DQAGE(3)

SYNOPSIS
SUBROUTINE DQAGE (F, A, B, EPSABS, EPSREL, KEY, LIMIT, RESULT, + ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST)

NAME
dqage - The routine calculates an approximation result to a given definite integral I = Integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

LIBRARY
SLATEC (QUADPACK)

CATEGORY
H2A1A1

TYPE
DOUBLE PRECISION (QAGE-S, DQAGE-D)

KEYWORDS
AUTOMATIC INTEGRATOR, GAUSS-KRONROD RULES, GENERAL-PURPOSE, GLOBALLY ADAPTIVE, INTEGRAND EXAMINATOR, QUADPACK, QUADRATURE

AUTHOR
Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven

DESCRIPTION
Computation of a definite integral Standard fortran subroutine Double precision version PARAMETERS ON ENTRY F - Double precision Function subprogram defining the integrand function F(X). The actual name for F needs to be declared E X T E R N A L in the driver program. A - Double precision Lower limit of integration B - Double precision Upper limit of integration EPSABS - Double precision Absolute accuracy requested EPSREL - Double precision Relative accuracy requested If EPSABS.LE.0 and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), the routine will end with IER = 6. KEY - Integer Key for choice of local integration rule A Gauss-Kronrod pair is used with 7 - 15 points if KEY.LT.2, 10 - 21 points if KEY = 2, 15 - 31 points if KEY = 3, 20 - 41 points if KEY = 4, 25 - 51 points if KEY = 5, 30 - 61 points if KEY.GT.5. LIMIT - Integer Gives an upper bound on the number of subintervals in the partition of (A,B), LIMIT.GE.1. ON RETURN RESULT - Double precision Approximation to the integral ABSERR - Double precision Estimate of the modulus of the absolute error, which should equal or exceed ABS(I-RESULT) NEVAL - Integer Number of integrand evaluations IER - Integer IER = 0 Normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. IER.GT.0 Abnormal termination of the routine The estimates for result and error are less reliable. It is assumed that the requested accuracy has not been achieved. ERROR MESSAGES IER = 1 Maximum number of subdivisions allowed has been achieved. One can allow more subdivisions by increasing the value of LIMIT. However, if this yields no improvement it is rather advised to analyze the integrand in order to determine the integration difficulties. If the position of a local difficulty can be determined(e.g. SINGULARITY, DISCONTINUITY within the interval) one will probably gain from splitting up the interval at this point and calling the integrator on the subranges. If possible, an appropriate special-purpose integrator should be used which is designed for handling the type of difficulty involved. = 2 The occurrence of roundoff error is detected, which prevents the requested tolerance from being achieved. = 3 Extremely bad integrand behaviour occurs at some points of the integration interval. = 6 The input is invalid, because (EPSABS.LE.0 and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), RESULT, ABSERR, NEVAL, LAST, RLIST(1) , ELIST(1) and IORD(1) are set to zero. ALIST(1) and BLIST(1) are set to A and B respectively. ALIST - Double precision Vector of dimension at least LIMIT, the first LAST elements of which are the left end points of the subintervals in the partition of the given integration range (A,B) BLIST - Double precision Vector of dimension at least LIMIT, the first LAST elements of which are the right end points of the subintervals in the partition of the given integration range (A,B) RLIST - Double precision Vector of dimension at least LIMIT, the first LAST elements of which are the integral approximations on the subintervals ELIST - Double precision Vector of dimension at least LIMIT, the first LAST elements of which are the moduli of the absolute error estimates on the subintervals IORD - Integer Vector of dimension at least LIMIT, the first K elements of which are pointers to the error estimates over the subintervals, such that ELIST(IORD(1)), ..., ELIST(IORD(K)) form a decreasing sequence, with K = LAST if LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST otherwise LAST - Integer Number of subintervals actually produced in the subdivision process

REFERENCES
(NONE)

ROUTINES CALLED
D1MACH, DQK15, DQK21, DQK31, DQK41, DQK51, DQK61, DQPSRT

REVISION HISTORY (YYMMDD)
800101 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)