jsci.maths.wavelet.splines

Class PiecewiseConstant

java.lang.Object

jsci.maths.wavelet.MultiscaleFunction

jsci.maths.wavelet.splines.Spline

jsci.maths.wavelet.splines.PiecewiseConstant

All Implemented Interfaces:

java.lang.Cloneable, Filter

public class PiecewiseConstant
extends Spline
implements Filter, java.lang.Cloneable

This class is used to generate piecewise constant splines to be used as wavelets or related functions. It can also be used for basic interpolation.

Constructor Summary

Constructors

Constructor and Description
PiecewiseConstant()
PiecewiseConstant(double[] v)

Method Summary

Modifier and Type	Method and Description
java.lang.Object	clone() Return a copy of this object
SumOfDiracs	derive() compute the derivative of the function - useful for numerical analysis
SumOfDiracs	derive(double a, double b) compute the derivative of the function - useful for numerical analysis
int	dimension() Number of knots
int	dimension(int j) Number of knots after j iterations
boolean	equals(java.lang.Object a) Check if another object is equal to this PiecewiseConstant object
double[]	evaluate(int j) Return as an array the sampled values of the function
int	getFilterType() This method is used to compute how the number of scaling functions changes from on scale to the other.
double	getValue(int i) Get the i th sampled value of the function.
double[]	highpass(double[] gete) This is the implementation of the highpass Filter.
double[]	highpass(double[] v, double[] param) This is the implementation of the highpass Filter.
double[]	interpolate(int j) Return as an array the interpolated values of the function.
double[]	lowpass(double[] gete) This is the implementation of the lowpass Filter.
double[]	lowpass(double[] v, double[] param) This is the implementation of the lowpass Filter.
double	mass(double a, double b) Compute the mass (integral)
int	previousDimension(int k) This method return the number of "scaling" functions at the previous scale given a number of scaling functions.
void	setValue(int i, double d) Set a particular value
void	setValues(double[] v) Set the sampled values of the function to the specified array
java.lang.String	toString() Return a String representation of the object

Methods inherited from class jsci.maths.wavelet.MultiscaleFunction

mass, mass

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

PiecewiseConstant

public PiecewiseConstant(double[] v)

PiecewiseConstant

public PiecewiseConstant()

Method Detail

toString

public java.lang.String toString()

Return a String representation of the object

Specified by:

toString in class Spline

equals

public boolean equals(java.lang.Object a)

Check if another object is equal to this PiecewiseConstant object

Specified by:

equals in class Spline

getFilterType

public int getFilterType()

This method is used to compute how the number of scaling functions changes from on scale to the other. Basically, if you have k scaling function and a Filter of type t, you'll have 2*k+t scaling functions at the next scale (dyadic case). Notice that this method assumes that one is working with the dyadic grid while the method "previousDimension" define in the interface "Filter" doesn't.

Specified by:

getFilterType in class Spline

previousDimension

public int previousDimension(int k)

This method return the number of "scaling" functions at the previous scale given a number of scaling functions. The answer is always smaller than the provided value (about half since this is a dyadic implementation). This relates to the same idea as the "Filter type". It is used by the interface "Filter".

Specified by:

previousDimension in interface Filter

lowpass

public double[] lowpass(double[] v,
                        double[] param)

This is the implementation of the lowpass Filter. It is used by the interface "Filter". Lowpass filters are normalized so that they preserve constants away from the boundaries.

Specified by:

lowpass in interface Filter

param - a parameter for the filter

highpass

public double[] highpass(double[] v,
                         double[] param)

This is the implementation of the highpass Filter. It is used by the interface "Filter". This class doesn't have a highpass Filter so that this method is only provided to be compatible with the interface.

Specified by:

highpass in interface Filter

param - a parameter for the filter

lowpass

public double[] lowpass(double[] gete)

This is the implementation of the lowpass Filter. It is used by the interface "Filter". Lowpass filters are normalized so that they preserve constants away from the boundaries.

Specified by:

lowpass in interface Filter

highpass

public double[] highpass(double[] gete)

This is the implementation of the highpass Filter. It is used by the interface "Filter". This class doesn't have a highpass Filter so that this method is only provided to be compatible with the interface.

Specified by:

highpass in interface Filter

clone

public java.lang.Object clone()

Return a copy of this object

Overrides:

clone in class Spline

getValue

public double getValue(int i)

Get the i th sampled value of the function.

Parameters:

i - position (knot)

Throws:

java.lang.IllegalArgumentException - if i is not a within 0 and the last knot (dimension()-1)

setValues

public void setValues(double[] v)

Set the sampled values of the function to the specified array

mass

public double mass(double a,
                   double b)

Compute the mass (integral)

Parameters:

a - left boundary of the interval

b - right boundary of the interval

setValue

public void setValue(int i,
                     double d)

Set a particular value

Parameters:

i - position (knot)

d - value

Throws:

java.lang.IllegalArgumentException - if the parameter i is negative

derive

public SumOfDiracs derive()

compute the derivative of the function - useful for numerical analysis

derive

public SumOfDiracs derive(double a,
                          double b)

compute the derivative of the function - useful for numerical analysis

Parameters:

a - left boundary of the interval

b - right boundary of the interval

dimension

public int dimension()

Number of knots

Specified by:

dimension in class Spline

dimension

public int dimension(int j)

Number of knots after j iterations

Specified by:

dimension in class Spline

Parameters:

j - number of iterations

interpolate

public double[] interpolate(int j)

Return as an array the interpolated values of the function. Will return the same values as the evaluate method because the Filter is interpolatory.

Specified by:

interpolate in class Spline

Parameters:

j - number of iterations

evaluate

public double[] evaluate(int j)

Return as an array the sampled values of the function

Specified by:

evaluate in class Spline

Parameters:

j - number of iterations