Dehint Dehint_r Deoint Deoint_r Qagi Qagi_r Qawf Qawf_r Qk15i Qk15i_r

Qawf() Sub Qawf ( F As  LongPtr, A As  Double, Omega As  Double, Integr As  Long, Result As  Double, Info As  Long, Optional AbsErr As  Double, Optional Neval As  Long, Optional EpsAbs As  Double = -1, Optional Limlst As  Long = -1, Optional Lst As  Long, Optional Limit As  Long = -1, Optional Maxp1 As  Long = -1  ) Semi-infinite interval adaptive quadrature for Fourier integrals (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) Purpose The routine calculates an approximation result to a Fourier integral I = ∫ f(x)*w(x) dx over [a, +∞] satisfying the requested accuracy, where the weight function w(x) = cos(ω*x) or sin(ω*x). The integration interval is divided into subintervals, and the integral of successive subintervals are computed by Qawo until the requested accuracy is satisfied and accumulated. The 25-point modified Clenshaw-Curtis rule and a 15-point Gauss-Kronrod rule are used. Parameters [in] F The user supplied subroutine which calculates the integrand function f(x) defined as follows. Function F(X As Double) As Double F = f(X) End Function X should not be changed. [in] A Lower limit of integration a. [in] Omega Parameter ω in the weight function. [in] Integr Indicates which weight function is to be used. = 1: w(x) = cos(ω*x) = 2: w(x) = sin(ω*x) [out] Result Approximation to the integral. [out] Info = 0: Successful exit. = -4: The argument Integr had an illegal value. (Integr <> 1 and Integr <> 2) = 1: Maximum number of subintervals Ck allowed has been achieved. = 4: Extrapolation table constructed for convergence acceleration does not converge to within the requested accuracy. = 7: Bad integrand behavior occurs within one or more of the subintervals. [out] AbsErr (Optional) Estimate of the modulus of the absolute error, which should equal or exceed the true error. [out] Neval (Optional) Number of integrand evaluations. [in] EpsAbs (Optional) Absolute accuracy requested. (EpsAbs > 0) (default = 1.0e-12) (If EpsAbs <= 0, the default value will be used) [in] Limlst (Optional) Maximum number of subintervals. (Limlst >= 3) (default = 50) (If Limlst < 3, the default value will be used) [out] Lst (Optional) Number of subintervals actually needed for the integration. [in] Limit (Optional) Maximum number of subintervals to be produced by Qawo to integrate each subinterval. (Limit >= 1) (default = 100) (If Limit < 1, the default value will be used) [in] Maxp1 (Optional) Upper bound on the number of Chebyshev moments which can be stored (Maxp1 >= 1) (default = 21) (If Maxp1 < 1, the default value will be used) Reference SLATEC (QUADPACK) Example Program Compute the following integral. ∫ exp(-x^2)cos(x) dx [0, +∞] (= exp(-1/4)*1/2*√π) Function F6(X As Double) As Double F6 = Exp(-X ^ 2) End Function Sub Ex_Qawf() Dim A As Double, Omega As Double, Integr As Long, Result As Double Dim Info As Long A = 0 Omega = 1 Integr = 1 Call Qawf(AddressOf F6, A, Omega, Integr, Result, Info) Debug.Print "S =", Result, "S(true) =", Exp(-1 / 4) * Dconst(17) / 2 Debug.Print "Info =", Info End Sub Example Results S = 0.690194223521571 S(true) = 0.690194223521572 Info = 0