SLATEC Routines --- QC25S ---

*DECK QC25S
      SUBROUTINE QC25S (F, A, B, BL, BR, ALFA, BETA, RI, RJ, RG, RH,
     +   RESULT, ABSERR, RESASC, INTEGR, NEV)
C***BEGIN PROLOGUE  QC25S
C***PURPOSE  To compute I = Integral of F*W over (BL,BR), with error
C            estimate, where the weight function W has a singular
C            behaviour of ALGEBRAICO-LOGARITHMIC type at the points
C            A and/or B. (BL,BR) is a part of (A,B).
C***LIBRARY   SLATEC (QUADPACK)
C***CATEGORY  H2A2A2
C***TYPE      SINGLE PRECISION (QC25S-S, DQC25S-D)
C***KEYWORDS  25-POINT CLENSHAW-CURTIS INTEGRATION, QUADPACK, QUADRATURE
C***AUTHOR  Piessens, Robert
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C           de Doncker, Elise
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C***DESCRIPTION
C
C        Integration rules for integrands having ALGEBRAICO-LOGARITHMIC
C        end point singularities
C        Standard fortran subroutine
C        Real version
C
C        PARAMETERS
C           F      - Real
C                    Function subprogram defining the integrand
C                    F(X). The actual name for F needs to be declared
C                    E X T E R N A L  in the driver program.
C
C           A      - Real
C                    Left end point of the original interval
C
C           B      - Real
C                    Right end point of the original interval, B.GT.A
C
C           BL     - Real
C                    Lower limit of integration, BL.GE.A
C
C           BR     - Real
C                    Upper limit of integration, BR.LE.B
C
C           ALFA   - Real
C                    PARAMETER IN THE WEIGHT FUNCTION
C
C           BETA   - Real
C                    Parameter in the weight function
C
C           RI,RJ,RG,RH - Real
C                    Modified CHEBYSHEV moments for the application
C                    of the generalized CLENSHAW-CURTIS
C                    method (computed in subroutine DQMOMO)
C
C           RESULT - Real
C                    Approximation to the integral
C                    RESULT is computed by using a generalized
C                    CLENSHAW-CURTIS method if B1 = A or BR = B.
C                    in all other cases the 15-POINT KRONROD
C                    RULE is applied, obtained by optimal addition of
C                    Abscissae to the 7-POINT GAUSS RULE.
C
C           ABSERR - Real
C                    Estimate of the modulus of the absolute error,
C                    which should equal or exceed ABS(I-RESULT)
C
C           RESASC - Real
C                    Approximation to the integral of ABS(F*W-I/(B-A))
C
C           INTEGR - Integer
C                    Which determines the weight function
C                    = 1   W(X) = (X-A)**ALFA*(B-X)**BETA
C                    = 2   W(X) = (X-A)**ALFA*(B-X)**BETA*LOG(X-A)
C                    = 3   W(X) = (X-A)**ALFA*(B-X)**BETA*LOG(B-X)
C                    = 4   W(X) = (X-A)**ALFA*(B-X)**BETA*LOG(X-A)*
C                                 LOG(B-X)
C
C           NEV    - Integer
C                    Number of integrand evaluations
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  QCHEB, QK15W, QWGTS
C***REVISION HISTORY  (YYMMDD)
C   810101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890531  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  QC25S