Programmer Guide/Command Reference/EVAL/smooth: Difference between revisions
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:;<var>type</var>:selects the smoothing algorithm (default=0) | :;<var>type</var>:selects the smoothing algorithm (default=0) | ||
:;<var>s</var>:output step size; 0 < ''s'' <= <code>nrow(''x'')/2</code> (default=1) | :;<var>s</var>:output step size; 0 < ''s'' <= <code>nrow(''x'')/2</code> (default=1) | ||
;Description: | ;Description: The smoothed value ''xs''[i] is computed from the data values ''x''[i-m] to ''x''[i+m]. The general form of the smoothing function is: | ||
The smoothed value ''xs''[i] is computed from the data values ''x''[i-m] to ''x''[i+m]. The general form of the smoothing function is: | |||
:<math>xs[i] = \frac{ \sum_{j=-m}^m{x[i+j].w[j]} }{ \sum_{j=-m}^m{w[j]} }</math> | :<math>xs[i] = \frac{ \sum_{j=-m}^m{x[i+j].w[j]} }{ \sum_{j=-m}^m{w[j]} }</math> | ||
:The weights ''w''[i] are selected by the argument ''type'' | :The weights ''w''[i] are selected by the argument ''type'' | ||
{|class="einrahmen" | {|class="einrahmen" | ||
!''type'' !! ''w''[j] | !''type'' !! ''w''[j] !! | ||
|- | |- | ||
|'''0''' | |'''0''' ||1 ||average | ||
|1 | |||
|- | |- | ||
|'''1''' | |'''1''' |||<nowiki>1 / (|j|+1)</nowiki> ||reciprokal weighted average | ||
|<nowiki>1 / (|j|+1)</nowiki> | |||
|} | |} | ||
;Result: A vector r with <code>nrow(''x'')/s</code> elements. The value ''r''[j] is set to the value ''xs''[j*s] of the smoothed data vector. | ;Result: A vector r with <code>nrow(''x'')/s</code> elements. The value ''r''[j] is set to the value ''xs''[j*s] of the smoothed data vector. | ||
Revision as of 13:10, 13 April 2011
Apply a smoothing to the vector x.
- Usage
smooth(x {, type=0 {, m=1 {, s=1}}})- x
- data vector
- m
- smoothing length; 0 < m <=
nrow(x)/2(default=1) - type
- selects the smoothing algorithm (default=0)
- s
- output step size; 0 < s <=
nrow(x)/2(default=1)
- Description
- The smoothed value xs[i] is computed from the data values x[i-m] to x[i+m]. The general form of the smoothing function is:
![{\displaystyle xs[i]={\frac {\sum _{j=-m}^{m}{x[i+j].w[j]}}{\sum _{j=-m}^{m}{w[j]}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b702c94129d969d381ef19fc1bbb61284930a52)
- The weights w[i] are selected by the argument type
| type | w[j] | |
|---|---|---|
| 0 | 1 | average |
| 1 | 1 / (|j|+1) | reciprokal weighted average |
- Result
- A vector r with
nrow(x)/selements. The value r[j] is set to the value xs[j*s] of the smoothed data vector.
