In linear regression, the underlying relationship among the data points is assumed to be a straight line.
However, in many applications, the underlying relationship cannot be assumed to be a straight. It can be quadratic, cubic, exponential, logarithmic, guassian, sinusoidal, etc. In many cases, the underlying relationship is unknown.
To solve this kind of problems, ChartDirector supports a general curve fitting algorithm known as LOWESS using
ArrayMath.lowess and
ArrayMath.lowess2.
LOWESS works by assuming a small segment of any curve can be approximated by a straight line. For each data point, LOWESS performs a weighted linear regression using nearby points. It then adjusts the data point using the result of the linear regression. The adjusted data points should form a smooth curve reflecting the underlying relationship. For further details, please refer to
ArrayMath.lowess.
In this example, the adjusted data points are joined together with a spline layer using
XYChart.addSplineLayer.
[File: pythondemo/curvefitting.py] (The CGI version is available as "pythondemo_cgi/curvefitting.py".)
#!/usr/bin/python
from pychartdir import *
#Use random table to generate a random series. The random table is set to 1 col
#x 51 rows, with 9 as the seed
rantable = RanTable(9, 1, 51)
#Set the 1st column to start from 100, with changes between rows from -5 to +5
rantable.setCol(0, 100, -5, 5)
#Get the 1st column of the random table as the data set
data = rantable.getCol(0)
#Create a XYChart object of size 600 x 300 pixels
c = XYChart(600, 300)
#Set the plotarea at (50, 35) and of size 500 x 240 pixels. Enable both the
#horizontal and vertical grids by setting their colors to grey (0xc0c0c0)
c.setPlotArea(50, 35, 500, 240).setGridColor(0xc0c0c0, 0xc0c0c0)
#Add a title to the chart using 18 point Times Bold Itatic font.
c.addTitle("LOWESS Generic Curve Fitting Algorithm", "timesbi.ttf", 18)
#Set the y axis line width to 3 pixels
c.yAxis().setWidth(3)
#Add a title to the x axis using 12 pts Arial Bold Italic font
c.xAxis().setTitle("Server Load (TPS)", "arialbi.ttf", 12)
#Set the x axis line width to 3 pixels
c.xAxis().setWidth(3)
#Set the x axis scale from 0 - 50, with major tick every 5 units and minor tick
#every 1 unit
c.xAxis().setLinearScale(0, 50, 5, 1)
#Add a blue layer to the chart
layer = c.addLineLayer2()
#Add a red (0x80ff0000) data set to the chart with square symbols
layer.addDataSet(data, 0x80ff0000).setDataSymbol(SquareSymbol)
#Set the line width to 2 pixels
layer.setLineWidth(2)
#Use lowess for curve fitting, and plot the fitted data using a spline layer
#with line width set to 3 pixels
c.addSplineLayer(ArrayMath(data).lowess().result(), 0xff).setLineWidth(3)
#Set zero affinity to 0 to make sure the line is displayed in the most detail
#scale
c.yAxis().setAutoScale(0, 0, 0)
#output the chart
c.makeChart("curvefitting.png")
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