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subroutine dqawse(f,a,b,alfa,beta,integr,epsabs,epsrel,limit,
* result,abserr,neval,ier,alist,blist,rlist,elist,iord,last)
c***begin prologue dqawse
c***date written 800101 (yymmdd)
c***revision date 830518 (yymmdd)
c***category no. h2a2a1
c***keywords automatic integrator, special-purpose,
c algebraico-logarithmic end point singularities,
c clenshaw-curtis method
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 definite integral i = integral of f*w over (a,b),
c (where w shows a singular behaviour at the end points,
c see parameter integr).
c hopefully satisfying following claim for accuracy
c abs(i-result).le.max(epsabs,epsrel*abs(i)).
c***description
c
c integration of functions having algebraico-logarithmic
c end point singularities
c standard fortran subroutine
c double precision version
c***references (none)
c***routines called d1mach,dqc25s,dqmomo,dqpsrt
c***end prologue dqawse
c
double precision a,abserr,alfa,alist,area,area1,area12,area2,a1,
* a2,b,beta,blist,b1,b2,centre,dabs,dmax1,d1mach,elist,epmach,
* epsabs,epsrel,errbnd,errmax,error1,erro12,error2,errsum,f,
* resas1,resas2,result,rg,rh,ri,rj,rlist,uflow
integer ier,integr,iord,iroff1,iroff2,k,last,limit,maxerr,nev,
* neval,nrmax
c
external f
c
dimension alist(limit),blist(limit),rlist(limit),elist(limit),
* iord(limit),ri(25),rj(25),rh(25),rg(25)
c
c list of major variables
c -----------------------
c
c
c***first executable statement dqawse
epmach = d1mach(4)
uflow = d1mach(1)
c
c test on validity of parameters
c ------------------------------
c
ier = 6
neval = 0
last = 0
rlist(1) = 0.0d+00
elist(1) = 0.0d+00
iord(1) = 0
result = 0.0d+00
abserr = 0.0d+00
if(b.le.a.or.(epsabs.eq.0.0d+00.and.
* epsrel.lt.dmax1(0.5d+02*epmach,0.5d-28)).or.alfa.le.(-0.1d+01)
* .or.beta.le.(-0.1d+01).or.integr.lt.1.or.integr.gt.4.or.
* limit.lt.2) go to 999
ier = 0
c
c compute the modified chebyshev moments.
c
call dqmomo(alfa,beta,ri,rj,rg,rh,integr)
c
c integrate over the intervals (a,(a+b)/2) and ((a+b)/2,b).
c
centre = 0.5d+00*(b+a)
call dqc25s(f,a,b,a,centre,alfa,beta,ri,rj,rg,rh,area1,
* error1,resas1,integr,nev)
neval = nev
call dqc25s(f,a,b,centre,b,alfa,beta,ri,rj,rg,rh,area2,
* error2,resas2,integr,nev)
last = 2
neval = neval+nev
result = area1+area2
abserr = error1+error2
c
c test on accuracy.
c
errbnd = dmax1(epsabs,epsrel*dabs(result))
c
c initialization
c --------------
c
if(error2.gt.error1) go to 10
alist(1) = a
alist(2) = centre
blist(1) = centre
blist(2) = b
rlist(1) = area1
rlist(2) = area2
elist(1) = error1
elist(2) = error2
go to 20
10 alist(1) = centre
alist(2) = a
blist(1) = b
blist(2) = centre
rlist(1) = area2
rlist(2) = area1
elist(1) = error2
elist(2) = error1
20 iord(1) = 1
iord(2) = 2
if(limit.eq.2) ier = 1
if(abserr.le.errbnd.or.ier.eq.1) go to 999
errmax = elist(1)
maxerr = 1
nrmax = 1
area = result
errsum = abserr
iroff1 = 0
iroff2 = 0
c
c main do-loop
c ------------
c
do 60 last = 3,limit
c
c bisect the subinterval with largest error estimate.
c
a1 = alist(maxerr)
b1 = 0.5d+00*(alist(maxerr)+blist(maxerr))
a2 = b1
b2 = blist(maxerr)
c
call dqc25s(f,a,b,a1,b1,alfa,beta,ri,rj,rg,rh,area1,
* error1,resas1,integr,nev)
neval = neval+nev
call dqc25s(f,a,b,a2,b2,alfa,beta,ri,rj,rg,rh,area2,
* error2,resas2,integr,nev)
neval = neval+nev
c
c improve previous approximations integral and error
c and test for accuracy.
c
area12 = area1+area2
erro12 = error1+error2
errsum = errsum+erro12-errmax
area = area+area12-rlist(maxerr)
if(a.eq.a1.or.b.eq.b2) go to 30
if(resas1.eq.error1.or.resas2.eq.error2) go to 30
c
c test for roundoff error.
c
if(dabs(rlist(maxerr)-area12).lt.0.1d-04*dabs(area12)
* .and.erro12.ge.0.99d+00*errmax) iroff1 = iroff1+1
if(last.gt.10.and.erro12.gt.errmax) iroff2 = iroff2+1
30 rlist(maxerr) = area1
rlist(last) = area2
c
c test on accuracy.
c
errbnd = dmax1(epsabs,epsrel*dabs(area))
if(errsum.le.errbnd) go to 35
c
c set error flag in the case that the number of interval
c bisections exceeds limit.
c
if(last.eq.limit) ier = 1
c
c
c set error flag in the case of roundoff error.
c
if(iroff1.ge.6.or.iroff2.ge.20) ier = 2
c
c set error flag in the case of bad integrand behaviour
c at interior points of integration range.
c
if(dmax1(dabs(a1),dabs(b2)).le.(0.1d+01+0.1d+03*epmach)*
* (dabs(a2)+0.1d+04*uflow)) ier = 3
c
c append the newly-created intervals to the list.
c
35 if(error2.gt.error1) go to 40
alist(last) = a2
blist(maxerr) = b1
blist(last) = b2
elist(maxerr) = error1
elist(last) = error2
go to 50
40 alist(maxerr) = a2
alist(last) = a1
blist(last) = b1
rlist(maxerr) = area2
rlist(last) = area1
elist(maxerr) = error2
elist(last) = error1
c
c call subroutine dqpsrt to maintain the descending ordering
c in the list of error estimates and select the subinterval
c with largest error estimate (to be bisected next).
c
50 call dqpsrt(limit,last,maxerr,errmax,elist,iord,nrmax)
c ***jump out of do-loop
if (ier.ne.0.or.errsum.le.errbnd) go to 70
60 continue
c
c compute final result.
c ---------------------
c
70 result = 0.0d+00
do 80 k=1,last
result = result+rlist(k)
80 continue
abserr = errsum
999 return
end
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