public class LagrangePolynomialApproximation extends InterpolationAlgorithm
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.

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.

boolean 
getIsThreadSafe()
Gets a value indicating if the methods on this instance are safe to call from
multiple threads simultaneously.

int 
getOrderRequired()
Gets 0, indicating that this interpolation algorithm does not require any derivatives.

int 
getRequiredDataPoints(int degree,
int inputOrder)
Returns the number of data points needed to interpolate with the desired degree of accuracy,
which is degree + 1.

double[] 
interpolate(double x,
double[] xTable,
double[] yTable,
int yStride,
int inputOrder,
int outputOrder,
int startIndex,
int length)
Interpolates values using this interpolation algorithm.

getDefinitionHashCode, interpolate, interpolateWithDegree, isSameDefinition
public LagrangePolynomialApproximation()
protected LagrangePolynomialApproximation(@Nonnull LagrangePolynomialApproximation existingInstance, @Nonnull CopyContext context)
See ICloneWithContext.clone(CopyContext)
for more information about how to implement this constructor
in a derived class.
existingInstance
 The existing instance to copy.context
 A CopyContext
that controls the depth of the copy.ArgumentNullException
 Thrown when existingInstance
or context
is null
.public Object clone(CopyContext 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:
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 (that is, if the reference some field is equal to the reference of the same field of another instance))
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:
CopyContext.updateReference(T)
. You should still call CopyContext.updateReference(T)
on any references to
nonevaluators.
IEvaluator.updateEvaluatorReferences(agi.foundation.infrastructure.CopyContext)
as the last line in the constructor and pass it the
same CopyContext
passed to the constructor.
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;
clone
in interface ICloneWithContext
clone
in class InterpolationAlgorithm
context
 The context to use to perform the copy.protected final boolean checkForSameDefinition(InterpolationAlgorithm other)
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 derivedclass instances.
Derived classes should check the type of other
to preserve the symmetric nature of IEquatableDefinition.isSameDefinition(java.lang.Object)
.checkForSameDefinition
in class InterpolationAlgorithm
other
 The other instance to compare to this one.true
if the two objects are defined equivalently, otherwise false
.protected boolean checkForSameDefinition(LagrangePolynomialApproximation other)
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 derivedclass instances.
Derived classes should check the type of other
to preserve the symmetric nature of IEquatableDefinition.isSameDefinition(java.lang.Object)
.other
 The other instance to compare to this one.true
if the two objects are defined equivalently, otherwise false
.protected int computeCurrentDefinitionHashCode()
LagrangePolynomialApproximation.checkForSameDefinition(agi.foundation.numericalmethods.advanced.InterpolationAlgorithm)
method.computeCurrentDefinitionHashCode
in class InterpolationAlgorithm
public boolean getIsThreadSafe()
If this property is true
, all methods and properties are guaranteed to be thread safe.
Conceptually, an object that returns true
for this method acts as if there is a lock
protecting each method and property such that only one thread at a time can be inside any method or
property in the class. In reality, such locks are generally not used and are in fact discouraged. However,
the user must not experience any exceptions or inconsistent behavior that would not be experienced if such
locks were used.
If this property is false
, the behavior when using this class from multiple threads
simultaneously is undefined and may include inconsistent results and exceptions. Clients wishing to use
multiple threads should call CopyForAnotherThread.copy(T)
to get a separate instance of the
object for each thread.
getIsThreadSafe
in interface IThreadAware
getIsThreadSafe
in class InterpolationAlgorithm
public int getOrderRequired()
getOrderRequired
in class InterpolationAlgorithm
public int getRequiredDataPoints(int degree, int inputOrder)
getRequiredDataPoints
in class InterpolationAlgorithm
degree
 The degree of polynomial approximation desired.inputOrder
 This parameter does not affect the result for Lagrange approximation.public double[] interpolate(double x, double[] xTable, double[] yTable, int yStride, int inputOrder, int outputOrder, int startIndex, int length)
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)
interpolate
in class InterpolationAlgorithm
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 nonzero 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.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.