agi.foundation.numericalmethods.advanced

(agi.foundation.core-2024r3.jar)

Class LagrangePolynomialApproximation

java.lang.Object

agi.foundation.infrastructure.DefinitionalObject

agi.foundation.numericalmethods.advanced.InterpolationAlgorithm

agi.foundation.numericalmethods.advanced.LagrangePolynomialApproximation

All Implemented Interfaces:

ICloneWithContext, IEnumerateDependencies, IEquatableDefinition, IFreezable

public class LagrangePolynomialApproximation
extends InterpolationAlgorithm

An algorithm that performs polynomial interpolation using Lagrange's algorithm.

Constructor Summary

Constructors

Modifier	Constructor and Description
	LagrangePolynomialApproximation() Initializes a new instance.
protected	LagrangePolynomialApproximation(LagrangePolynomialApproximation existingInstance, CopyContext context) Initializes a new instance as a copy of an existing instance.

Method Summary

Modifier and Type	Method and Description
protected boolean	checkForSameDefinition(InterpolationAlgorithm other) Checks to determine if another instance has the same definition as this instance and returns true if it does.
protected boolean	checkForSameDefinition(LagrangePolynomialApproximation other) Checks to determine if another instance has the same definition as this instance and returns true if it does.
Object	clone(CopyContext context) Clones this object using the specified context.
protected int	computeCurrentDefinitionHashCode() Computes a hash code based on the current properties of this object.
int	getDegreeRequired() Gets the minimum degree of approximation that this interpolator can perform.
Interpolator	getInterpolator(EvaluatorGroup group) Gets an evaluator which can compute the interpolated value of a function.
int	getOrderRequired() Gets the number of derivatives of the dependent variable that are required on input in order to interpolate using this interpolation algorithm.
static int	getRequiredDataPoints(int degree) Gets the number of data points needed to interpolate with the desired degree of accuracy, which is degree + 1.
static double[]	interpolate(double x, double[] xTable, double[] yTable, int yStride, int inputOrder, int outputOrder, int startIndex, int length) Interpolates values using this interpolation algorithm.

Methods inherited from class agi.foundation.numericalmethods.advanced.InterpolationAlgorithm

checkForSameDefinition, getInterpolator

Methods inherited from class agi.foundation.infrastructure.DefinitionalObject

areSameDefinition, areSameDefinition, areSameDefinition, areSameDefinition, areSameDefinition, collectionItemsAreSameDefinition, collectionItemsAreSameDefinition, collectionItemsAreSameDefinition, dictionaryItemsAreSameDefinition, enumerateDependencies, freeze, freezeAggregatedObjects, getCollectionHashCode, getCollectionHashCode, getCollectionHashCode, getDefinitionHashCode, getDefinitionHashCode, getDefinitionHashCode, getDefinitionHashCode, getDefinitionHashCode, getDefinitionHashCode, getDictionaryHashCode, getIsFrozen, isSameDefinition, throwIfFrozen

Methods inherited from class java.lang.Object

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

Constructor Detail

LagrangePolynomialApproximation

public LagrangePolynomialApproximation()

Initializes a new instance.

LagrangePolynomialApproximation

protected LagrangePolynomialApproximation(@Nonnull
                                          LagrangePolynomialApproximation existingInstance,
                                          @Nonnull
                                          CopyContext context)

Initializes a new instance as a copy of an existing instance.

See ICloneWithContext.clone(CopyContext) for more information about how to implement this constructor in a derived class.

Parameters:

existingInstance - The existing instance to copy.

context - A CopyContext that controls the depth of the copy.

Throws:

ArgumentNullException - Thrown when existingInstance or context is null.

Method Detail

clone

public Object clone(CopyContext context)

Clones this object using the specified context.

This method should be implemented to call a copy constructor on the class of the object being cloned. The copy constructor should take the CopyContext as a parameter in addition to the existing instance to copy. The copy constructor should first call CopyContext.addObjectMapping(T, T) to identify the newly constructed instance as a copy of the existing instance. It should then copy all fields, using CopyContext.updateReference(T) to copy any reference fields.

A typical implementation of ICloneWithContext:

public static class MyClass implements ICloneWithContext {
    public MyClass(MyClass existingInstance, CopyContext context) {
        context.addObjectMapping(existingInstance, this);
        someReference = context.updateReference(existingInstance.someReference);
    }

    @Override
    public final Object clone(CopyContext context) {
        return new MyClass(this, context);
    }

    private Object someReference;
}

In general, all fields that are reference types should be copied with a call to CopyContext.updateReference(T). There are a couple of exceptions:

1. Fields that are aggregate parts of the object should always be copied. A referenced object is an aggregate if properties or methods on the object being copied can modify the externally-visible value of the referenced object.
2. If the semantics of the referenced object require that it have a single parent, owner, context, etc., and the object being copied is that parent, owner, or context, then the referenced object should always be copied.

If one of these exceptions applies, the CopyContext should be given an opportunity to update the reference before the reference is copied explicitly. Use CopyContext.updateReference(T) to update the reference. If CopyContext.updateReference(T) returns the original object, indicating that the context does not have a replacement registered, then copy the object manually by invoking a Clone method, a copy constructor, or by manually constructing a new instance and copying the values.

alwaysCopy = context.updateReference(existingInstance.alwaysCopy);
if (existingInstance.alwaysCopy != null && alwaysCopy == existingInstance.alwaysCopy) {
    alwaysCopy = (AlwaysCopy) existingInstance.alwaysCopy.clone(context);
}

If you are implementing an evaluator (a class that implements IEvaluator), the IEvaluator.updateEvaluatorReferences(agi.foundation.infrastructure.CopyContext) method shares some responsibilities with the copy context constructor. Code duplication can be avoided by doing the following:

1. For references to other evaluators ONLY, simply assign the reference in the constructor instead of calling CopyContext.updateReference(T). You should still call CopyContext.updateReference(T) on any references to non-evaluators.
2. Call IEvaluator.updateEvaluatorReferences(agi.foundation.infrastructure.CopyContext) as the last line in the constructor and pass it the same CopyContext passed to the constructor.
3. Implement IEvaluator.updateEvaluatorReferences(agi.foundation.infrastructure.CopyContext) as normal. See the reference documentation for IEvaluator.updateEvaluatorReferences(agi.foundation.infrastructure.CopyContext) for more information on implementing that method.

public MyClass(MyClass existingInstance, CopyContext context) {
    super(existingInstance, context);
    someReference = context.updateReference(existingInstance.someReference);
    evaluatorReference = existingInstance.evaluatorReference;
    updateEvaluatorReferences(context);
}

@Override
public void updateEvaluatorReferences(CopyContext context) {
    evaluatorReference = context.updateReference(evaluatorReference);
}

@Override
public Object clone(CopyContext context) {
    return new MyClass(this, context);
}

private Object someReference;
private IEvaluator evaluatorReference;

Specified by:

clone in interface ICloneWithContext

Specified by:

clone in class DefinitionalObject

Parameters:

context - The context to use to perform the copy.

Returns:

A new instance which is a copy of this object.

checkForSameDefinition

protected final boolean checkForSameDefinition(InterpolationAlgorithm other)

Checks to determine if another instance has the same definition as this instance and returns true if it does. Derived classes MUST override this method and check all new fields introduced by the derived class for definitional equivalence. It is NOT necessary to check base class fields because the base class will already have done that. When overriding this method, you should NOT call the base implementation because it will return false for all derived-class instances. Derived classes should check the type of other to preserve the symmetric nature of IEquatableDefinition.isSameDefinition(java.lang.Object).

Specified by:

checkForSameDefinition in class InterpolationAlgorithm

Parameters:

other - The other instance to compare to this one.

Returns:

true if the two objects are defined equivalently; otherwise false.

checkForSameDefinition

protected boolean checkForSameDefinition(LagrangePolynomialApproximation other)

Checks to determine if another instance has the same definition as this instance and returns true if it does. Derived classes MUST override this method and check all new fields introduced by the derived class for definitional equivalence. It is NOT necessary to check base class fields because the base class will already have done that. When overriding this method, you should NOT call the base implementation because it will return false for all derived-class instances. Derived classes should check the type of other to preserve the symmetric nature of IEquatableDefinition.isSameDefinition(java.lang.Object).

Parameters:

other - The other instance to compare to this one.

Returns:

true if the two objects are defined equivalently; otherwise false.

computeCurrentDefinitionHashCode

protected int computeCurrentDefinitionHashCode()

Computes a hash code based on the current properties of this object. Derived classes MUST override this method and compute a hash code that combines: a unique hash code seed, the base implementation result, and the hash codes of all new fields introduced by the derived class which are used in the LagrangePolynomialApproximation.checkForSameDefinition(agi.foundation.numericalmethods.advanced.InterpolationAlgorithm) method.

Overrides:

computeCurrentDefinitionHashCode in class InterpolationAlgorithm

Returns:

The computed hash code.

getDegreeRequired

public int getDegreeRequired()

Gets the minimum degree of approximation that this interpolator can perform.

Specified by:

getDegreeRequired in class InterpolationAlgorithm

getOrderRequired

public int getOrderRequired()

Gets the number of derivatives of the dependent variable that are required on input in order to interpolate using this interpolation algorithm.

This class returns zero, indicating that this interpolation algorithm does not require derivative information.

Specified by:

getOrderRequired in class InterpolationAlgorithm

getInterpolator

public Interpolator getInterpolator(EvaluatorGroup group)

Gets an evaluator which can compute the interpolated value of a function.

Specified by:

getInterpolator in class InterpolationAlgorithm

Parameters:

group - The group with which to associate the new evaluator. By grouping evaluators that are often evaluated at the same Julian dates, common computations can be performed only once for the entire group instead of multiple times for each evaluator.

Returns:

An interpolator for this interpolation algorithm.

getRequiredDataPoints

public static int getRequiredDataPoints(int degree)

Gets the number of data points needed to interpolate with the desired degree of accuracy, which is degree + 1.

Parameters:

degree - The degree of polynomial approximation desired.

Returns:

The number of data points needed to interpolate with the desired degree of accuracy.

interpolate

@Nonnull
public static double[] interpolate(double x,
                                             @Nonnull
                                             double[] xTable,
                                             @Nonnull
                                             double[] yTable,
                                             int yStride,
                                             int inputOrder,
                                             int outputOrder,
                                             int startIndex,
                                             int length)

Interpolates values using this interpolation algorithm.

The xTable array should contain one more than the desired interpolation degree. For example, for a 7th degree interpolation, xTable should contain 8 elements. The yTable array should contain a number of elements equal to: * * ( + 1)

Parameters:

x - The independent variable for which the dependent variables will be interpolated.

xTable - The array of independent variables to use to interpolate. The values in this array must be in increasing order and the same value must not occur twice in the array.

yTable - The array of dependent variables to use to interpolate. There can be multiple values corresponding to each independent values in xTable. For a set of three dependent values (p,q,w) and their derivatives (dp, dq, dw) at time 1 and time 2 this should be as follows: {p1, q1, w1, dp1, dq1, dw1, p2, q2, w2, dp2, dq2, dw2}.

yStride - The number of dependent variable values in yTable corresponding to each independent variable value in xTable. If inputOrder is greater than 0, this is also the number of first derivative values, second derivative values, etc. corresponding to each value in xTable.

inputOrder - The number of dependent variable derivatives in yTable. If this value is 0, the yTable is assumed to contain only dependent variable values, with each yStride of them corresponding to a single independent variable in the xTable. If this value is 1, the yTable is assumed to contain not only the dependent variable values but also their derivatives. There are yStride dependent variable values followed by yStride dependent variable first derivatives corresponding to each independent variable value in xTable. Similarly if this value is 2, the yTable contains dependent values, first derivatives, and second derivatives.

outputOrder - The number of derivatives to return. To return just the dependent variable values, pass 0 for this parameter. To return the first derivatives along with the dependent variable values, pass 1. A Lagrange polynomial has length-1 non-zero derivatives. This algorithm bases the derivation off of the highest input order, so, for example, if you passed in an inputOrder of 2 and a length of 4, the output from zeroth order to fifth order would be nonzero.

startIndex - The index in xTable of the first value to use in the interpolation. The index of the first value in yTable to use is calculated as: * * ( + 1)

length - The number of values to use in the interpolation. This value should be one more than the desired interpolation degree. For example for 7th degree interpolation, this parameter should be 8.

Returns:

An array of interpolated values. The array contains at least yStride elements, each of which is an interpolated dependent variable value. If outputOrder is greater than zero, the array contains an additional number of yStride elements, for each output order.

Throws:

ArgumentNullException - Thrown when xTable or yTable is null.