subroutine qawf(f,a,omega,integr,epsabs,result,abserr,neval,ier,
* limlst,lst,leniw,maxp1,lenw,iwork,work)
c***begin prologue qawf
c***date written 800101 (yymmdd)
c***revision date 830518 (yymmdd)
c***category no. h2a3a1
c***keywords automatic integrator, special-purpose,fourier
c integral, integration between zeros with dqawoe,
c convergence acceleration with dqext
c***author piessens,robert ,appl. math. & progr. div. - k.u.leuven
c de doncker,elise,appl. math & progr. div. - k.u.leuven
c***purpose the routine calculates an approximation result to a given
c fourier integral
c i = integral of f(x)*w(x) over (a,infinity)
c where w(x) = cos(omega*x) or w(x) = sin(omega*x).
c hopefully satisfying following claim for accuracy
c abs(i-result).le.epsabs.
c***description
c
c computation of fourier integrals
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 omega - real
c parameter in the integrand weight function
c
c integr - integer
c indicates which of the weight functions is used
c integr = 1 w(x) = cos(omega*x)
c integr = 2 w(x) = sin(omega*x)
c if integr.ne.1.and.integr.ne.2, the routine
c will end with ier = 6.
c
c epsabs - real
c absolute accuracy requested, epsabs.gt.0.
c if epsabs.le.0, 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 if omega.ne.0
c ier = 1 maximum number of cycles allowed
c has been achieved, i.e. of subintervals
c (a+(k-1)c,a+kc) where
c c = (2*int(abs(omega))+1)*pi/abs(omega),
c for k = 1, 2, ..., lst.
c one can allow more cycles by increasing
c the value of limlst (and taking the
c according dimension adjustments into
c account). examine the array iwork which
c contains the error flags on the cycles, in
c order to look for eventual local
c integration difficulties.
c if the position of a local difficulty
c can be 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
c appropriate integrators on the subranges.
c = 4 the extrapolation table constructed for
c convergence accelaration of the series
c formed by the integral contributions over
c the cycles, does not converge to within
c the requested accuracy.
c as in the case of ier = 1, it is advised
c to examine the array iwork which contains
c the error flags on the cycles.
c = 6 the input is invalid because
c (integr.ne.1 and integr.ne.2) or
c epsabs.le.0 or limlst.lt.1 or
c leniw.lt.(limlst+2) or maxp1.lt.1 or
c lenw.lt.(leniw*2+maxp1*25).
c result, abserr, neval, lst are set to
c zero.
c = 7 bad integrand behaviour occurs within
c one or more of the cycles. location and
c type of the difficulty involved can be
c determined from the first lst elements of
c vector iwork. here lst is the number of
c cycles actually needed (see below).
c iwork(k) = 1 the maximum number of
c subdivisions (=(leniw-limlst)
c /2) has been achieved on the
c k th cycle.
c = 2 occurrence of roundoff error
c is detected and prevents the
c tolerance imposed on the k th
c cycle, from being achieved
c on this cycle.
c = 3 extremely bad integrand
c behaviour occurs at some
c points of the k th cycle.
c = 4 the integration procedure
c over the k th cycle does
c not converge (to within the
c required accuracy) due to
c roundoff in the extrapolation
c procedure invoked on this
c cycle. it is assumed that the
c result on this interval is
c the best which can be
c obtained.
c = 5 the integral over the k th
c cycle is probably divergent
c or slowly convergent. it must
c be noted that divergence can
c occur with any other value of
c iwork(k).
c if omega = 0 and integr = 1,
c the integral is calculated by means of dqagie,
c and ier = iwork(1) (with meaning as described
c for iwork(k),k = 1).
c
c dimensioning parameters
c limlst - integer
c limlst gives an upper bound on the number of
c cycles, limlst.ge.3.
c if limlst.lt.3, the routine will end with ier = 6.
c
c lst - integer
c on return, lst indicates the number of cycles
c actually needed for the integration.
c if omega = 0, then lst is set to 1.
c
c leniw - integer
c dimensioning parameter for iwork. on entry,
c (leniw-limlst)/2 equals the maximum number of
c subintervals allowed in the partition of each
c cycle, leniw.ge.(limlst+2).
c if leniw.lt.(limlst+2), the routine will end with
c ier = 6.
c
c maxp1 - integer
c maxp1 gives an upper bound on the number of
c chebyshev moments which can be stored, i.e. for
c the intervals of lengths abs(b-a)*2**(-l),
c l = 0,1, ..., maxp1-2, maxp1.ge.1.
c if maxp1.lt.1, the routine will end with ier = 6.
c lenw - integer
c dimensioning parameter for work
c lenw must be at least leniw*2+maxp1*25.
c if lenw.lt.(leniw*2+maxp1*25), the routine will
c end with ier = 6.
c
c work arrays
c iwork - integer
c vector of dimension at least leniw
c on return, iwork(k) for k = 1, 2, ..., lst
c contain the error flags on the cycles.
c
c work - real
c vector of dimension at least
c on return,
c work(1), ..., work(lst) contain the integral
c approximations over the cycles,
c work(limlst+1), ..., work(limlst+lst) contain
c the error extimates over the cycles.
c further elements of work have no specific
c meaning for the user.
c
c***references (none)
c***routines called qawfe,xerror
c***end prologue qawf
c
real a,abserr,epsabs,f,omega,result,work
integer ier,integr,leniw,limit,limlst,lvl,lst,l1,l2,l3,l4,l5,l6,
* maxp1,neval
c
dimension iwork(leniw),work(lenw)
c
external f
c
c check validity of limlst, leniw, maxp1 and lenw.
c
c***first executable statement qawf
ier = 6
neval = 0
last = 0
result = 0.0e+00
abserr = 0.0e+00
if(limlst.lt.3.or.leniw.lt.(limlst+2).or.maxp1.lt.1.or.lenw.lt.
* (leniw*2+maxp1*25)) go to 10
c
c prepare call for qawfe
c
limit = (leniw-limlst)/2
l1 = limlst+1
l2 = limlst+l1
l3 = limit+l2
l4 = limit+l3
l5 = limit+l4
l6 = limit+l5
ll2 = limit+l1
call qawfe(f,a,omega,integr,epsabs,limlst,limit,maxp1,result,
* abserr,neval,ier,work(1),work(l1),iwork(1),lst,work(l2),
* work(l3),work(l4),work(l5),iwork(l1),iwork(ll2),work(l6))
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 qawf,
* 26,ier,lvl)
return
end