Programmer Guide/Command Reference/EVAL/smooth: Difference between revisions
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{{DISPLAYTITLE:{{SUBPAGENAME}}}} | {{DISPLAYTITLE:{{SUBPAGENAME}}}} | ||
Apply | Apply smoothing to the vector or matrix <var>x</var>. | ||
;Usage:<code>smooth(<var>x</var> {, <var>type</var>=0 {, <var>m</var>=1 {, <var>s</var>=1}}})</code> | ;Usage:<code>smooth(<var>x</var> {, <var>type</var>=0 {, <var>m</var>=1 {, <var>s</var>=1}}})</code> | ||
:;<var>x</var>:data vector | :;<var>x</var>:data vector or matrix | ||
:;<var>m</var>:smoothing length; 0 < ''m'' | :;<var>m</var>:smoothing length; 0 < ''m'' ≤ <code>nrow(''x'')/2</code> (default=1) | ||
:;<var>type</var>:selects the | :;<var>type</var>:selects the weighting coefficients (default=0) | ||
:;<var>s</var>:output step size; 0 < ''s'' | :;<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 weighting coefficients ''w''[i] depend on the value of the argument ''type'' | ||
:The | ::{|class="einrahmen" | ||
{|class="einrahmen" | !''type'' !! ''w''[j] !! | ||
!''type'' !! | |||
|- | |- | ||
|'''0''' | | |'''0''' ||1 ||average | ||
|- | |- | ||
|''' | |'''1''' |||<nowiki>1 / (|j|+1)</nowiki> ||''distance'' weighted average | ||
| | |||
| | |||
| | |||
|'' | |||
|} | |} | ||
;Result: A vector r with <code>nrow(''x'')/s</code> | ;Result: A vector or matrix ''r'' with <code>nrow(''x'')/s</code> rows and the same number of clumns as <code>''x''</code>. The value ''r''[j] is set to the value ''xs''[j*s] of the smoothed data vector. | ||
;See also: [[../optmm|optmm]] | |||
[[../#Functions|<function list>]] | |||
Latest revision as of 12:09, 12 May 2017
Apply smoothing to the vector or matrix x.
- Usage
smooth(x {, type=0 {, m=1 {, s=1}}})- x
- data vector or matrix
- m
- smoothing length; 0 < m ≤
nrow(x)/2(default=1) - type
- selects the weighting coefficients (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:
- The weighting coefficients w[i] depend on the value of the argument type
![{\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)
type w[j] 0 1 average 1 1 / (|j|+1) distance weighted average
- Result
- A vector or matrix r with
nrow(x)/srows and the same number of clumns asx. The value r[j] is set to the value xs[j*s] of the smoothed data vector. - See also
- optmm
