Qagp Qagp_r Qawc Qawc_r Qawo Qawo_r Qaws Qaws_r

Qawc() Sub Qawc ( F As  LongPtr, A As  Double, B As  Double, C As  Double, 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  ) Finite interval adaptive quadrature for Cauchy principal values (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) Purpose The routine calculates an approximation result to a Cauchy principal value I = integral of f(x)*w(x) over [a, b] satisfying the requested accuracy, where the weight function w(x) = 1/(x - c). 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] C Parameter in the weight function. (C <> A and C <> B) [out] Result Cauchy principal value of the integral of f(x)/(x - c) over [a, b] [out] Info = 0: Successful exit. = -4: The argument C had an illegal value. (C = A or C = B) = 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. [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. Reference SLATEC (QUADPACK) Example Program Compute the following integral. ∫ 1/(x*(5*x^3 + 6)) dx [-1, 5] (= -0.08994401) Function F3(X As Double) As Double F3 = 1 / (5 * X ^ 3 + 6) End Function Sub Ex_Qawc() Dim A As Double, B As Double, C As Double, Result As Double, Info As Long A = -1: B = 5: C = 0 Call Qawc(AddressOf F3, A, B, C, Result, Info) Debug.Print "S =", Result Debug.Print "Info =", Info End Sub Example Results S = -8.99440069577173E-02 Info = 0