ChartDirector Ver 4.1 (PHP Edition Edition)

General Curve Fitting




This example demonstrates the LOWESS general purpose curve fitting that is built into ChartDirector.

In linear regression, the relationship among the x and y coordinates are assumed to be linear.

However, in many applications, that relationship cannot be assumed to be linear. It can be polynomial, exponential, logarithmic, gaussian, sinusoidal, etc. In many cases, the relationship is not even known.

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 lie on the smooth curve reflecting the underlying relationship. For further details, please refer to ArrayMath.lowess.

The LOWESS algorithm only adjusts the points to smoothen them. They still need to be joined together. In this example, the adjusted points are joined with a spline layer using XYChart.addSplineLayer.

Source Code Listing

[File: phpdemo/curvefitting.php]
<?php
require_once("../lib/phpchartdir.php");

# 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 = 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
$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(), 0x0000ff);
$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));
?>