org.mathIT.approximation

Class Regression

java.lang.Object

org.mathIT.approximation.Regression

public class Regression
extends Object

This class enables to generate objects from data points (t, y) such as time series and to compute regression polynomials from them. There are multiple data series possible, i.e., y is an array.

Version:

1.1

Author:

Andreas de Vries

Constructor Summary

Constructors

Constructor and Description
Regression(double[] t, double[][] y) constructor for time series with unknown measurement errors.
Regression(double[] t, double[][] y, double[][] deltaY) constructor for time series with known measurement errors.

Method Summary

Modifier and Type	Method and Description
void	computeCoefficients(int rMax) polynomial regression for given data points
double[]	getT() Returns the t-values of the data points (t, y).
double[][]	getY() Returns the array of y-values of the data points (t, y).
double[][]	polynomial(double t, double chi2, double p, int nr, int nf) computes the value eta(t) on the regression curve at t and its distance from the confidence limits, if the measurement errors are unknown.
double[][]	polynomial(double t, double p, int nr) computes the value on the regression curve at t and its distance from the confidence limits, if the measurement errors are known.
double[]	polynomial(double t, int nr) computes the value on the regression curve at t.

Methods inherited from class java.lang.Object

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

Constructor Detail

Regression

public Regression(double[] t,
                  double[][] y)

constructor for time series with unknown measurement errors.

Parameters:

t - the t-values of the data points (t, y)

y - an array of the y-values of the data points (t, y)

Regression

public Regression(double[] t,
                  double[][] y,
                  double[][] deltaY)

constructor for time series with known measurement errors.

Parameters:

t - the t-values of the data points (t, y)

y - an array of the y-values of the data points (t, y)

deltaY - the measurement errors

Method Detail

getT

public double[] getT()

Returns the t-values of the data points (t, y).

Returns:

the t-values of the data points (t, y).

getY

public double[][] getY()

Returns the array of y-values of the data points (t, y).

Returns:

the array of y-values of the data points (t, y).

computeCoefficients

public void computeCoefficients(int rMax)

polynomial regression for given data points.

y(t) = x₀ f₀(t) + x₁ f₁(t) + ... + x_r f_r(t),

Parameters:

rMax - maximal number of parameters

polynomial

public double[] polynomial(double t,
                           int nr)

computes the value on the regression curve at t. It does not return its distance from the confidence limit, so it does not matter whether the measurement errors are known or not.

Parameters:

t - value of the control variable

nr - the degree of the regression polynomial

Returns:

regression value, for each y-data row

polynomial

public double[][] polynomial(double t,
                             double p,
                             int nr)

computes the value on the regression curve at t and its distance from the confidence limits, if the measurement errors are known.

Parameters:

t - value of the control variable

p - probability of the confidence limit

nr - number of parameters r in the polynomial

Returns:

for each y-data row, an array consisting of the regression value and its distance from the confidence limits

polynomial

public double[][] polynomial(double t,
                             double chi2,
                             double p,
                             int nr,
                             int nf)

computes the value eta(t) on the regression curve at t and its distance from the confidence limits, if the measurement errors are unknown. The distance of eta(t) from the confidence limits depends on chi2, the value of the least square fit for adjusting a polynomial of degree r-1 under the assumption that all measurement errors sigma_i = 1. It must be positive, chi2 %gt; 0.

Parameters:

t - value of the control variable

chi2 - value of the least square fit for adjusting a polynomial of degree r-1

p - probability of the confidence limit

nr - number of parameters r in the polynomial

nf - number f = N - r of degrees of freedom

Returns:

for each y-data row, an array consisting of the regression value and its distance from the confidence limits