# qawse.f

          SUBROUTINE QAWSE (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL,
         +   LIMIT, RESULT, ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST,
         +   IORD, LAST)
    C***BEGIN PROLOGUE  QAWSE
    C***PURPOSE  The routine calculates an approximation result to a given
    C            definite integral I = Integral of F*W over (A,B),
    C            (where W shows a singular behaviour at the end points,
    C            see parameter INTEGR).
    C            Hopefully satisfying following claim for accuracy
    C            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
    C***LIBRARY   SLATEC (QUADPACK)
    C***CATEGORY  H2A2A1
    C***TYPE      SINGLE PRECISION (QAWSE-S, DQAWSE-D)
    C***KEYWORDS  ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES,
    C             AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD, QUADPACK,
    C             QUADRATURE, SPECIAL-PURPOSE
    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 of functions having algebraico-logarithmic
    C        end point singularities
    C        Standard fortran subroutine
    C        Real version
    C
    C        PARAMETERS
    C         ON ENTRY
    C            F      - Real
    C                     Function subprogram defining the integrand
    C                     function F(X). The actual name for F needs to be
    C                     declared E X T E R N A L in the driver program.
    C
    C            A      - Real
    C                     Lower limit of integration
    C
    C            B      - Real
    C                     Upper limit of integration, B.GT.A
    C                     If B.LE.A, the routine will end with IER = 6.
    C
    C            ALFA   - Real
    C                     Parameter in the WEIGHT function, ALFA.GT.(-1)
    C                     If ALFA.LE.(-1), the routine will end with
    C                     IER = 6.
    C
    C            BETA   - Real
    C                     Parameter in the WEIGHT function, BETA.GT.(-1)
    C                     If BETA.LE.(-1), the routine will end with
    C                     IER = 6.
    C
    C            INTEGR - Integer
    C                     Indicates which WEIGHT function is to be used
    C                     = 1  (X-A)**ALFA*(B-X)**BETA
    C                     = 2  (X-A)**ALFA*(B-X)**BETA*LOG(X-A)
    C                     = 3  (X-A)**ALFA*(B-X)**BETA*LOG(B-X)
    C                     = 4  (X-A)**ALFA*(B-X)**BETA*LOG(X-A)*LOG(B-X)
    C                     If INTEGR.LT.1 or INTEGR.GT.4, the routine
    C                     will end with IER = 6.
    C
    C            EPSABS - Real
    C                     Absolute accuracy requested
    C            EPSREL - Real
    C                     Relative accuracy requested
    C                     If  EPSABS.LE.0
    C                     and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
    C                     the routine will end with IER = 6.
    C
    C            LIMIT  - Integer
    C                     Gives an upper bound on the number of subintervals
    C                     in the partition of (A,B), LIMIT.GE.2
    C                     If LIMIT.LT.2, the routine will end with IER = 6.
    C
    C         ON RETURN
    C            RESULT - Real
    C                     Approximation to the integral
    C
    C            ABSERR - Real
    C                     Estimate of the modulus of the absolute error,
    C                     which should equal or exceed ABS(I-RESULT)
    C
    C            NEVAL  - Integer
    C                     Number of integrand evaluations
    C
    C            IER    - Integer
    C                     IER = 0 Normal and reliable termination of the
    C                             routine. It is assumed that the requested
    C                             accuracy has been achieved.
    C                     IER.GT.0 Abnormal termination of the routine
    C                             the estimates for the integral and error
    C                             are less reliable. It is assumed that the
    C                             requested accuracy has not been achieved.
    C            ERROR MESSAGES
    C                         = 1 Maximum number of subdivisions allowed
    C                             has been achieved. One can allow more
    C                             subdivisions by increasing the value of
    C                             LIMIT. However, if this yields no
    C                             improvement, it is advised to analyze the
    C                             integrand in order to determine the
    C                             integration difficulties which prevent the
    C                             requested tolerance from being achieved.
    C                             In case of a jump DISCONTINUITY or a local
    C                             SINGULARITY of algebraico-logarithmic type
    C                             at one or more interior points of the
    C                             integration range, one should proceed by
    C                             splitting up the interval at these
    C                             points and calling the integrator on the
    C                             subranges.
    C                         = 2 The occurrence of roundoff error is
    C                             detected, which prevents the requested
    C                             tolerance from being achieved.
    C                         = 3 Extremely bad integrand behaviour occurs
    C                             at some points of the integration
    C                             interval.
    C                         = 6 The input is invalid, because
    C                             B.LE.A or ALFA.LE.(-1) or BETA.LE.(-1), or
    C                             INTEGR.LT.1 or INTEGR.GT.4, or
    C                             (EPSABS.LE.0 and
    C                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
    C                             or LIMIT.LT.2.
    C                             RESULT, ABSERR, NEVAL, RLIST(1), ELIST(1),
    C                             IORD(1) and LAST are set to zero. ALIST(1)
    C                             and BLIST(1) are set to A and B
    C                             respectively.
    C
    C            ALIST  - Real
    C                     Vector of dimension at least LIMIT, the first
    C                      LAST  elements of which are the left
    C                     end points of the subintervals in the partition
    C                     of the given integration range (A,B)
    C
    C            BLIST  - Real
    C                     Vector of dimension at least LIMIT, the first
    C                      LAST  elements of which are the right
    C                     end points of the subintervals in the partition
    C                     of the given integration range (A,B)
    C
    C            RLIST  - Real
    C                     Vector of dimension at least LIMIT, the first
    C                      LAST  elements of which are the integral
    C                     approximations on the subintervals
    C
    C            ELIST  - Real
    C                     Vector of dimension at least LIMIT, the first
    C                      LAST  elements of which are the moduli of the
    C                     absolute error estimates on the subintervals
    C
    C            IORD   - Integer
    C                     Vector of dimension at least LIMIT, the first K
    C                     of which are pointers to the error
    C                     estimates over the subintervals, so that
    C                     ELIST(IORD(1)), ..., ELIST(IORD(K)) with K = LAST
    C                     If LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST
    C                     otherwise form a decreasing sequence
    C
    C            LAST   - Integer
    C                     Number of subintervals actually produced in
    C                     the subdivision process
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  QC25S, QMOMO, QPSRT, R1MACH
    C***REVISION HISTORY  (YYMMDD)
    C   800101  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890831  Modified array declarations.  (WRB)
    C   890831  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C***END PROLOGUE  QAWSE