Programmer Guide/Command Reference/EVAL/smooth: Difference between revisions
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:;<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 smoothing function is selected by the argument ''type''. The smoothed value ''xs''[i] is computed from the data values ''x''[i-m] to ''x''[i+m]. | The smoothing function is selected by the argument ''type''. 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>x+y</math> | |||
{|class="einrahmen" | {|class="einrahmen" | ||
!''type'' !! smoothing algorithm !! ''xs''[i] = | !''type'' !! smoothing algorithm !! ''xs''[i] = | ||
| Line 13: | Line 14: | ||
|'''0''' | |'''0''' | ||
|average | |average | ||
|(''x''[i-''m'']+''x''[i-''m''+1 | |(''x''[i-''m'']+''x''[i-''m''+1]+..+''x''[i]+..+''x''[i+''m''-1]+ x[i+''m'']) / (2*''m''+1) | ||
|- | |- | ||
|'''0''' | |'''0''' | ||
|average with | |average with reciprocal weights | ||
|(''x''[i-''m'']/m + .. + x[i] + .. + x[i+''m'']) / (2*''m''+1) | |(''x''[i-''m'']/(m+1)''x''[i-''m''+1]/m+..+''x''[i]+..+''x''[i+''m''-1]/m+ x[i+''m'']/(m+1)) / (1 + 2*''m''+1) | ||
|} | |} | ||
;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 13:30, 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)
- soutput step size; 0 < s <=
nrow(x)/2(default=1)
- Description
The smoothing function is selected by the argument type. 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:
| type | smoothing algorithm | xs[i] = |
|---|---|---|
| 0 | average | (x[i-m]+x[i-m+1]+..+x[i]+..+x[i+m-1]+ x[i+m]) / (2*m+1) |
| 0 | average with reciprocal weights | (x[i-m]/(m+1)x[i-m+1]/m+..+x[i]+..+x[i+m-1]/m+ x[i+m]/(m+1)) / (1 + 2*m+1) |
- 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.
