org.matheclipse.core.reflection.system

Class InterpolatingPolynomial

java.lang.Object

org.matheclipse.core.eval.interfaces.AbstractEvaluator

org.matheclipse.core.reflection.system.InterpolatingPolynomial

All Implemented Interfaces:

IFunctionEvaluator, IEvaluator

public class InterpolatingPolynomial
extends AbstractEvaluator

Newton polynomial interpolation , is the interpolation polynomial for a given set of data points in the Newton form. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated using divided differences.

See: Wikipedia - Polynomial interpolation and Wikipedia - Newton Polynomial

Constructor Summary

Constructors

Constructor and Description
InterpolatingPolynomial()

Method Summary

Modifier and Type	Method and Description
protected static IExpr[]	computeDividedDifference(IExpr[] x, IExpr[] y) Return a copy of the divided difference array.
IExpr	evaluate(IAST ast, EvalEngine engine) Symbolic evaluation of a function.
void	setUp(ISymbol symbol) Evaluate built-in rules and define Attributes for a function.

Methods inherited from class org.matheclipse.core.eval.interfaces.AbstractEvaluator

numericEval

Methods inherited from class java.lang.Object

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

Constructor Detail

InterpolatingPolynomial

public InterpolatingPolynomial()

Method Detail

computeDividedDifference

protected static IExpr[] computeDividedDifference(IExpr[] x,
                                                  IExpr[] y)

Return a copy of the divided difference array.

The divided difference array is defined recursively by

 f[x0] = f(x0)
 f[x0,x1,...,xk] = (f[x1,...,xk] - f[x0,...,x[k-1]]) / (xk - x0)
 

The computational complexity is O(N^2).

Parameters:

x - Interpolating points array.

y - Interpolating values array.

Returns:

a fresh copy of the divided difference array.

Throws:

org.apache.commons.math4.exception.DimensionMismatchException - if the array lengths are different.

org.apache.commons.math4.exception.NumberIsTooSmallException - if the number of points is less than 2.

org.apache.commons.math4.exception.NonMonotonicSequenceException - if x is not sorted in strictly increasing order.

evaluate

public IExpr evaluate(IAST ast,
                      EvalEngine engine)

Description copied from class: AbstractEvaluator

Symbolic evaluation of a function. ast.get(0) (or alternatively ast.head()) contains the head (i.e. the function symbol) of this abstract syntax tree (AST).
From ast.arg1() to ast.get(n) the ast contains the first to n-th argument of the function (alternatively you get the first to fifth argument with the methods arg1(), arg2(),... arg5()).
If necessary use the methods from the Validate class to check the number or types of arguments in the evaluate method.
Note: if the symbolic evaluation isn't possible or no result is found the evaluate method returns with a null value without throwing an exception!

Specified by:

evaluate in interface IFunctionEvaluator

Specified by:

evaluate in class AbstractEvaluator

Parameters:

ast - the abstract syntax tree (AST) which should be evaluated

engine - the users current evaluation engine

Returns:

the evaluated object or null, if evaluation isn't possible

See Also:

Validate, IExpr.head(), IAST.arg1(), IAST.arg2(), IAST.arg3()

setUp

public void setUp(ISymbol symbol)

Description copied from class: AbstractEvaluator

Evaluate built-in rules and define Attributes for a function.

Specified by:

setUp in interface IEvaluator

Overrides:

setUp in class AbstractEvaluator

Parameters:

symbol - the symbol which should be set up