| parameter | data type | default value | description |
| ------ | ------ | ------ | ---- |
| rel_change_rate_min | float | `0.1` | Lower bound for the relative difference, a value has to have to its preceeding value, to be a candidate for being break-flagged. See condition (2).|
| abs_change_min | float | `0.01` | Lower bound for the absolute difference, a value has to have to its preceeding value, to be a candidate for being break-flagged. See condition (1).|
| first_der_factor | float | `10` | Factor of the second derivates "arithmetic middle bound". See condition (3).|
| first_der_window_size | string | `"12h"` | Options: <br/> - any offset String <br/><br/> Determining the size of the window, covering all the values included in the the arithmetic middle calculation of condition (3).|
| scnd_der_ratio_margin_1 | float | `0.05` | Range of the area, covering all the values of the second derivatives quotient, that are regarded "sufficiently close to 1" for signifying a break. See condition (5).|
| scnd_der_ratio_margin_2 | float | `10.0` | Lower bound for the break succeeding second derivatives quotients. See condition (5). |
| smooth_poly_order | integer | `2` | When calculating derivatives from smoothed timeseries (diff_method="savgol"), this value gives the order of the fitting polynomial calculated in the smoothing process.|
| filter_window_size | Nonetype or string | `None` | Options: <br/> - `None`<br/> - any offset string <br/><br/> Controlls the range of the smoothing window applied with the Savitsky-Golay filter. If None is passed (default), the window size will be two times the sampling rate. (Thus, covering 3 values.) If you are not very well knowing what you are doing - do not change that value. Broader window sizes caused unexpected results during testing phase.|
The function flags breaks (jumps/drops) in input measurement series by
evaluating its derivatives.
NOTE, that the dataseries-to-be flagged is supposed to be harmonized to an
equadistant frequencie grid.
NOTE, that the derivatives are calculated after applying a savitsky-golay filter
to $`x`$.
A value $`x_k`$ of a data series $`x`$, is flagged a break, if:
1. $`x_k`$ represents a sufficient absolute jump in the course of data values:
* $`|x_k - x_{k-1}| >`$ `abs_change_min`
2. $`x_k`$ represents a sufficient relative jump in the course of data values:
3. Let $`X_k`$ be the set of all values that lie within a `first_der_window_range` range around $`x_k`$. Then, for its arithmetic mean $`\bar{X_k}`$, following equation has to hold:
| parameter | data type | default value | description |
| ------ | ------ | ------ | ---- |
| rel_change_rate_min | float | `0.1` | Lower bound for the relative difference, a value has to have to its preceeding value, to be a candidate for being break-flagged. See condition (2). |
| abs_change_min | float | `0.01` | Lower bound for the absolute difference, a value has to have to its preceeding value, to be a candidate for being break-flagged. See condition (1). |
| first_der_factor | float | `10` | Factor of the second derivates "arithmetic middle bound". See condition (3). |
| first_der_window_size | string | `"12h"` | Options: <br/> - any offset String <br/><br/> Determining the size of the window, covering all the values included in the the arithmetic middle calculation of condition (3). |
| scnd_der_ratio_margin_1 | float | `0.05` | Range of the area, covering all the values of the second derivatives quotient, that are regarded "sufficiently close to 1" for signifying a break. See condition (5). |
| scnd_der_ratio_margin_2 | float | `10.0` | Lower bound for the break succeeding second derivatives quotients. See condition (5). |
| smooth_poly_order | integer | `2` | When calculating derivatives from smoothed timeseries (diff_method="savgol"), this value gives the order of the fitting polynomial calculated in the smoothing process. |
| filter_window_size | Nonetype or string | `None` | Options: <br/> - `None`<br/> - any offset string <br/><br/> Controlls the range of the smoothing window applied with the Savitsky-Golay filter. If None is passed (default), the window size will be two times the sampling rate. (Thus, covering 3 values.) If you are not very well knowing what you are doing - do not change that value. Broader window sizes caused unexpected results during testing phase. |
The function flags breaks (jumps/drops) by evaluating the derivatives of a time series.
A value $`x_k`$ of a data series $`x`$, is flagged a break, if:
1. $`x_k`$ represents a sufficient absolute jump in the course of data values:
* $`|x_k - x_{k-1}| >`$ `abs_change_min`
2. $`x_k`$ represents a sufficient relative jump in the course of data values:
3. Let $`X_k`$ be the set of all values that lie within a `first_der_window_range` range around $`x_k`$. Then, for its arithmetic mean $`\bar{X_k}`$, following equation has to hold:
