Qagp Qagp_r Qawc Qawc_r Qawo Qawo_r Qaws Qaws_r

Qawo_r() Sub Qawo_r ( A As  Double, B As  Double, Omega As  Double, Integr As  Long, Result As  Double, Info As  Long, XX As  Double, YY As  Double, IRev 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) (reverse communication version) 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] 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] XX When returned with IRev = 1, XX contains the abscissa where the function value should be evaluated and given in the next call. [in] YY When returned with IRev = 1, the function value should be given in YY in the next call. [in,out] IRev Control variable for reverse communication. [in] Before first call, IRev should be initialized to zero. On succeeding calls, IRev should not be altered. [out] If IRev is not zero, complete the following tasks and call this routine again without changing IRev. = 0: Computation finished. See return code in Info. = 1: User should set the function values at XX in YY. Do not alter any variables other than YY. [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) Sub Ex_Qawo_r() Dim A As Double, B As Double, Result As Double, Info As Long Dim Omega As Double, Integr As Long Dim XX As Double, YY As Double, IRev As Long A = 0: B = 1 Omega = 10 * Dconst(13) '10*π Integr = 2 IRev = 0 Do Call Qawo_r(A, B, Omega, Integr, Result, Info, XX, YY, IRev) If IRev = 1 Then YY = 0 If XX > 0 Then YY = Log(XX) End If Loop While IRev <> 0 Debug.Print "S =", Result Debug.Print "Info =", Info End Sub Example Results S = -0.128136848399167 Info = 0