Qagp Qagp_r Qawc Qawc_r Qawo Qawo_r Qaws Qaws_r

Qawo() Sub Qawo ( F As  LongPtr, A As  Double, B 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 EpsRel As  Double = -1, Optional Limit As  Long = -1, Optional Last As  Long, Optional Maxp1 As  Long = -1  ) Finite interval adaptive quadrature for oscillatory functions (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) Purpose The routine calculates an approximation result to a definite integral I = integral of f(x)*w(x) over [a, b] satisfying the requested accuracy, where the weight function w(x) = cos(ω*x) or sin(ω*x). Result is obtained by the adaptive integration applying a 25-point modified Clenshaw-Curtis rule and a 15-point Gauss-Kronrod rule to satisfy the requested accuracy. 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] B Upper limit of integration b. [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. = -5: The argument Integr had an illegal value. (Integr <> 1 and Integr <> 2) = 1: Maximum number of subdivisions allowed has been reached. = 2: Requested tolerance cannot be achieved due to roundoff error. = 3: Bad integrand behavior found in the integration interval. = 4: Algorithm does not converge due to the roundoff error in the extrapolation table. = 5: The integral is probably divergent, or slowly convergent. [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. (default = 0) The requested accuracy is assumed to be satisfied if AbsErr <= max(EpsAbs, EpsRel*|Result|)) (If EpsAbs < 0, the default value will be used) [in] EpsRel (Optional) Relative accuracy requested. (default = 1.0e-12) The requested accuracy is assumed to be satisfied if AbsErr <= max(EpsAbs, EpsRel*|Result|)) If EpsAbs <= 0 and EpsRel < 50*eps, EpsRel is assumed to be 50*eps, where eps is the machine precision. (If EpsRel < 0, the default value will be used) [in] Limit (Optional) Maximum number of subintervals in the partition of the given integration interval [a, b] (limit >= 1) (default = 100) (If Limit < 1, the default value will be used) [out] Last (Optional) Number of subintervals produced in the subdivision process. [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. ∫ ln(x)sin(10πx) dx [0, 1] (= -0.1281368) Function F5(X As Double) As Double F5 = 0 If X > 0 Then F5 = Log(X) End Function Sub Ex_Qawo() Dim A As Double, B As Double, Result As Double, Info As Long Dim Omega As Double, Integr As Long A = 0: B = 1 Omega = 10 * Dconst(13) '10*π Integr = 2 Call Qawo(AddressOf F5, A, B, Omega, Integr, Result, Info) Debug.Print "S =", Result Debug.Print "Info =", Info End Sub Example Results S = -0.128136848399167 Info = 0