NAG Library Function Document
nag_running_median_smoother (g10cac) computes a smoothed data sequence using running median smoothers.
||nag_running_median_smoother (Nag_Smooth_Type smoother,
const double y,
Given a sequence of observations recorded at equally spaced intervals, nag_running_median_smoother (g10cac) fits a smooth curve through the data using one of two smoothers. They are based on the use of running medians and averages to summarize the overlapping segments. The fit is called the smooth, the residuals the rough and they obey the following:
Data = Smooth + Rough
The two smoothers are :
- 4253H, twice consisting of a running median of 4, then 2, then 5, then 3 followed by Hanning. Hanning is a running weighted average, the weights being 1/4, 1/2 and 1/4. The result of this smoothing is then reroughed by computing residuals, applying the same smoother to them and adding the result to the smooth of the first pass.
- 3RSSH, twice consisting of a running median of 3, two splitting operations named S to improve the smooth sequence, each of which is followed by a running median of 3, and finally Hanning. The end points are dealt with using the method described by Velleman and Hoaglin (1981). The full smoother 3RSSH, twice is produced by reroughing as described above.
The compound smoother 4253H, twice is recommended. The smoother 3RSSH, twice is popular when calculating by hand as it requires simpler computations and is included for comparison purposes.
Tukey J W (1977) Exploratory Data Analysis Addison–Wesley
Velleman P F and Hoaglin D C (1981) Applications, Basics, and Computing of Exploratory Data Analysis Duxbury Press, Boston, MA
smoother – Nag_Smooth_TypeInput
must specify the method to be used.
- 4253H, twice is used.
- 3RSSH, twice is used.
n – IntegerInput
On entry: the number, , of the observations.
If then the sequence is not long enough to carry out smoothing.
y[n] – const doubleInput
On entry: the sample observations.
smooth[n] – doubleOutput
On exit: contains the smooth.
rough[n] – doubleOutput
On exit: contains the rough.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument smoother
had an illegal value.
On entry, .
The example program reads in a sequence of 49 data taken from Tukey (1977)
, above. Results are obtained using the two smoothing methods described.
9.1 Program Text
Program Text (g10cace.c)
9.2 Program Data
Program Data (g10cace.d)
9.3 Program Results
Program Results (g10cace.r)