Module org.bzdev.math

Package org.bzdev.math

Class LeastSquaresFit.FunctionBasis

java.lang.Object

org.bzdev.math.RealValuedFunctionVA

org.bzdev.math.RealValuedFunction

org.bzdev.math.LeastSquaresFit

org.bzdev.math.LeastSquaresFit.Linear

org.bzdev.math.LeastSquaresFit.FunctionBasis

All Implemented Interfaces:

DoubleUnaryOperator, RealValuedDomainOps, RealValuedFunctOps, RealValuedFunctVAOps, VADomainOps

Enclosing class:

LeastSquaresFit

public static class LeastSquaresFit.FunctionBasis
extends LeastSquaresFit.Linear

Linear least squares fit using a specified function basis. The parameters are provided in an array with an ordering matching that of the basis functions passed as the variable-length argument for this class' constructors.

See Also:

• LeastSquaresFit.Linear

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
FunctionBasis(double[] x, double[] y, double[] sigma, RealValuedFunctionVA.Linear f)	Constructor given the standard deviations for the Y values and a real-valued function that is a linear combination of basis functions.
FunctionBasis(double[] x, double[] y, double[] sigma, T... fs)	Constructor given the standard deviations for the Y values.
FunctionBasis(double[] x, double[] y, double sigma, RealValuedFunctionVA.Linear f)	Constructor given the standard deviation for the Y values and a real-valued function that is a linear combination of basis functions.
FunctionBasis(double[] x, double[] y, double sigma, T... fs)	Constructor given the standard deviation for the Y values.
FunctionBasis(double[] x, double[] y, RealValuedFunctionVA.Linear f)	Constructor given a real-valued function that is a linear combination of basis functions.
FunctionBasis(double[] x, double[] y, T... fs)	Constructor.

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.
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.
double	valueAt(double arg)	Call the function.

Methods inherited from class org.bzdev.math.LeastSquaresFit.Linear

createCovariance, getDecomp, setDecomp, setDecomp, setVariance

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, setParameters, 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

FunctionBasis

@SafeVarargs
public FunctionBasis(double[] x,
 double[] y,
 T... fs)

Constructor. The number of basis functions determines the number of parameters. If RealValuedFunction.derivAt(double) or RealValuedFunction.secondDerivAt(double) are used, the basis functions must implement the corresponding derivatives.

Type Parameters:

T - a type that implements or extends RealValuedFunctionops

Parameters:

y - the values for y_i

x - the values for x_i

fs - the basis functions

Throws:

IllegalArgumentException - an argument was null

FunctionBasis

public FunctionBasis(double[] x,
 double[] y,
 RealValuedFunctionVA.Linear f)

Constructor given a real-valued function that is a linear combination of basis functions. The number of basis functions determines the number of parameters. If RealValuedFunction.derivAt(double) or RealValuedFunction.secondDerivAt(double) are used, the basis functions used by f must implement the corresponding derivatives.

Parameters:

x - the values for x_i

y - the values for y_i

f - a real-valued function with multiple arguments

FunctionBasis

@SafeVarargs
public FunctionBasis(double[] x,
 double[] y,
 double sigma,
 T... fs)

Constructor given the standard deviation for the Y values. The number of basis functions determines the number of parameters. If RealValuedFunction.derivAt(double) or RealValuedFunction.secondDerivAt(double) are used, the basis functions must implement the corresponding derivatives.

Type Parameters:

T - a subtype of RealValuedFunctOps

Parameters:

x - the values for x_i

y - the values for y_i

sigma - the standard deviation for every y value

fs - the basis functions

FunctionBasis

public FunctionBasis(double[] x,
 double[] y,
 double sigma,
 RealValuedFunctionVA.Linear f)

Constructor given the standard deviation for the Y values and a real-valued function that is a linear combination of basis functions. The number of basis functions determines the number of parameters. If RealValuedFunction.derivAt(double) or RealValuedFunction.secondDerivAt(double) are used, the basis functions used by f must implement the corresponding derivatives.

Parameters:

x - the values for x_i

y - the values for y_i

sigma - the standard deviation for every y value

f - a real-valued function with multiple arguments

FunctionBasis

@SafeVarargs
public FunctionBasis(double[] x,
 double[] y,
 double[] sigma,
 T... fs)

Constructor given the standard deviations for the Y values. The number of basis functions determines the number of parameters. If RealValuedFunction.derivAt(double) or RealValuedFunction.secondDerivAt(double) are used, the basis functions must implement the corresponding derivatives.

Type Parameters:

T - the type of the functions

Parameters:

x - the values for x_i

y - the values for y_i

sigma - the standard deviations σ_i for the corresponding Y value y_i

fs - the basis functions

FunctionBasis

public FunctionBasis(double[] x,
 double[] y,
 double[] sigma,
 RealValuedFunctionVA.Linear f)

Constructor given the standard deviations for the Y values and a real-valued function that is a linear combination of basis functions. The number of basis functions determines the number of parameters. If RealValuedFunction.derivAt(double) or RealValuedFunction.secondDerivAt(double) are used, the basis functions used by f must implement the corresponding derivatives.

Parameters:

x - the values for x_i

y - the values for y_i

sigma - the standard deviations σ_i for the corresponding Y value y_i

f - a real-valued function with multiple arguments

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

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)
               throws UnsupportedOperationException

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

Throws:

UnsupportedOperationException - the operation is not supported.

secondDerivAt

public double secondDerivAt(double arg)
                     throws UnsupportedOperationException

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

Throws:

UnsupportedOperationException - the operation is not supported.