ChartDirector Ver 3.0 (Perl 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: perldemo/curvefitting.pl] (The CGI version is available as "perldemo_cgi/curvefitting.pl".)
#!/usr/bin/perl use perlchartdir; #Use random table to generate a random series. The random table is set to 1 col #x 51 rows, with 9 as the seed my $rantable = new 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 my $data = $rantable->getCol(0); #Create a XYChart object of size 600 x 300 pixels my $c = new 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 my $layer = $c->addLineLayer2(); #Add a red (0x80ff0000) data set to the chart with square symbols $layer->addDataSet($data, 0x80ff0000)->setDataSymbol($perlchartdir::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 $c->addSplineLayer(new ArrayMath($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")