/**
* Utility to facilitate fitting data plotted in JFreeChart Provide data in JFReeChart format
* (XYSeries), and retrieve univariate function parameters that best fit (using least squares) the
* data. All data points will be weighted equally.
*
* <p>TODO: investigate whether weighting (possibly automatic weighting) can improve accuracy
*
* @param data xy series in JFReeChart format
* @param type one of the Fitter.FunctionType predefined functions
* @param guess initial guess for the fit. The number and meaning of these parameters depends on
* the FunctionType. Implemented: Gaussian: 0: Normalization, 1: Mean 2: Sigma
* @return array with parameters, whose meaning depends on the FunctionType. Use the function
* getXYSeries to retrieve the XYDataset predicted by this fit
*/
public static double[] fit(XYSeries data, FunctionType type, double[] guess) {
if (type == FunctionType.NoFit) {
return null;
}
// create the commons math data object from the JFreeChart data object
final WeightedObservedPoints obs = new WeightedObservedPoints();
for (int i = 0; i < data.getItemCount(); i++) {
obs.add(1.0, data.getX(i).doubleValue(), data.getY(i).doubleValue());
}
double[] result = null;
switch (type) {
case Pol1:
final PolynomialCurveFitter fitter1 = PolynomialCurveFitter.create(1);
result = fitter1.fit(obs.toList());
break;
case Pol2:
final PolynomialCurveFitter fitter2 = PolynomialCurveFitter.create(2);
result = fitter2.fit(obs.toList());
break;
case Pol3:
final PolynomialCurveFitter fitter3 = PolynomialCurveFitter.create(3);
result = fitter3.fit(obs.toList());
break;
case Gaussian:
final GaussianWithOffsetCurveFitter gf = GaussianWithOffsetCurveFitter.create();
if (guess != null) {
gf.withStartPoint(guess);
}
result = gf.fit(obs.toList());
}
return result;
}
/**
* Returns the average of the ys in a XYSeries
*
* @param data input data
* @return y average
*/
public static double getYAvg(XYSeries data) {
double avg = 0;
for (int i = 0; i < data.getItemCount(); i++) {
avg += data.getY(i).doubleValue();
}
avg = avg / data.getItemCount();
return avg;
}
/**
* Returns <code>true</code> if all the y-values for the specified x-value are <code>null</code>
* and <code>false</code> otherwise.
*
* @param x the x-value.
* @return A boolean.
*/
protected boolean canPrune(Number x) {
for (int s = 0; s < this.data.size(); s++) {
XYSeries series = (XYSeries) this.data.get(s);
if (series.getY(series.indexOf(x)) != null) {
return false;
}
}
return true;
}
/**
* Returns the value (the ordianate) of a point given its abscissa.
*
* @param abscissa abscissa of the considered point
* @return return the value of the considered point (returns -1 if there is no points with the
* given abscissa in the signal).
*/
public double getValueOfAbscissa(double abscissa) {
int isInSeries = data.indexOf(abscissa);
if (isInSeries >= 0) {
return data.getY(isInSeries).doubleValue();
} else {
System.out.println("There is no point whith the abscissa " + abscissa + " in the signal.\n");
return -1;
}
}
/**
* Finds the x value corresponding to the maximum function value within the range of the provided
* data set.
*
* @param type one of the Fitter.FunctionType predefined functions
* @param parms parameters describing the function. These need to match the selected function or
* an IllegalArgumentEception will be thrown
* @param data JFreeChart series, used to bracket the range in which the maximum will be found
* @return x value corresponding to the maximum function value
*/
public static double getXofMaxY(XYSeries data, FunctionType type, double[] parms) {
double xAtMax = 0.0;
double minX = data.getMinX();
double maxX = data.getMaxX();
switch (type) {
case NoFit:
// find the position in data with the highest y value
double highestScore = data.getY(0).doubleValue();
int highestIndex = 0;
for (int i = 1; i < data.getItemCount(); i++) {
double newVal = data.getY(i).doubleValue();
if (newVal > highestScore) {
highestScore = newVal;
highestIndex = i;
}
}
return data.getX(highestIndex).doubleValue();
case Pol1:
case Pol2:
case Pol3:
checkParms(type, parms);
PolynomialFunction derivativePolFunction =
(new PolynomialFunction(parms)).polynomialDerivative();
final double relativeAccuracy = 1.0e-12;
final double absoluteAccuracy = 1.0e-8;
final int maxOrder = 5;
UnivariateSolver solver =
new BracketingNthOrderBrentSolver(relativeAccuracy, absoluteAccuracy, maxOrder);
xAtMax = solver.solve(100, derivativePolFunction, minX, maxX);
break;
case Gaussian:
// for a Gaussian we can take the mean and be sure it is the maximum
// note that this may be outside our range of X values, but
// this will be caught by our sanity checks below
xAtMax = parms[1];
}
// sanity checks
if (xAtMax > maxX) xAtMax = maxX;
if (xAtMax < minX) xAtMax = minX;
return xAtMax;
}
/**
* Displays a signal (using the JFreeChart package).
*
* @param useChart if set to true, the signal is displaied as a bar chart (this is used for
* histograms).
*/
public void display(boolean useChart) {
JFreeChart chart;
int nbSamples = getNbSamples();
if (useChart) {
String[] categories = new String[nbSamples];
for (int i = 0; i < nbSamples; i++) {
categories[i] = data.getX(i).toString();
}
String[] categoryNames = {"Histogram"};
double[][] categoryData = new double[1][nbSamples];
for (int i = 0; i < nbSamples; i++) {
categoryData[0][i] = data.getY(i).doubleValue();
}
CategoryDataset categoryDataset =
DatasetUtilities.createCategoryDataset(categoryNames, categories, categoryData);
chart =
ChartFactory.createBarChart(
"Histogram", // Title
"Data Value", // X axis label
"Number of Elements", // Y axis label
categoryDataset, // dataset
PlotOrientation.VERTICAL, // orientation
true, // legends
true, // tool tips
true);
} else {
XYDataset xyDataSet = new XYSeriesCollection(this.data);
chart =
ChartFactory.createXYLineChart(
"Example Dataset", // Title
"Abscissa", // X axis label
"Ordinate", // Y axis label
xyDataSet, // dataset
PlotOrientation.VERTICAL, // orientation
true, // legends
true, // tool tips
true); // urls
XYPlot plot = (XYPlot) chart.getPlot();
XYItemRenderer r = plot.getRenderer();
if (r instanceof XYLineAndShapeRenderer) {
XYLineAndShapeRenderer renderer = (XYLineAndShapeRenderer) r;
renderer.setSeriesShapesVisible(0, true);
renderer.setSeriesShapesFilled(0, true);
}
}
ChartFrame frame = new ChartFrame("Frame Title", chart);
frame.setVisible(true);
frame.setSize(512, 512);
}
/**
* Calculates a measure for the goodness of fit as defined here:
* http://en.wikipedia.org/wiki/Coefficient_of_determination R^2 = 1 - (SSres/SStot) where SSres =
* SUM(i) (yi - fi)^2 end SStot = SUM(i) (yi - yavg)^2
*
* @param data input data (raw data that were fitted
* @param type function type used for fitting
* @param parms function parameters derived in the fit
* @return
*/
public static double getRSquare(XYSeries data, FunctionType type, double[] parms) {
// calculate SStot
double yAvg = getYAvg(data);
double ssTot = 0.0;
for (int i = 0; i < data.getItemCount(); i++) {
double y = data.getY(i).doubleValue();
ssTot += (y - yAvg) * (y - yAvg);
}
// calculate SSres
double ssRes = 0.0;
for (int i = 0; i < data.getItemCount(); i++) {
double y = data.getY(i).doubleValue();
double f = getFunctionValue(data.getX(i).doubleValue(), type, parms);
ssRes += (y - f) * (y - f);
}
return 1.0 - (ssRes / ssTot);
}
/**
* Save the current signal in the file named filename.
*
* @param filename name of the file where to store the signal.
*/
public void save(String filename) {
int nbSamples = this.getNbSamples();
String fileContent = "% Signal from Computer Exercise\n";
fileContent += "#" + nbSamples + "\n";
fileContent += "\n";
for (int i = 0; i < nbSamples; i++) {
fileContent += data.getX(i) + "\t \t" + data.getY(i) + "\n";
}
fileContent += "\n";
try {
BufferedWriter out = new BufferedWriter(new FileWriter(filename));
out.write(fileContent);
out.close();
} catch (IOException e) {
System.out.println("Could not save file " + filename + " sorry...\n");
}
}
/**
* Gives the entered value at the index index. Caution ! No check is performed on the value of the
* index (this method may throw an outofbound exception).
*
* @param index of the point (abscissa, value)
* @return the corresponding value.
*/
public double getValueOfIndex(int index) {
return data.getY(index).doubleValue();
}