diff --git a/docs/funcs/FormalDescriptions.md b/docs/funcs/FormalDescriptions.md index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..d037145f59d102700b73d64a5acae95df84192b0 100644 --- a/docs/funcs/FormalDescriptions.md +++ b/docs/funcs/FormalDescriptions.md @@ -0,0 +1,24 @@ +# Mathematical descriptions + +A collection of detailed mathematical descriptions. + +## Index + +- [spikes_flagRaise](#spikes_flagraise) + + +## spikes_flagRaise + +The value $`x_{k}`$ of a time series $`x`$ with associated +timestamps $`t_i`$, is flagged a rise, if: + +1. There is any value $`x_{s}`$, preceeding $`x_{k}`$ within `raise_window` range, so that: + * $` M = |x_k - x_s | > `$ `thresh` $` > 0`$ +2. The weighted average $`\mu^*`$ of the values, preceeding $`x_{k}`$ within `average_window` range indicates, that $`x_{k}`$ doesnt return from an outliererish value course, meaning that: + * $` x_k > \mu^* + ( M `$ / `mean_raise_factor` $`)`$ +3. Additionally, if `min_slope` is not `None`, $`x_{k}`$ is checked for being sufficiently divergent from its very predecessor $`x_{k-1}`$, meaning that, it is additionally checked if: + * $`x_k - x_{k-1} > `$ `min_slope` + * $`t_k - t_{k-1} > `$ `min_slope_weight`*`intended_freq` + +The weighted average $`\mu^*`$ was calculated with weights $`w_{i}`$, defined by: +* $`w_{i} = (t_i - t_{i-1})`$ / `intended_freq`, if $`(t_i - t_{i-1})`$ < `intended_freq` and $`w_i =1`$ otherwise. \ No newline at end of file