Sparse matrix error: detect ill conditions on-the-fly #1205
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Signed-off-by: Martijn Govers <[email protected]>
mgovers
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Signed-off-by: Martijn Govers <[email protected]>
Signed-off-by: Martijn Govers <[email protected]>
Signed-off-by: Martijn Govers <[email protected]>
mgovers
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Dec 3, 2025
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| .binaryExpr( | ||
| (matrix.col(pivot).tail(size - pivot - 1) * matrix.row(pivot).tail(size - pivot - 1)), |
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TODO: also add the contribution from the accumulated_error.col(pivot).tail(size - pivot - 1) * matrix.row(pivot).tail(size - pivot - 1)) and (matrix.col(pivot).tail(size - pivot - 1) * accumulated_error.row(pivot).tail(size - pivot - 1)
mgovers
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Dec 3, 2025
| // check stability | ||
| Scalar const piv_size = cabs(matrix(pivot, pivot)); | ||
| double const piv_error = accumulated_error(pivot, pivot); | ||
| if (cabs(matrix(pivot, pivot)) <= std::max(accumulated_error.row(pivot).tail(size - pivot).maxCoeff(), |
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this is actually a very weak criterion. by the time your accumulated error even becomes close to your pivot element size, the rest of your calculation may already become garbage. E.g., if you want a precision of 1E-5, odds are that your calculation will not be as precise anymore when your matrix element precision is something like 1E-1. This criterion probably should be stricter:
Suggested change
| if (cabs(matrix(pivot, pivot)) <= std::max(accumulated_error.row(pivot).tail(size - pivot).maxCoeff(), | |
| if (cabs(matrix(pivot, pivot)) <= threshold * std::max(accumulated_error.row(pivot).tail(size - pivot).maxCoeff(), |
mgovers
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Dec 3, 2025
mgovers
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Dec 3, 2025
Signed-off-by: Martijn Govers <[email protected]> Signed-off-by: Martijn Govers <[email protected]> Apply suggestion from @mgovers Signed-off-by: Martijn Govers <[email protected]>
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This is an experiment. Do not merge yet!
Rather than using some form of condition numbers to detect unsolvable matrix decompositions, we now detect them on-the-fly
NOTE: some ill-conditioned cases now actually fail even though they did not do so before!!! It is dependent on the calculation method and whether the calculation is symmetric or asymmetric whether the system raises errors or not.