# Possible numerical edge case in QR-based ML objective with zero custom trend

**URL:** <https://uqworld.org/t/possible-numerical-edge-case-in-qr-based-ml-objective-with-zero-custom-trend/9181>\
**Category:** Community Q&A and How To\
**Tags:** pce, metamodeling, uqlab-bug, kriging\
**Created:** [June 5, 2026, 10:11am UTC](https://uqworld.org/t/possible-numerical-edge-case-in-qr-based-ml-objective-with-zero-custom-trend/9181 "2026-06-05T10:11:30Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Alessandro\_Baravelli](https://uqworld.org/user_avatar/uqworld.org/alessandro_baravelli/32/2345_2.png) [@Alessandro\_Baravelli](https://uqworld.org/u/Alessandro_Baravelli)\
**Post date:** [June 5, 2026, 10:11am UTC](https://uqworld.org/t/possible-numerical-edge-case-in-qr-based-ml-objective-with-zero-custom-trend/9181/1 "2026-06-05T10:11:31Z")

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When the trend design matrix is identically zero, qr(Ftilde,0) may return a nonzero orthonormal vector Q with R=0. This is a valid QR factorization, but using Q to project Ytilde removes a component of Ytilde even though the column space of Ftilde is {0}. Therefore the QR-based ML variance estimate is not equivalent to the intended zero-mean likelihood in this degenerate trend case.

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**Author:** ![styfen.schaer](https://uqworld.org/user_avatar/uqworld.org/styfen.schaer/32/849_2.png) [@styfen.schaer](https://uqworld.org/u/styfen.schaer)\
**Post date:** [June 10, 2026, 2:37pm UTC](https://uqworld.org/t/possible-numerical-edge-case-in-qr-based-ml-objective-with-zero-custom-trend/9181/2 "2026-06-10T14:37:43Z")

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Hi @Alessandro_Baravelli

Could you provide a bit more context about where you encountered this issue?

In particular:

- Which module or function are you referring to?
- Do you have a minimal example that reproduces this behavior, or is this a theoretical concern based on your inspection of the implementation?

Best regards,  
Styfen