diff --git a/docs/funcs/FormalDescriptions.md b/docs/funcs/FormalDescriptions.md index 7ea4a9748d6bc26662d3a27bd888c218423c1f88..12f286add9f9c5a488025d00b6d232eb02c2f38c 100644 --- a/docs/funcs/FormalDescriptions.md +++ b/docs/funcs/FormalDescriptions.md @@ -7,6 +7,7 @@ A collection of detailed mathematical descriptions. - [spikes_flagRaise](#spikes_flagraise) - [spikes_flagSpektrumBased](#spikes_flagspektrumbased) - [breaks_flagSpektrumBased](#breaks_flagspektrumbased) +- [sm_flagConstants](#sm_flagconstants) ## spikes_flagRaise @@ -71,4 +72,15 @@ A value $`x_k`$ of a time series $`x_t`$ with timestamps $`t_i`$, is considered 5. The ratio (this/next) of the second derivatives is sufficiently height: - $`|\frac{x''_{k}}{x''_{k+1}}| > `$`scnd_der_ratio_margin_2` \ No newline at end of file + $`|\frac{x''_{k}}{x''_{k+1}}| > `$`scnd_der_ratio_margin_2` + +## sm_flagConstants + +Any set of consecutive values +$`x_k,..., x_{k+n}`$, of a time series $`x`$ is flagged, if: + +1. $`n > `$`window` +2. $`\sigma(x_k, x_{k+1},..., x_{k+n}) < `$`thresh` +3. $`\max(x'_{k-n-s}, x'_{k-n-s+1},..., x'_{k-n+s}) \geq`$ `deriv_min`, with $`s`$ denoting periods per `precipitation_window` +4. $`\min(x'_{k-n-s}, x'_{k-n-s+1},..., x'_{k-n+s}) \leq`$ `deriv_max`, with $`s`$ denoting periods per `precipitation_window` +5. $`\mu(x_k, x_{k+1},..., x_{k+n}) \le \max(x) \cdot`$ `tolerance` \ No newline at end of file