MAINT: optimize._chandrupatla: reduce xatol #20501
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I think it's sensible to try to compute roots near zero more accurately in the default case. A roughly 20-fold increase in the maximum number of iterations for dtype double is not so bad really, unless someone is using this with a very costly function.
I saw that you set the xatol and xrtol based on the dtype so had one suggestion to do this for maxiter as well. On the whole I think this looks good.
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Reference issue
NA
What does this implement/fix?
The default absolute x-tolerance on the bracketing (scalar) root finders is quite large, which can lead to premature termination when the root is near zero. If the root is near zero, we can and probably should find the root more precisely. In preparation for a PR to make this feature public, this PR reduces the absolute x-tolerance for
_chandrupatla.Additional information
Before merge:
@steppi Should the default maximum number of iterations be increased? Assuming the algorithm resorts to bisection, it takes 2048 iterations to converge from the largest possible floating point bracket to the smallest normal floating point bracket. The current default is only 100 iterations, so we run the risk of converging due to the iteration limit well before successful convergence would occur.