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

The QawfIntegration type exposes the following members.

Constructors
 NameDescription
Public methodQawfIntegration Creates an instance of this integration class with a default integration rule and default debug flag setting.
Public methodQawfIntegration(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)
Public methodIntegrate(FuncDouble, Double, Double, OscillatoryTerm, Double, Double, Int32, Double, Double) 
Public methodIntegrate(FuncDouble, Double, Double, OscillatoryTerm, Double, Double, Int32, Boolean, Double, Double) 
Public methodIntegrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Double, Double)
(Inherited from QawoIntegration)
Public methodIntegrate(FuncDouble, Double, Double, Double, OscillatoryTerm, Double, Double, Double, Int32, Boolean, Double, Double)
(Inherited from QawoIntegration)
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
 NameDescription
Protected field_debug
(Inherited from QawoIntegration)
Protected field_qawoTable
(Inherited from QawoIntegration)
Protected field_workSpace
(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).
C#
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           +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,
C#
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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/)

See Also