Qagp Qagp_r Qawc Qawc_r Qawo Qawo_r Qaws Qaws_r

Qaws() Sub Qaws ( F As  LongPtr, A As  Double, B As  Double, Alpha As  Double, Beta 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  ) Finite interval adaptive quadrature for singular 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) has algebraic-logarithmic singularities at the end points of an integration region. See parameter Integr. 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] Alpha Parameter α in the weight function. (Alpha > -1) [in] Beta Parameter β in the weight function. (Beta > -1) [in] Integr Indicates the form of weight function w(x) = 1: w(x) = (x - a)^α * (b - x)^β = 2: w(x) = (x - a)^α * (b - x)^β * ln(x - a) = 3: w(x) = (x - a)^α * (b - x)^β * ln(b - x) = 4: w(x) = (x - a)^α * (b - x)^β * ln(x - a) * ln(b - x) [out] Result Approximation to the integral. [out] Info = 0: Successful exit. = -2: The argument A (or B) had an illegal value. (A >= B) = -4: The argument Alpha had an illegal value. (Alpha <= -1) = -5: The argument Beta had an illegal value. (Beta <= -1) = -6: The argument Integr had an illegal value. (Integr < 1 or Integr > 4) = 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 >= 2) (default = 100) (If Limit < 2, 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. ∫ ln(x)/(1 + ln(x)^2)^2 dx [0, 1] (= 0.1892752) Function F4(X As Double) As Double F4 = 0 If X > 0 Then F4 = 1 / (1 + Log(X) ^ 2) ^ 2 End Function Sub Ex_Qaws() Dim A As Double, B As Double, Result As Double, Info As Long Dim Alpha As Double, Beta As Double, Integr As Long A = 0: B = 1 Alpha = 0: Beta = 0: Integr = 2 Call Qaws(AddressOf F4, A, B, Alpha, Beta, Integr, Result, Info) Debug.Print "S =", Result Debug.Print "Info =", Info End Sub Example Results S = -0.189275187882035 Info = 0