Module org.bzdev.math

Package org.bzdev.math

Class LeastSquaresFit.BSpline

java.lang.Object

org.bzdev.math.RealValuedFunctionVA

org.bzdev.math.RealValuedFunction

org.bzdev.math.LeastSquaresFit

org.bzdev.math.LeastSquaresFit.BSpline

All Implemented Interfaces:

DoubleUnaryOperator, RealValuedDomainOps, RealValuedFunctOps, RealValuedFunctVAOps, VADomainOps

Enclosing class:

LeastSquaresFit

public static class LeastSquaresFit.BSpline
extends LeastSquaresFit

Class providing a least squares fit using a BSpline. The spline can be adjusted by changing its degree and the number of control points it uses. One can optionally specify the either end of the spline or both is/are clamped, or that the spline is periodic. The default is an unclamped, non-periodic spline.

Nested Class Summary

Nested classes/interfaces inherited from class org.bzdev.math.LeastSquaresFit

LeastSquaresFit.BSpline, LeastSquaresFit.FunctionBasis, LeastSquaresFit.Linear, LeastSquaresFit.NonLinear, LeastSquaresFit.Polynomial

Field Summary

Fields inherited from class org.bzdev.math.RealValuedFunction

xFunction

Constructor Summary

Constructors

Constructor	Description
BSpline(int degree, int n, double[] x, double[] y)	Constructor specifying a B-spline's degree, number of control points, and a set of Y values for given X values.
BSpline(int degree, int n, double[] x, double[] y, double sigma)	Constructor specifying a B-spline's degree, number of control points, and a set of Y values for given X values, with a specified error for the Y values.
BSpline(int degree, int n, double[] x, double[] y, double[] sigma)	Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values and their standard deviations for given X values.
BSpline(int degree, int n, BSpline.Mode mode, double[] x, double[] y)	Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values for given X values.
BSpline(int degree, int n, BSpline.Mode mode, double[] x, double[] y, double sigma)	Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values for given X values, with a specified error for the Y values.
BSpline(int degree, int n, BSpline.Mode mode, double[] x, double[] y, double[] sigma)	Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values and their standard deviations for given X values.

Method Summary

Modifier and Type	Method	Description
double	covariance(double x1, double x2)	Compute the covariance for the y values associated with two data points.
protected void	createCovariance()	Create the covariance array.
double	derivAt(double arg)	Evaluate the function's first derivative.
protected LeastSquaresFit	getFit()	Get a copy of this least squares fit but without its parameters, degrees of freedom, chi square value, reduced chi square value, or covariance set.
double	secondDerivAt(double arg)	Evaluate the function's second derivative.
protected void	setParameters(double[] parameters)	Set the parameters array.
double	valueAt(double arg)	Call the function.

Methods inherited from class org.bzdev.math.LeastSquaresFit

chiSquare, chiSquare, getChiSquare, getCovarianceArray, getCovarianceMatrix, getCovarianceMatrix, getDegreesOfFreedom, getFunction, getNumberOfParameters, getParameters, getParameters, getParametersArray, getReducedChiSquare, getStat, setChiSquare, setCovariance, setDegreesOfFreedom, setReducedChiSquare, sumOfSquares

Methods inherited from class org.bzdev.math.RealValuedFunction

deriv, deriv, derivAt, domainMaxClosed, domainMaxClosed, domainMinClosed, domainMinClosed, getDomainMax, getDomainMax, getDomainMin, getDomainMin, isInDomain, isInDomain, secondDeriv, secondDerivAt, valueAt

Methods inherited from class org.bzdev.math.RealValuedFunctionVA

jacobian, jacobian, maxArgLength, minArgLength

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.bzdev.math.RealValuedFunctOps

andThen, andThen, applyAsDouble, compose, compose, maxArgLength, minArgLength

Constructor Details

BSpline

public BSpline(int degree,
 int n,
 double[] x,
 double[] y)

Constructor specifying a B-spline's degree, number of control points, and a set of Y values for given X values. The number of X,Y data points must be larger than the number of control points. A default mode (BSpline.Mode.UNCLAMPED) will be used.

Parameters:

degree - the degree of the B-spline that will be created

n - the number of control points

x - values in the domain of the spline

y - values in the range of the spline

BSpline

public BSpline(int degree,
 int n,
 BSpline.Mode mode,
 double[] x,
 double[] y)

Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values for given X values. The number of X,Y data points must be larger than the number of control points. If the mode argument is null, it must be cast to the type BSpline.Mode to a void a conflict with a constructor that uses three arrays of double.

Parameters:

degree - the degree of the B-spline that will be created

n - the number of control points

mode - the mode for the B-spline (either BSpline.Mode.UNCLAMPED, BSpline.Mode.CLAMPED, BSpline.Mode.CLAMPED_LEFT, BSpline.Mode.CLAMPED_RIGHT, or BSpline.Mode.PERIODIC); null for the default (BSpline.Mode.UNCLAMPED)

x - values in the domain of the spline

y - values in the range of the spline

BSpline

public BSpline(int degree,
 int n,
 double[] x,
 double[] y,
 double sigma)

Constructor specifying a B-spline's degree, number of control points, and a set of Y values for given X values, with a specified error for the Y values. The number of X,Y data points must be larger than the number of control points. A default mode (BSpline.Mode.UNCLAMPED) will be used.

Parameters:

degree - the degree of the B-spline that will be created

n - the number of control points

x - values in the domain of the spline

y - values in the range of the spline

sigma - the standard deviation for the Y values

BSpline

public BSpline(int degree,
 int n,
 BSpline.Mode mode,
 double[] x,
 double[] y,
 double sigma)

Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values for given X values, with a specified error for the Y values. The number of X,Y data points must be larger than the number of control points.

Parameters:

degree - the degree of the B-spline that will be created

n - the number of control points

mode - the mode for the B-spline (either BSpline.Mode.UNCLAMPED, BSpline.Mode.CLAMPED, BSpline.Mode.CLAMPED_LEFT, BSpline.Mode.CLAMPED_RIGHT, or BSpline.Mode.PERIODIC); null for the default (BSpline.Mode.UNCLAMPED).

x - values in the domain of the spline

y - values in the range of the spline

sigma - the standard deviation for the Y values

BSpline

public BSpline(int degree,
 int n,
 double[] x,
 double[] y,
 double[] sigma)

Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values and their standard deviations for given X values. The number of X,Y data points must be larger than the number of control points. A default mode (BSpline.Mode.UNCLAMPED) will be used.

Parameters:

degree - the degree of the B-spline that will be created

n - the number of control points

x - values in the domain of the spline

y - values in the range of the spline

sigma - the standard deviations for the values provided by the argument y

BSpline

public BSpline(int degree,
 int n,
 BSpline.Mode mode,
 double[] x,
 double[] y,
 double[] sigma)

Constructor specifying a B-spline's degree, number of control points, mode, and a set of Y values and their standard deviations for given X values. The number of X,Y data points must be larger than the number of control points.

Parameters:

degree - the degree of the B-spline that will be created

n - the number of control points

mode - the mode for the B-spline (either BSpline.Mode.UNCLAMPED, BSpline.Mode.CLAMPED, BSpline.Mode.CLAMPED_LEFT, BSpline.Mode.CLAMPED_RIGHT, or BSpline.Mode.PERIODIC); null for the default (BSpline.Mode.UNCLAMPED)

x - values in the domain of the spline

y - values in the range of the spline

sigma - the standard deviations for the values provided by the argument y

Method Details

getFit

protected LeastSquaresFit getFit()

Description copied from class: LeastSquaresFit

Get a copy of this least squares fit but without its parameters, degrees of freedom, chi square value, reduced chi square value, or covariance set.

This method is used by LeastSquaresFit.getFunction(double[]), which only provides a real-valued function. The only methods that will be called on the value returned are LeastSquaresFit.setChiSquare(double), LeastSquaresFit.setDegreesOfFreedom(int), LeastSquaresFit.setReducedChiSquare(double), LeastSquaresFit.setParameters(double[]), RealValuedFunction.valueAt(double), RealValuedFunction.derivAt(double), and RealValuedFunction.secondDerivAt(double).

Specified by:

getFit in class LeastSquaresFit

Returns:

a least squares fit

createCovariance

protected void createCovariance()

Description copied from class: LeastSquaresFit

Create the covariance array. Subclasses must implement this method, which is expected to set up the covariance array and then call LeastSquaresFit.setCovariance(double[][]) to make it available.

Specified by:

createCovariance in class LeastSquaresFit

setParameters

protected void setParameters(double[] parameters)

Description copied from class: LeastSquaresFit

Set the parameters array. Subclasses must call this method, generally in a constructor.

Overrides:

setParameters in class LeastSquaresFit

Parameters:

parameters - the array to use to store parameters

covariance

public double covariance(double x1,
 double x2)

Description copied from class: LeastSquaresFit

Compute the covariance for the y values associated with two data points. The covariance for two random variables X and Y is E[(X-E[X](Y-E[Y])] where E[Z] is the expected value of a random variable Z. The covariance of X and X is simply the variance of X. The value returned allows one to estimate the error in the fit at any point, not just the data points, and whether errors at different values of X are correlated.

Specified by:

covariance in class LeastSquaresFit

Parameters:

x1 - the x value for the first y value

x2 - the x value for the second y value

Returns:

the covariance

valueAt

public double valueAt(double arg)

Description copied from class: RealValuedFunction

Call the function.

Specified by:

valueAt in interface RealValuedFunctOps

Overrides:

valueAt in class RealValuedFunction

Parameters:

arg - the function's argument

Returns:

the value of the function for the given argument

derivAt

public double derivAt(double arg)

Description copied from class: RealValuedFunction

Evaluate the function's first derivative.

Overrides:

derivAt in class RealValuedFunction

Parameters:

arg - the function's argument

Returns:

the value of the function for the given argument

secondDerivAt

public double secondDerivAt(double arg)

Description copied from class: RealValuedFunction

Evaluate the function's second derivative.

Overrides:

secondDerivAt in class RealValuedFunction

Parameters:

arg - the function's argument

Returns:

the value of the function for the given argument