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NAG Toolbox: nag_smooth_data_runningmedian (g10ca)

Purpose

nag_smooth_data_runningmedian (g10ca) computes a smoothed data sequence using running median smoothers.

Syntax

[smooth, rough, ifail] = g10ca(itype, y, 'n', n)
[smooth, rough, ifail] = nag_smooth_data_runningmedian(itype, y, 'n', n)

Description

Given a sequence of nn observations recorded at equally spaced intervals, nag_smooth_data_runningmedian (g10ca) fits a smooth curve through the data using one of two smoothers. The two smoothers are based on the use of running medians and averages to summarise overlapping segments. The fit and the residuals are called the smooth and the rough respectively. They obey the following:
Data = Smooth + Rough.
Data=Smooth+Rough.
The two smoothers are:
  1. 4253H,twice consisting of a running median of 44, then 22, then 55, then 33 followed by hanning. Hanning is a running weighted average, the weights being 1 / 41/4, 1 / 21/2 and 1 / 41/4. 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.
  2. 3RSSH,twice consisting of a running median of 33, two splitting operations named S to improve the smooth sequence, each of which is followed by a running median of 33, 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.

References

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

Parameters

Compulsory Input Parameters

1:     itype – int64int32nag_int scalar
Specifies the method to be used.
  • If itype = 0itype=0, 4253H,twice is used.
  • If itype = 1itype=1, 3RSSH,twice is used.
Constraint: itype = 0itype=0 or 11.
2:     y(n) – double array
n, the dimension of the array, must satisfy the constraint n > 6n>6.
The sample observations.

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The dimension of the array y.
nn, the number of observations.
Constraint: n > 6n>6.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

1:     smooth(n) – double array
Contains the smooth.
2:     rough(n) – double array
Contains the rough.
3:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry,itype < 0itype<0,
oritype > 1itype>1.
  ifail = 2ifail=2
On entry,n6n6.

Accuracy

Not applicable.

Further Comments

Alternative methods of smoothing include the use of splines; see nag_smooth_fit_spline (g10ab) and nag_smooth_fit_spline_parest (g10ac).

Example

function nag_smooth_data_runningmedian_example
itype = int64(1);
y = [569;
     416;
     422;
     565;
     484;
     520;
     573;
     518;
     501;
     505;
     468;
     382;
     310;
     334;
     359;
     372;
     439;
     446;
     349;
     395;
     461;
     511;
     583;
     590;
     620;
     578;
     534;
     631;
     600;
     438;
     516;
     534;
     467;
     457;
     392;
     467;
     500;
     493;
     410;
     412;
     416;
     403;
     422;
     459;
     467;
     512;
     534;
     552;
     545];
[smooth, rough, ifail] = nag_smooth_data_runningmedian(itype, y)
 

smooth =

  416.0000
  416.0000
  431.5000
  473.0000
  509.5000
  520.6875
  521.5625
  518.0000
  510.0000
  496.5000
  455.2500
  387.5000
  339.7500
  334.9375
  353.9375
  376.1250
  392.2500
  396.2500
  403.0000
  427.2500
  461.3750
  513.3125
  567.5625
  590.0000
  593.5000
  595.2500
  590.9375
  566.8125
  531.5000
  516.0000
  516.0000
  501.8750
  473.6250
  457.0000
  452.0000
  440.1250
  421.3750
  412.0000
  412.0000
  412.0000
  411.0625
  410.6875
  422.0000
  446.6250
  476.3750
  509.0000
  534.0000
  545.0000
  547.7500


rough =

  153.0000
         0
   -9.5000
   92.0000
  -25.5000
   -0.6875
   51.4375
         0
   -9.0000
    8.5000
   12.7500
   -5.5000
  -29.7500
   -0.9375
    5.0625
   -4.1250
   46.7500
   49.7500
  -54.0000
  -32.2500
   -0.3750
   -2.3125
   15.4375
         0
   26.5000
  -17.2500
  -56.9375
   64.1875
   68.5000
  -78.0000
         0
   32.1250
   -6.6250
         0
  -60.0000
   26.8750
   78.6250
   81.0000
   -2.0000
         0
    4.9375
   -7.6875
         0
   12.3750
   -9.3750
    3.0000
         0
    7.0000
   -2.7500


ifail =

                    0


function g10ca_example
itype = int64(1);
y = [569;
     416;
     422;
     565;
     484;
     520;
     573;
     518;
     501;
     505;
     468;
     382;
     310;
     334;
     359;
     372;
     439;
     446;
     349;
     395;
     461;
     511;
     583;
     590;
     620;
     578;
     534;
     631;
     600;
     438;
     516;
     534;
     467;
     457;
     392;
     467;
     500;
     493;
     410;
     412;
     416;
     403;
     422;
     459;
     467;
     512;
     534;
     552;
     545];
[smooth, rough, ifail] = g10ca(itype, y)
 

smooth =

  416.0000
  416.0000
  431.5000
  473.0000
  509.5000
  520.6875
  521.5625
  518.0000
  510.0000
  496.5000
  455.2500
  387.5000
  339.7500
  334.9375
  353.9375
  376.1250
  392.2500
  396.2500
  403.0000
  427.2500
  461.3750
  513.3125
  567.5625
  590.0000
  593.5000
  595.2500
  590.9375
  566.8125
  531.5000
  516.0000
  516.0000
  501.8750
  473.6250
  457.0000
  452.0000
  440.1250
  421.3750
  412.0000
  412.0000
  412.0000
  411.0625
  410.6875
  422.0000
  446.6250
  476.3750
  509.0000
  534.0000
  545.0000
  547.7500


rough =

  153.0000
         0
   -9.5000
   92.0000
  -25.5000
   -0.6875
   51.4375
         0
   -9.0000
    8.5000
   12.7500
   -5.5000
  -29.7500
   -0.9375
    5.0625
   -4.1250
   46.7500
   49.7500
  -54.0000
  -32.2500
   -0.3750
   -2.3125
   15.4375
         0
   26.5000
  -17.2500
  -56.9375
   64.1875
   68.5000
  -78.0000
         0
   32.1250
   -6.6250
         0
  -60.0000
   26.8750
   78.6250
   81.0000
   -2.0000
         0
    4.9375
   -7.6875
         0
   12.3750
   -9.3750
    3.0000
         0
    7.0000
   -2.7500


ifail =

                    0



PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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