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***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