maspack.interpolation

Class LinearSpline1d

java.lang.Object

maspack.function.Diff1Function1x1Base

maspack.interpolation.LinearSpline1d

All Implemented Interfaces:

java.lang.Cloneable, java.lang.Iterable<LinearSpline1d.Knot>, Diff1Function1x1, Diff1FunctionNx1, Function1x1, FunctionNx1, Clonable, Scannable

public class LinearSpline1d
extends Diff1Function1x1Base
implements java.lang.Iterable<LinearSpline1d.Knot>

Implements 1D piecewise-linear spline interpolation. The spline is defined by a sequence of knots delimiting the boundaries between linear interpolation segements.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LinearSpline1d.Knot

Constructor Summary

Constructors

Constructor and Description
LinearSpline1d() Creates a empty spline
LinearSpline1d(double[] x, double[] y) Creates a spline from specified values of x and y at each knot point.
LinearSpline1d(LinearSpline1d spline) Creates a spline from a copy of an existing one.

Method Summary

Modifier and Type	Method and Description
LinearSpline1d.Knot	addKnot(double x, double y) Adds another knot point to this spline at a specified x coordinate.
void	clearKnots() Removes all knots from from this spline.
LinearSpline1d	clone()
LinearSpline1d	copy() Creates a copy of this spline.
boolean	equals(LinearSpline1d spline) Queries whether this spline is equal to another spline.
double	eval(double x) Evaluates the y value of this spline for a specific x value.
double	eval(DoubleHolder deriv, double x) Evaluates both the value and first derivative of this function at a specified input value.
double	eval(double x, IntHolder lastIdx) Evaluates the y value of this spline for a specific x value.
double	evalDeriv(double x) Evaluates first derivative of this function at a specified input value.
double	evalDy(double x) Evaluates the derivative (with respect to x) of this spline for a specific x value.
double	evalDy(double x, IntHolder lastIdx) Evaluates the derivative (with respect to the parameter) of this spline for a specific x value.
LinearSpline1d.Knot	getFirstKnot() Returns the first knot in this spline, or null if there are no knots.
LinearSpline1d.Knot	getKnot(int idx) Returns the idx-th knot in this spline.
LinearSpline1d.Knot	getLastKnot() Returns the last knot in this spline, or null if there are no knots.
LinearSpline1d.Knot	getNextKnot(double x) Find the knot immediately following x.
LinearSpline1d.Knot	getPreceedingKnot(double x) Find the knot immediately preceeding x.
LinearSpline1d.Knot	getPreceedingKnot(double x, IntHolder lastIdx) Find the knot immediately preceeding x.
double	getX0() Returns the firxt x value of this spline.
double	getXLast() Returns the last x value of this spline.
double[]	getXValues() Returns an array giving the values of x at each knot.
boolean	isWritable() Returns true if this component should in fact be written to secondary storage.
java.util.Iterator<LinearSpline1d.Knot>	iterator() Returns an iterator for the knots in this spline.
int	numKnots() Returns the number of knots in this spline.
boolean	removeKnot(LinearSpline1d.Knot knot) Removes a knot from this spline.
void	scan(ReaderTokenizer rtok, java.lang.Object ref) Scans this spline from a ReaderTokenizer.
void	set(double[] x, double[] y) Sets this spline from specified values of x and y at each knot point.
void	set(LinearSpline1d spline) Sets this spline to be a copy of another spline.
void	write(java.io.PrintWriter pw, NumberFormat fmt, java.lang.Object ref) Writes a text description of this spline to a PrintWriter.

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface maspack.function.Diff1Function1x1

eval, evalDeriv

Methods inherited from interface maspack.function.Function1x1

eval, inputSize

Constructor Detail

LinearSpline1d

public LinearSpline1d()

Creates a empty spline

LinearSpline1d

public LinearSpline1d(double[] x,
                      double[] y)

Creates a spline from specified values of x and y at each knot point. The values of x should be in strictly ascending order.

Parameters:

x - x values at each knot point

y - y values at each knot point

LinearSpline1d

public LinearSpline1d(LinearSpline1d spline)

Creates a spline from a copy of an existing one.

Parameters:

spline - spline to copy

Method Detail

set

public void set(double[] x,
                double[] y)

Sets this spline from specified values of x and y at each knot point. The values of x should be in strictly ascending order.

Parameters:

x - x values at each knot point

y - y values at each knot point

getXValues

public double[] getXValues()

Returns an array giving the values of x at each knot.

Returns:

array of x values

addKnot

public LinearSpline1d.Knot addKnot(double x,
                                   double y)

Adds another knot point to this spline at a specified x coordinate.

Parameters:

x - x value at the knot

y - y value at the knot

removeKnot

public boolean removeKnot(LinearSpline1d.Knot knot)

Removes a knot from this spline.

Parameters:

knot - knot to remove

clearKnots

public void clearKnots()

Removes all knots from from this spline.

getPreceedingKnot

public LinearSpline1d.Knot getPreceedingKnot(double x)

Find the knot immediately preceeding x. Specifically, find the nearest knot for which knot.getX0() <= x. If no such knot exists, null is returned.

Parameters:

x - value for which preceeding knot is sought

getPreceedingKnot

public LinearSpline1d.Knot getPreceedingKnot(double x,
                                             IntHolder lastIdx)

Find the knot immediately preceeding x. Specifically, find the nearest knot for which knot.getX0() <= x. If no such knot exists, null is returned.

The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of x.

Parameters:

x - value for which preceeding knot is sought

lastIdx - if non-null, specifies a index value giving a hint on where to start the knot search. On output, this value is set to the index of the returned knot, or -1 if no knot is found.

getNextKnot

public LinearSpline1d.Knot getNextKnot(double x)

Find the knot immediately following x. Specifically, find the nearest knot for which knot.x0 > x. If no such knot exists, null is returned.

Parameters:

x - value for which next knot is sought

eval

public double eval(double x)

Evaluates the y value of this spline for a specific x value. For parameter values outside the knot range, the value is lineraly extrapolated based on derivatives at the first or last knots. An empty spline evaluates to 0.

Specified by:

eval in interface Function1x1

Specified by:

eval in class Diff1Function1x1Base

Parameters:

x - value at which the y value should be computed

Returns:

function output value

eval

public double eval(double x,
                   IntHolder lastIdx)

Evaluates the y value of this spline for a specific x value. For parameter values outside the knot range, the value is lineraly extrapolated based on derivatives at the first or last knots. An empty spline evaluates to 0.

The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of x.

Parameters:

x - value at which the y value should be computed

lastIdx - if non-null, specifies a index value giving a hint on where to search for the knot preceeding x. On output, this value is set to the index of the preceeding knot, or -1 if no preceeding knot is found.

evalDy

public double evalDy(double x)

Evaluates the derivative (with respect to x) of this spline for a specific x value. For parameter values outside the knot range, the value is set to the derivative at either the first or last knot. An empty spline evaluates to 0.

Parameters:

x - value at which the derivative should be computed

eval

public double eval(DoubleHolder deriv,
                   double x)

Description copied from class: Diff1Function1x1Base

Evaluates both the value and first derivative of this function at a specified input value.

Specified by:

eval in interface Diff1Function1x1

Specified by:

eval in class Diff1Function1x1Base

Parameters:

deriv - if non-null, returns the derivative value

x - input value

Returns:

function value

evalDeriv

public double evalDeriv(double x)

Description copied from interface: Diff1Function1x1

Evaluates first derivative of this function at a specified input value.

Specified by:

evalDeriv in interface Diff1Function1x1

Parameters:

x - input value

Returns:

derivative value

evalDy

public double evalDy(double x,
                     IntHolder lastIdx)

Evaluates the derivative (with respect to the parameter) of this spline for a specific x value. For parameter values outside the knot range, the value is set to the derivative at either the first or last knot. An empty spline evaluates to 0.

The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of x.

Parameters:

x - value for which the derivative should be computed

lastIdx - if non-null, specifies a index value giving a hint on where to search for the knot preceeding x. On output, this value is set to the index of the preceeding knot, or -1 if no preceeding knot is found.

scan

public void scan(ReaderTokenizer rtok,
                 java.lang.Object ref)
          throws java.io.IOException

Scans this spline from a ReaderTokenizer. The expected format consists of an opening square bracket, followed by 2 n numeric values giving the x and y values for each of the n knots, and terminated with a closing square bracket. Whitespace characters are ignored. For example,

  [  0.0 1.0
     2.0 4.3
     3.0 5.0
  ]
 

describes a spline with three knots, with x and y equal to (0, 1), (2, 4.4), and (3, 5), respectively.

Specified by:

scan in interface Scannable

Overrides:

scan in class Diff1Function1x1Base

Parameters:

rtok - Tokenizer from which to scan the spline

ref - optional reference object (not used)

Throws:

java.io.IOException - if an I/O or formatting error occured

write

public void write(java.io.PrintWriter pw,
                  NumberFormat fmt,
                  java.lang.Object ref)
           throws java.io.IOException

Writes a text description of this spline to a PrintWriter. The format is the same as that described for scan.

Specified by:

write in interface Scannable

Overrides:

write in class Diff1Function1x1Base

Parameters:

pw - writer to which the spline should be written

fmt - describes how the numbers should be formatted

ref - optional reference object (not used)

Throws:

java.io.IOException - if an I/O error occured

isWritable

public boolean isWritable()

Returns true if this component should in fact be written to secondary storage. This gives subclasses control over whether or not they are actually written out.

Specified by:

isWritable in interface Scannable

Overrides:

isWritable in class Diff1Function1x1Base

Returns:

true if this component should be written to secondary storage.

numKnots

public int numKnots()

Returns the number of knots in this spline.

Returns:

number of knots

getKnot

public LinearSpline1d.Knot getKnot(int idx)

Returns the idx-th knot in this spline.

Parameters:

idx - index of the requested knot

Returns:

idx-th knot

getFirstKnot

public LinearSpline1d.Knot getFirstKnot()

Returns the first knot in this spline, or null if there are no knots.

Returns:

first knot

getLastKnot

public LinearSpline1d.Knot getLastKnot()

Returns the last knot in this spline, or null if there are no knots.

Returns:

last knot

getX0

public double getX0()

Returns the firxt x value of this spline.

Returns:

starting x value

getXLast

public double getXLast()

Returns the last x value of this spline.

Returns:

last x value

iterator

public java.util.Iterator<LinearSpline1d.Knot> iterator()

Returns an iterator for the knots in this spline.

Specified by:

iterator in interface java.lang.Iterable<LinearSpline1d.Knot>

Returns:

spline knot iterator

set

public void set(LinearSpline1d spline)

Sets this spline to be a copy of another spline.

Parameters:

spline - spline to copy

copy

public LinearSpline1d copy()

Creates a copy of this spline.

equals

public boolean equals(LinearSpline1d spline)

Queries whether this spline is equal to another spline.

Parameters:

spline - spline to compare to this one

Returns:

true if the splines are equal

clone

public LinearSpline1d clone()

Specified by:

clone in interface Clonable

Overrides:

clone in class Diff1Function1x1Base