From dc654e9ac668421e315c679e36d871005cedc35d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20L=C3=BCnenschlo=C3=9F?= <peter.luenenschloss@ufz.de>
Date: Thu, 30 Jul 2020 08:47:59 +0200
Subject: [PATCH] Update FormalDescriptions.md
---
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1 file changed, 24 insertions(+)
diff --git a/docs/funcs/FormalDescriptions.md b/docs/funcs/FormalDescriptions.md
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+# 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.
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