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CurveFitting

  

Lowess

  

produces lowess smoothed functions

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Lowess(xydata, opts)

Lowess(xdata, ydata, opts)

Parameters

xydata

-

list, listlist, Array, DataFrame, or Matrix of the form x0,1,x0,2,,x0,M1,y0,x1,1,x1,2,,x1,M1,y1,,xN,1,xN,2,,xN,M1,yN; data points of M dimensions

xdata

-

list, listlist, Array, DataSeries, or Matrix of the form x0,1,x0,2,,x0,M1,x1,1,x1,2,,x1,M1,,xN,1,xN,2,,xN,M1; independent values of data points of M dimensions

ydata

-

list, Array, DataSeries, or Vector of the form y1,y2,,yN; dependent values of data points

opts

-

(optional) one or more equations of the form fitorder=n, bandwidth=r, or iters=nonnegint

Description

• 

The Lowess command creates a function whose values represent the result of the lowess data smoothing algorithm applied to the input data.

• 

This command calls Statistics[Lowess]. See its help page for more examples and a detailed description.

Examples

withStatistics:

Create a data sample and apply to it some error.

XSampleUniform0,π,200

_rtable18446884385106089134

(1)

YerrorSampleNormal0,0.1,200

_rtable18446884384987179838

(2)

Ymapsin,X+Yerror

_rtable18446884384987168030

(3)

Create the function whose graph is the smoothed curve.

LCurveFitting:-LowessX,Y,fitorder=1,bandwidth=0.3:

Plot the data sample, smoothed curve, and the region between the x-axis and the curve for π8x3π8.

PScatterPlotX,Y

QplotLx,x=0..π

Rplots:-shadebetweenLx,0,x=π8..3π8,showboundary=false,positiveonly

plots:-displayP,Q,R

Find the area of the shaded region.

intL,π8..3π8,numeric,ε=0.01

0.538403465288975

(4)

And find the maximum.

Optimization:-MaximizeL,mapunapply,x,xπ,x,optimalitytolerance=0.001

1.00180213049318700,1.5815245901456092

(5)

Compatibility

• 

The CurveFitting[Lowess] command was introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

Statistics[Lowess]