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 for all  j {\displaystyle w[j]={\begin{cases}1&{\mbox{for all }}j\end{cases}}} $w[j]={\begin{cases}1&{\mbox{for all }}j\end{cases}}$
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)/s elements. The value r[j] is set to the value xs[j*s] of the smoothed data vector.