Represents a numerical integrator that uses the left point rule.
Namespace: Extreme.Mathematics.Calculus
Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public NotInheritable Class LeftPointIntegrator _ Inherits NumericalIntegrator |
| C# |
|---|
public sealed class LeftPointIntegrator : NumericalIntegrator |
| C++ |
|---|
public ref class LeftPointIntegrator sealed : public NumericalIntegrator |
Methods
| Icon | Type | Description |
|---|---|---|
 | Equals(Object) | |
 | Finalize() | |
| GetHashCode() | Serves as a hash function for a particular type. |
| GetType() | Gets the Type of the current instance. |
| IncrementEvaluations() |
Increments the number of evaluations by one.
|
| IncrementEvaluations(Int32) |
Increments the number of evaluations by the specified amount.
|
| Integrate() |
Numerically integrates a function of one variable.
|
| Integrate(Double, Double) |
Numerically integrates a function of one variable.
|
| Integrate(RealFunction, Double, Double) |
Numerically integrates a function of one variable.
|
| MemberwiseClone() | Creates a shallow copy of the current Object. |
| SetResultProperties(Object, Double, AlgorithmStatus, Int32) |
Sets the results of an algorithm's execution.
|
| SetResultProperties(Object, Double) |
Sets the results of an algorithm's execution.
|
| ThrowException() |
Interprets the AlgorithmStatus and
throws the appropriate exception.
|
| ToString() |
Constructors
| Icon | Type | Description |
|---|---|---|
| LeftPointIntegratorNew() |
Constructs a new LeftPointIntegrator object.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | AbsoluteTolerance |
Gets or sets the absolute tolerance used in the
convergence test.
|
| ConvergenceCriterion |
Gets or sets a value specifying the criterion that is
to be used in the convergence test for the algorithm.
|
| EstimatedError |
Gets a value indicating the size of the absolute
error of the result.
|
| EvaluationsNeeded |
Gets the number of evaluations needed to execute the algorithm.
|
| EvaluationsRemaining |
Gets the number of evaluations still available.
|
| FunctionEvaluationsNeeded |
Gets the number of function evaluations performed by the
algorithm.
|
| Integrand |
Gets or sets the function to integrate.
|
| IterationResultCode |
Gets the AlgorithmStatus following
an execution of the algorithm.
|
| IterationsNeeded |
Gets the number of iterations needed by the
algorithm to reach the desired accuracy.
|
| IterationsRemaining |
Gets the number of iterations remaining.
|
| LowerBound |
Gets or sets the lower bound of the integration interval.
|
| MaxEvaluations |
Gets or sets the maximum number of evaluations during the calculation.
|
| MaxIterations | Gets or sets the maximum number of iterations
to use when approximating the roots of the target
function.
|
| Order |
Gets the order of the numerical integrator.
|
| RelativeTolerance |
Gets or sets the relative tolerance used in the
convergence test.
|
| Result |
Gets the result of an algorithm after it has executed.
|
| Status |
Gets the AlgorithmStatus following
an execution of the algorithm.
|
| ThrowExceptionOnFailure |
Gets or sets a value indicating whether to throw an
exception when the algorithm fails to converge.
|
| UpperBound |
Gets or sets the upper bound of the integration interval.
|
Remarks
The left point rule is one of the simplest numerical
integration algorithms around. The interval is divided into smaller
intervals, and the function value on the left side of the subinterval is
taken as an approximation for the function over the entire subinterval.
This algorithm is of order 1. In each iteration, the number of points is doubled. The difference between successive approximations is taken as the estimate for the integration error.
Because the order of the algorithm is so low, use of this algorithm is not generally recommended for general use. It does provide a unique feature in that can produce absolute bounds on the value of the integral of some functions. It produces a lower bound for monotonically increasing integrands, and an upper bound for monotonically decreasing integrands. Complementary bounds are produced by the RightPointIntegrator.
Inheritance Hierarchy
System.Object
Extreme.Mathematics.IterativeAlgorithm
Extreme.Mathematics.Calculus.NumericalIntegrator
Extreme.Mathematics.Calculus.LeftPointIntegrator
Extreme.Mathematics.IterativeAlgorithm
Extreme.Mathematics.Calculus.NumericalIntegrator
Extreme.Mathematics.Calculus.LeftPointIntegrator
