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Originally Posted by Ether
Be aware: There are already two events (Oregon and Traverse City) for which data is missing for the entire event. No guarantee that won't happen for more events as the season rolls on. Not counting these two events, over 12% of the data is missing for the other events.
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Twitter data is missing entirely for the San Diego, Oregon, Traverse City, Sacramento, and Utah events.
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For this application, LDLT would be far faster* and plenty accurate.
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The alliance selection algorithm in the qualification match scheduling software used for FRC events pretty much guarantees that the design matrix A (i.e. Ax≈b) will be full rank and well-conditioned. This means that forming the normal equations (Px=A
TAx=A
Tb=S) and solving with Cholesky decomposition (LL
T or LDL
T) will give excellent numerical stability and accuracy and be far faster than other methods (and require much less memory). Furthermore, the normal equations can be formed directly in one pass (without the need to form the design matrix and multiply it by its transpose) when the raw data is read and parsed.