org.matheclipse.core.reflection.system

Class NIntegrate

java.lang.Object

org.matheclipse.core.eval.interfaces.AbstractEvaluator

org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator

org.matheclipse.core.reflection.system.NIntegrate

All Implemented Interfaces:

IFunctionEvaluator, IEvaluator

public class NIntegrate
extends AbstractFunctionEvaluator

Function for numerical integration of univariate real functions. Uses the Commons math LegendreGaussIntegrator, RombergIntegrator, SimpsonIntegrator, TrapezoidIntegrator implementations.

Field Summary

Fields

Modifier and Type	Field and Description
static int	DEFAULT_MAX_ITERATIONS
static int	DEFAULT_MAX_POINTS
static ISymbol	LegendreGauss

Constructor Summary

Constructors

Constructor and Description
NIntegrate()

Method Summary

Modifier and Type	Method and Description
IExpr	evaluate(IAST ast, EvalEngine engine) Symbolic evaluation of a function.
static double	integrate(java.lang.String method, IAST list, double min, double max, IExpr function, int maxPoints, int maxIterations) Integrate a function numerically.
void	setUp(ISymbol symbol) Evaluate built-in rules and define Attributes for a function.

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

createRuleFromMethod, getNormalizedNegativeExpression, getNormalizedNegativeExpression, getPeriodicParts, getPureImaginaryPart, getRuleAST, initSerializedRules, isNegativeExpression

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

Field Detail

DEFAULT_MAX_POINTS

public static final int DEFAULT_MAX_POINTS

See Also:

Constant Field Values

DEFAULT_MAX_ITERATIONS

public static final int DEFAULT_MAX_ITERATIONS

See Also:

Constant Field Values

LegendreGauss

public static final ISymbol LegendreGauss

Constructor Detail

NIntegrate

public NIntegrate()

Method Detail

evaluate

public IExpr evaluate(IAST ast,
                      EvalEngine engine)

Description copied from class: AbstractFunctionEvaluator

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 AbstractFunctionEvaluator

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()

integrate

public static double integrate(java.lang.String method,
                               IAST list,
                               double min,
                               double max,
                               IExpr function,
                               int maxPoints,
                               int maxIterations)
                        throws org.apache.commons.math4.exception.ConvergenceException

Integrate a function numerically.

Parameters:

method - the following methods are possible: LegendreGauss, Simpson, Romberg, Trapezoid

list - a list of the form {x, lowerBound, upperBound}, where lowerBound and upperBound are numbers which could be converted to a Java double value.

function - the function which should be integrated.

maxPoints - maximum number of points

maxIterations - maximum number of iterations

Returns:

Throws:

org.apache.commons.math4.exception.ConvergenceException

setUp

public void setUp(ISymbol symbol)

Description copied from class: AbstractFunctionEvaluator

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

Specified by:

setUp in interface IEvaluator

Overrides:

setUp in class AbstractFunctionEvaluator

Parameters:

symbol - the symbol which should be set up