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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: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
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public class QawoIntegration : IntegrationBase

The QawoIntegration type exposes the following members.

Constructors
 NameDescription
Public methodQawoIntegration Creates an instance of this integration class with a default integration rule and default debug flag setting.
Public methodQawoIntegration(Boolean) Creates an instance of this integration class with specified integration rule and specified debug flag setting.
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Methods
 NameDescription
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodStatic membergsl_integration_qawo 
Public methodIntegrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Double, Double) 
Public methodIntegrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Boolean, Double, Double) 
Public methodStatic memberIntegration 
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
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Fields
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:
C#
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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/)

See Also