subroutine qags(f,a,b,epsabs,epsrel,result,abserr,neval,ier,
* limit,lenw,last,iwork,work)
c***begin prologue qags
c***date written 800101 (yymmdd)
c***revision date 830518 (yymmdd)
c***category no. h2a1a1
c***keywords automatic integrator, general-purpose,
c (end-point) singularities, extrapolation,
c globally adaptive
c***author piessens,robert,appl. math. & progr. div. - k.u.leuven
c de doncker,elise,appl. math. & prog. div. - k.u.leuven
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***description
c
c computation of a definite integral
c standard fortran subroutine
c real version
c
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 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 ier = 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. it is presumed that
c the requested tolerance cannot be
c achieved, and that the returned result is
c the best which can be 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 or limit.lt.1 or lenw.lt.limit*4.
c result, abserr, neval, last are set to
c zero.except when limit or lenw 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 subintervals
c in the partition of the given integration interval
c (a,b), limit.ge.1.
c if limit.lt.1, 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 subintervals
c produced in the subdivision process, detemines the
c number of significant elements actually in the work
c arrays.
c
c work arrays
c iwork - integer
c vector of dimension at least 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 at least 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) contain
c the integral approximations over the subintervals,
c work(limit*3+1), ..., work(limit*3+last)
c contain the error estimates.
c
c
c
c***references (none)
c***routines called qagse,xerror
c***end prologue qags
c
c
real a,abserr,b,epsabs,epsrel,f,result,work
integer ier,iwork,lenw,limit,lvl,l1,l2,l3,neval
c
dimension iwork(limit),work(lenw)
c
external f
c
c check validity of limit and lenw.
c
c***first executable statement qags
ier = 6
neval = 0
last = 0
result = 0.0e+00
abserr = 0.0e+00
if(limit.lt.1.or.lenw.lt.limit*4) go to 10
c
c prepare call for qagse.
c
l1 = limit+1
l2 = limit+l1
l3 = limit+l2
c
call qagse(f,a,b,epsabs,epsrel,limit,result,abserr,neval,
* ier,work(1),work(l1),work(l2),work(l3),iwork,last)
c
c call error handler if necessary.
c
lvl = 0
10 if(ier.eq.6) lvl = 1
if(ier.ne.0) call xerror(26habnormal return from qags,
* 26,ier,lvl)
return
end