mefp: Error in root.matrix(crossprod(X)): matrix is not positive semidefinite

[GreatEmerald]

I have run into a (rare) case where the root of a matrix cannot be found because it's indefinite. Here's a reprex using the bfast package:

library(bfast)
BugTS = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, NA, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, NA, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, NA, 2, 2, 3, 5, NA, NA, 3, 2, 3, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, NA, 0, 1, NA, 0, 1)
BugTS = ts(BugTS, start=2009, frequency = 23)
bfastmonitor(BugTS, start=2016, type = "ME")
#> Error in root.matrix(crossprod(X)): matrix is not positive semidefinite

^{Created on 2020-04-07 by the reprex package (v0.3.0)}

Using @appelmar's C++ code, the same error is rendered as:

Error in .sc_cpp_efp_process_me(X, y, rescale, h) : 
  sqrtmat_sympd(): transformation failed

This fails when type is set to ME, but it works with any other mefp types.

Is there a way to detect that this would happen, and then fall back to some other fluctuation process type instead?

[appelmar]

I could reproduce this and found the negative Eigenvalue producing the error being -4.283014e-16, which makes me wonder whether this is a numerical issue :-/. I don't think there is a cheap way to identify these cases in advance (without computing the Eigenvalues) but maybe we can just improve the error message suggesting that other fluctuation processes may work? Falling back to other processes would also be possible but I think it would be important to communicate this to the user (e.g., as a warning).

[GreatEmerald]

My own preference would then be to do a try/tryCatch and then retry with a different process, with a warning about it, as that helps people who are trying to use BFAST at a large scale.