SLATEC Routines --- QAWS ---
*DECK QAWS
SUBROUTINE QAWS (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL,
+ RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
C***BEGIN PROLOGUE QAWS
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 (QAWS-S, DQAWS-D)
C***KEYWORDS ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES,
C AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD,
C GLOBALLY ADAPTIVE, QUADPACK, 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 integrand 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 integrand 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 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 IER = 1 Maximum number of subdivisions allowed
C has been achieved. One can allow more
C subdivisions by increasing the value of
C LIMIT (and taking the according dimension
C adjustments into account). However, if
C this yields no improvement it is advised
C to analyze the integrand, in order to
C determine the integration difficulties
C which prevent the requested tolerance from
C being achieved. In case of a jump
C discontinuity or a local singularity
C of algebraico-logarithmic type at one or
C more interior points of the integration
C range, one should proceed by splitting up
C the interval at these points and calling
C the integrator on the 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 or 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 or LENW.LT.LIMIT*4.
C RESULT, ABSERR, NEVAL, LAST are set to
C zero. Except when LENW or LIMIT is invalid
C IWORK(1), WORK(LIMIT*2+1) and
C WORK(LIMIT*3+1) are set to zero, WORK(1)
C is set to A and WORK(LIMIT+1) to B.
C
C DIMENSIONING PARAMETERS
C LIMIT - Integer
C Dimensioning parameter for IWORK
C LIMIT determines the maximum number of
C subintervals in the partition of the given
C integration interval (A,B), LIMIT.GE.2.
C If LIMIT.LT.2, the routine will end with IER = 6.
C
C LENW - Integer
C Dimensioning parameter for WORK
C LENW must be at least LIMIT*4.
C If LENW.LT.LIMIT*4, the routine will end
C with IER = 6.
C
C LAST - Integer
C On return, LAST equals the number of
C subintervals produced in the subdivision process,
C which determines the significant number of
C elements actually in the WORK ARRAYS.
C
C WORK ARRAYS
C IWORK - Integer
C Vector of dimension LIMIT, the first K
C elements of which contain pointers
C to the error estimates over the subintervals,
C such that WORK(LIMIT*3+IWORK(1)), ...,
C WORK(LIMIT*3+IWORK(K)) form a decreasing
C sequence with K = LAST if LAST.LE.(LIMIT/2+2),
C and K = LIMIT+1-LAST otherwise
C
C WORK - Real
C Vector of dimension LENW
C On return
C WORK(1), ..., WORK(LAST) contain the left
C end points of the subintervals in the
C partition of (A,B),
C WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
C the right end points,
C WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST)
C contain the integral approximations over
C the subintervals,
C WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
C contain the error estimates.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED QAWSE, XERMSG
C***REVISION HISTORY (YYMMDD)
C 800101 DATE WRITTEN
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 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C***END PROLOGUE QAWS