QawoIntegration Class

QAWO adaptive integration for oscillatory functions

Inheritance Hierarchy

SystemObject
  Altaxo.Calc.IntegrationIntegrationBase
    Altaxo.Calc.IntegrationQawoIntegration
      Altaxo.Calc.IntegrationQawfIntegration

Namespace: Altaxo.Calc.Integration
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)

Syntax

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public class QawoIntegration : IntegrationBase

The QawoIntegration type exposes the following members.

Constructors

	Name	Description
	QawoIntegration	Creates an instance of this integration class with a default integration rule and default debug flag setting.
	QawoIntegration(Boolean)	Creates an instance of this integration class with specified debug flag setting.

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	gsl_integration_qawo	Core implementation of the QAWO algorithm for oscillatory weighted integrals. This method mirrors the original GSL implementation (integration/qawo.c).
	Integrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Double, Double)	Integrate an oscillatory integral using the instance's debug setting.
	Integrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Boolean, Double, Double)	Integrate an oscillatory integral with an explicit debug flag for this call.
	Integration	Static helper that integrates an oscillatory integral using a reusable temporary storage object.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Fields

	Name	Description
	_debug
	_defaultOscTableLength
	_qawoTable
	_workSpace

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Remarks

The QAWO algorithm is designed for integrands with an oscillatory factor, sin(wx) or cos(wx). In order to work efficiently the algorithm requires a table of Chebyshev moments which must be pre-computed with calls to the functions below. This function uses an adaptive algorithm to compute the integral of f over (a, b) with the weight function sin(wx) or cos(wx) defined by the table wf:

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           b                                   b
I = Integral dx f(x) sin(wt)   or   I = Integral dx f(x) cos(wx)
           a                                   a

The results are extrapolated using the epsilon-algorithm to accelerate the convergence of the integral. The function returns the final approximation from the extrapolation, result, and an estimate of the absolute error, abserr. The subintervals and their results are stored in the memory provided by workspace. The maximum number of subintervals is given by limit, which may not exceed the allocated size of the workspace. Those subintervals with "large" widths d where dw > 4 are computed using a 25-point Clenshaw-Curtis integration rule, which handles the oscillatory behavior. Subintervals with a "small" widths where dw < 4 are computed using a 15-point Gauss-Kronrod integration.

Ref.: GNU Scientific Library reference manual (http://www.gnu.org/software/gsl/)

Reference

Altaxo.Calc.Integration Namespace