ChartDirector Ver 3.0 (Python Edition)

General Curve Fitting




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.

Source Code Listing

[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")