joptima

Class ChiSquaredFitter2D

java.lang.Object

joptima.Fitter

joptima.ChiSquaredFitter2D

All Implemented Interfaces:

Function, Minimizable

public class ChiSquaredFitter2D
extends Fitter

χ² fitter. This class can be passed to a Minimizer to minimize χ² of a sum of one or more functions fit to the given two-dimensional data set. Error bars may be provided for the data points if the data has compounded errors that are Gaussian. sqrt(z) errors are assumed otherwise.

Note that the usual two-dimensional matrix of values is passed to this function unfolded into a single array, i.e. the (x[i], y[i], z[i]) tuple for an m by n histogram where z = f(x, y) will have indices running from 0 through m * n - 1.

A typical usage of this class would go as follows:

   // The data points.
   double[] x = new double[]{  1,   2,   3,
                               1,   2,   3,
                               1,   2,   3};
   double[] y = new double[]{  1,   1,   1,
                               2,   2,   2,
                               3,   3,   3};
   double[] z = new double[]{1.1, 4.0, 8.7,
                             3.9,  16,  24,
                             9.2,  22,  38};

   // The Function to fit to the data points.
   Function2D f = new Sum2D(new Quadratic(), new Quadratic);

   ChiSquaredFitter2D fitter = new ChiSquaredFitter2D();
   fitter.setData(x, y, z);
   fitter.addFunction(f);
   Minimizer.minimize(fitter);

   // At this point, if the fit converged, the Function f will have
   // its Parameters set to the optimal values.
 

Constructor Summary

Constructors

Constructor and Description
ChiSquaredFitter2D() Constructor.
ChiSquaredFitter2D(double[] x, double[] y, double[] z) Constructor.
ChiSquaredFitter2D(double[] x, double[] y, double[] z, double[] errors) Constructor.
ChiSquaredFitter2D(double[] x, double[] y, double[] z, double[] errors, Function f) Constructor.
ChiSquaredFitter2D(double[] x, double[] y, double[] z, Function f) Constructor.

Method Summary

Modifier and Type	Method and Description
void	addFunction(Function f) Invalidates this signature of this method on the superclass.
void	addFunction(Function2D f) Adds a Function2D to this Fitter.
void	addFunction1Dx(Function f) Adds a one-dimensional Function to this Fitter.
void	addFunction1Dy(Function f) Adds a one-dimensional Function to this Fitter.
double	calculate() Calculates the χ² given parameter values set by a Minimizer using reflection.
void	setData(double[] x, double[] y, double[] z) Fit the sum of functions to this set of points.
void	setData(double[] x, double[] y, double[] z, double[] errors) Fit the sum of functions to this set of points.

Methods inherited from class joptima.Fitter

calculate, getName, getParameters, removeAllFunctions, setName

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ChiSquaredFitter2D

public ChiSquaredFitter2D()

Constructor.

ChiSquaredFitter2D

public ChiSquaredFitter2D(double[] x,
                          double[] y,
                          double[] z)

Constructor. Assumes sqrt(z) errors.

Parameters:

x - the x coordinates of points

y - the y coordinates of points

z - the z coordinates of points

ChiSquaredFitter2D

public ChiSquaredFitter2D(double[] x,
                          double[] y,
                          double[] z,
                          double[] errors)

Constructor.

Parameters:

x - the x coordinates of points

y - the y coordinates of points

z - the z coordinates of points

errors - the error bars on z coordinates of points

ChiSquaredFitter2D

public ChiSquaredFitter2D(double[] x,
                          double[] y,
                          double[] z,
                          Function f)

Constructor. Assumes sqrt(y) errors.

Parameters:

x - the x coordinates of points

y - the y coordinates of points

z - the z coordinates of points

f - the Function to fit to the given set of points

ChiSquaredFitter2D

public ChiSquaredFitter2D(double[] x,
                          double[] y,
                          double[] z,
                          double[] errors,
                          Function f)

Constructor.

Parameters:

x - the x coordinates of points

y - the y coordinates of points

z - the z coordinates of points

errors - the error bars on z coordinates of points

f - the Function to fit to the given set of points

Method Detail

addFunction

public void addFunction(Function f)

Invalidates this signature of this method on the superclass. This form throws an UnsupportedOperationException() because its meaning is ambiguous for a 2D fitter. Use addFunction(joptima.Function) instead.

Overrides:

addFunction in class Fitter

addFunction

public void addFunction(Function2D f)

Adds a Function2D to this Fitter.

addFunction1Dx

public void addFunction1Dx(Function f)

Adds a one-dimensional Function to this Fitter. This form makes 2D extension of the given function along the y-axis, i.e. makes a Sum2D(function, null).

Parameters:

f - the one-dimensional function to extend along the y-axis

addFunction1Dy

public void addFunction1Dy(Function f)

Adds a one-dimensional Function to this Fitter. This form makes 2D extension of the given function along the x-axis, i.e. makes a Sum2D(null, function).

Parameters:

f - the one-dimensional function to extend along the x-axis

setData

public void setData(double[] x,
                    double[] y,
                    double[] z)

Fit the sum of functions to this set of points. Assumes sqrt(y) error bars.

Parameters:

x - the x coordinates of points

y - the y coordinates of points

z - the z coordinates of points

setData

public void setData(double[] x,
                    double[] y,
                    double[] z,
                    double[] errors)

Fit the sum of functions to this set of points.

Parameters:

x - the x coordinates of points

y - the y coordinates of points

z - the z coordinates of points

errors - the error bars on y coordinates of points

calculate

public double calculate()

Calculates the χ² given parameter values set by a Minimizer using reflection. The formula is:

   for each point in the data set {
     f = 0
     for each Function {
       f += Function.calculate(double)(x[point], y[point])
     }
     χ² += (y[point] - f)² / error[point]²
   }