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: phpdemo/curvefitting.php".]
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 = 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)
$plotAreaObj = $c->setPlotArea(50, 35, 500, 240);
$plotAreaObj->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
$dataSetObj = $layer->addDataSet($data, 0x80ff0000);
$dataSetObj->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
$curve = new ArrayMath($data);
$curve->lowess();
$splineLayerObj = $c->addSplineLayer($curve->result(), 0xff);
$splineLayerObj->setLineWidth(3);
#Set zero affinity to 0 to make sure the line is displayed in the most detail
#scale
$c->yAxis->setAutoScale(0, 0, 0);
#output the chart
header("Content-type: image/png");
print($c->makeChart2(PNG));
?> |
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