SLATEC Routines --- QAGE ---
*DECK QAGE
SUBROUTINE QAGE (F, A, B, EPSABS, EPSREL, KEY, LIMIT, RESULT,
+ ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST)
C***BEGIN PROLOGUE QAGE
C***PURPOSE The routine calculates an approximation result to a given
C definite integral I = Integral of F over (A,B),
C hopefully satisfying following claim for accuracy
C ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A1A1
C***TYPE SINGLE PRECISION (QAGE-S, DQAGE-D)
C***KEYWORDS AUTOMATIC INTEGRATOR, GAUSS-KRONROD RULES,
C GENERAL-PURPOSE, GLOBALLY ADAPTIVE, INTEGRAND EXAMINATOR,
C 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 Computation of a definite integral
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
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 KEY - Integer
C Key for choice of local integration rule
C A Gauss-Kronrod pair is used with
C 7 - 15 points if KEY.LT.2,
C 10 - 21 points if KEY = 2,
C 15 - 31 points if KEY = 3,
C 20 - 41 points if KEY = 4,
C 25 - 51 points if KEY = 5,
C 30 - 61 points if KEY.GT.5.
C
C LIMIT - Integer
C Gives an upper bound on the number of subintervals
C in the partition of (A,B), LIMIT.GE.1.
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 result and error are
C 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
C of LIMIT.
C However, if this yields no improvement it
C is rather advised to analyze the integrand
C in order to determine the integration
C difficulties. If the position of a local
C difficulty can be determined(e.g.
C SINGULARITY, DISCONTINUITY within the
C interval) one will probably gain from
C splitting up the interval at this point
C and calling the integrator on the
C subranges. If possible, an appropriate
C special-purpose integrator should be used
C which is designed for handling the type of
C difficulty involved.
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 (EPSABS.LE.0 and
C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
C RESULT, ABSERR, NEVAL, LAST, RLIST(1) ,
C ELIST(1) and IORD(1) are set to zero.
C ALIST(1) 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
C integral 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 elements of which are pointers to the
C error estimates over the subintervals,
C such that ELIST(IORD(1)), ...,
C ELIST(IORD(K)) form a decreasing sequence,
C with K = LAST if LAST.LE.(LIMIT/2+2), and
C K = LIMIT+1-LAST otherwise
C
C LAST - Integer
C Number of subintervals actually produced in the
C subdivision process
C
C***REFERENCES (NONE)
C***ROUTINES CALLED QK15, QK21, QK31, QK41, QK51, QK61, 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 QAGE