QawfIntegration Class

QAWF adaptive integration for Fourier integrals.

Inheritance Hierarchy

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

Namespace: Altaxo.Calc.Integration
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)

Syntax

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public class QawfIntegration : QawoIntegration

The QawfIntegration type exposes the following members.

Constructors

	Name	Description
	QawfIntegration	Creates an instance of this integration class with a default integration rule and default debug flag setting.
	QawfIntegration(Boolean)	Creates an instance of this integration class with the 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)
	Integrate(FuncDouble, Double, Double, OscillatoryTerm, Double, Double, Int32, Double, Double)	Integrate a Fourier-type integral using the instance's debug setting.
	Integrate(FuncDouble, Double, Double, OscillatoryTerm, Double, Double, Int32, Boolean, Double, Double)	Integrate a Fourier-type integral with an explicit debug flag for this call.
	Integrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Double, Double)	Integrate an oscillatory integral using the instance's debug setting. (Inherited from QawoIntegration)
	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. (Inherited from QawoIntegration)
	Integration	Static helper that integrates a Fourier-type 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	Stores the debug flag that controls error handling behavior. (Inherited from QawoIntegration)
	_qawoTable	Stores the reusable QAWO moment table. (Inherited from QawoIntegration)
	_workSpace	Stores the reusable workspace for adaptive integration. (Inherited from QawoIntegration)

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Remarks

This class attempts to compute a Fourier integral of the function f over the semiinfinite interval [a,+Infinity).


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

The parameter w and choice of sin or cos is taken from the table wf (the length L can take any value, since it is overridden by this function to a value appropriate for the fourier integration). The integral is computed using the QAWO algorithm over each of the subintervals,


             C1 = [a, a + c]
             C2 = [a + c, a + 2c]
             . . . = . . .
             Ck = [a + (k - 1)c, a + kc]

where c = (2floor(|w|) + 1)Pi/|w|. The width c is chosen to cover an odd number of periods so that the contributions from the intervals alternate in sign and are monotonically decreasing when f is positive and monotonically decreasing. The sum of this sequence of contributions is accelerated using the epsilon-algorithm.

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

Reference

Altaxo.Calc.Integration Namespace