
Ivo Houtzager (2026). JQR/JRQ/JQL/JLQ factorizations (https://github.com/iwoodsawyer/hyperbolic/releases/tag/v1.4.1.1), GitHub. Retrieved .
General Information
- Version 1.4.1.1 (14.7 KB)
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View License on GitHub
MATLAB Release Compatibility
- Compatible with any release
Platform Compatibility
- Windows
- macOS
- Linux
| Version | Published | Release Notes | Action |
|---|---|---|---|
| 1.4.1.1 | See release notes for this release on GitHub: https://github.com/iwoodsawyer/hyperbolic/releases/tag/v1.4.1.1 |
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| 1.4.0.1 | See release notes for this release on GitHub: https://github.com/iwoodsawyer/hyperbolic/releases/tag/v1.4.0.1 |
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| 1.4.0.0 | Fixes to prevent overflow/underflow
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| 1.3.0.0 | Small code improvements
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| 1.2.0.0 | Made the diagonal values of the returned R matrix positive. |
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| 1.1.0.0 | Changed default tolerance to be based on frobenius norm for speed |
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| 1.0.0.0 |
