QAGIE(3)

SYNOPSIS
SUBROUTINE QAGIE (F, BOUND, INF, EPSABS, EPSREL, LIMIT, RESULT, + ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST)

NAME
qagie - The routine calculates an approximation result to a given integral I = Integral of F over (BOUND,+INFINITY) or I = Integral of F over (-INFINITY,BOUND) or I = Integral of F over (-INFINITY,+INFINITY), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

LIBRARY
SLATEC (QUADPACK)

CATEGORY
H2A3A1, H2A4A1

TYPE
SINGLE PRECISION (QAGIE-S, DQAGIE-D)

KEYWORDS
AUTOMATIC INTEGRATOR, EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE, INFINITE INTERVALS, QUADPACK, QUADRATURE, TRANSFORMATION

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

DESCRIPTION
Integration over infinite intervals Standard fortran subroutine F - Real 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. BOUND - Real Finite bound of integration range (has no meaning if interval is doubly-infinite) INF - Real Indicating the kind of integration range involved INF = 1 corresponds to (BOUND,+INFINITY), INF = -1 to (-INFINITY,BOUND), INF = 2 to (-INFINITY,+INFINITY). EPSABS - Real Absolute accuracy requested EPSREL - Real 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. LIMIT - Integer Gives an upper bound on the number of subintervals in the partition of (A,B), LIMIT.GE.1 ON RETURN RESULT - Real Approximation to the integral ABSERR - Real 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 (and taking the according dimension adjustments into account). However, if this yields no improvement it is 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. The error may be under-estimated. = 3 Extremely bad integrand behaviour occurs at some points of the integration interval. = 4 The algorithm does not converge. Roundoff error is detected in the extrapolation table. It is assumed that the requested tolerance cannot be achieved, and that the returned result is the best which can be obtained. = 5 The integral is probably divergent, or slowly convergent. It must be noted that divergence can occur with any other value of IER. = 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 0 and 1 respectively. ALIST - Real 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 transformed integration range (0,1). BLIST - Real 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 transformed integration range (0,1). RLIST - Real Vector of dimension at least LIMIT, the first LAST elements of which are the integral approximations on the subintervals ELIST - Real 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 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
QELG, QK15I, QPSRT, R1MACH

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)