SLATEC Routines --- QAWSE ---

```*DECK QAWSE
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***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***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
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