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.
[The following project is available in "cppdemo/curvefitting".]
#include "chartdir.h"
int main(int argc, char *argv[])
{
//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 = 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
DoubleArray data = rantable->getCol(0);
//Create a XYChart object of size 600 x 300 pixels
XYChart *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
LineLayer *layer = c->addLineLayer();
//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(), 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");
//free up resources
delete rantable;
delete c;
return 0;
}
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