SLATEC Routines --- QAGSE ---
*DECK QAGSE
SUBROUTINE QAGSE (F, A, B, EPSABS, EPSREL, LIMIT, RESULT, ABSERR,
+ NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST)
C***BEGIN PROLOGUE QAGSE
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-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A1A1
C***TYPE SINGLE PRECISION (QAGSE-S, DQAGSE-D)
C***KEYWORDS AUTOMATIC INTEGRATOR, END POINT SINGULARITIES,
C EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE,
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 LIMIT - Integer
C Gives an upper bound on the number of subintervals
C in the partition of (A,B)
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 integral and error are
C 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 sub-
C divisions by increasing the value of LIMIT
C (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. If
C the position of a local difficulty can be
C determined (e.g. singularity,
C discontinuity within the interval) one
C will probably gain from splitting up the
C interval at this point and calling the
C integrator on the subranges. If possible,
C an appropriate special-purpose integrator
C should be used, which is designed for
C handling the type of difficulty involved.
C = 2 The occurrence of roundoff error is detec-
C ted, which prevents the requested
C tolerance from being achieved.
C The error may be under-estimated.
C = 3 Extremely bad integrand behaviour
C occurs at some points of the integration
C interval.
C = 4 The algorithm does not converge.
C Roundoff error is detected in the
C extrapolation table.
C It is presumed that the requested
C tolerance cannot be achieved, and that the
C returned result is the best which can be
C obtained.
C = 5 The integral is probably divergent, or
C slowly convergent. It must be noted that
C divergence can occur with any other value
C of IER.
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 IORD(1) and ELIST(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 end points
C of the subintervals in the partition of the
C 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 end points
C of the subintervals in the partition of the given
C 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 elements of which are pointers to the
C error estimates over the subintervals,
C such that ELIST(IORD(1)), ..., ELIST(IORD(K))
C form a decreasing sequence, with K = LAST
C If LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST
C otherwise
C
C LAST - Integer
C Number of subintervals actually produced in the
C subdivision process
C
C***REFERENCES (NONE)
C***ROUTINES CALLED QELG, QK21, 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 QAGSE