Programmer Guide/Command Reference/EVAL/smooth

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:

x s [ i ] = ∑ j = − m m x [ i + j ] . w [ j ] ∑ j = − m m w [ j ] {\displaystyle xs[i]={\frac {\sum _{j=-m}^{m}{x[i+j].w[j]}}{\sum _{j=-m}^{m}{w[j]}}}} $xs[i]={\frac {\sum _{j=-m}^{m}{x[i+j].w[j]}}{\sum _{j=-m}^{m}{w[j]}}}$

The weights w[i] are selected by the argument type

type	weights
0	w [ j ] = 1 {\displaystyle w[j]=1} $w[j]=1$
1	w [ j ] = 1 | j | + 1 {\displaystyle w[j]={\frac {1}{|j|+1}}} $w[j]={\frac {1}{|j|+1}}$

Result

A vector r with nrow(x)/s elements. The value r[j] is set to the value xs[j*s] of the smoothed data vector.