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fvn_integ/dqag_2d_outer.f
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! fvn comment :
! Modified version of the dqag quadpack routine from http://www.netlib.org/quadpack
!
! + The call to xerror is replaced by a simple write(*,*)
! + The external 'f' function is a 2 parameters function f(x,y). The routine
! takes two more parameters 'g' and 'h' which are two external functions :
! g represent the lower bound of the integral for y parameter
! h represent the higher bound of the integral for y parameter
! The routine compute the double integral of function f with x between a and b
! and y between g(x) and h(x)
subroutine dqag_2d_outer(f,a,b,g,h,epsabs,epsrel,key,result, &
abserr,neval,ier,limit,lenw,last,iwork,work)
!***begin prologue dqag
!***date written 800101 (yymmdd)
!***revision date 830518 (yymmdd)
!***category no. h2a1a1
!***keywords automatic integrator, general-purpose,
! integrand examinator, globally adaptive,
! gauss-kronrod
!***author piessens,robert,appl. math. & progr. div - k.u.leuven
! de doncker,elise,appl. math. & progr. div. - k.u.leuven
!***purpose 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-result)le.max(epsabs,epsrel*abs(i)).
!***description
!
! computation of a definite integral
! standard fortran subroutine
! double precision version
!
! f - double precision
! function subprogam 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 accoracy 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.
!
! 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 (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.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))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
!
! dimensioning parameters
! limit - integer
! dimensioning parameter for iwork
! limit determines the maximum number of subintervals
! in the partition of the given integration interval
! (a,b), limit.ge.1.
! if limit.lt.1, the routine will end with ier = 6.
!
! lenw - integer
! dimensioning parameter for work
! lenw must be at least limit*4.
! if lenw.lt.limit*4, the routine will end with
! ier = 6.
!
! last - integer
! on return, last equals the number of subintervals
! produced in the subdiviosion process, which
! determines the number of significant elements
! actually in the work arrays.
!
! work arrays
! iwork - integer
! vector of dimension at least limit, the first k
! elements of which contain pointers to the error
! estimates over the subintervals, such that
! work(limit*3+iwork(1)),... , work(limit*3+iwork(k))
! form a decreasing sequence with k = last if
! last.le.(limit/2+2), and k = limit+1-last otherwise
!
! work - double precision
! vector of dimension at least lenw
! on return
! work(1), ..., work(last) contain the left end
! points of the subintervals in the partition of
! (a,b),
! work(limit+1), ..., work(limit+last) contain the
! right end points,
! work(limit*2+1), ..., work(limit*2+last) contain
! the integral approximations over the subintervals,
! work(limit*3+1), ..., work(limit*3+last) contain
! the error estimates.
!
!***references (none)
!***routines called dqage,xerror
!***end prologue dqag
double precision a,abserr,b,epsabs,epsrel,result,work
integer ier,iwork,key,last,lenw,limit,lvl,l1,l2,l3,neval
!
dimension iwork(limit),work(lenw)
!
double precision,external :: f,g,h
!
! check validity of lenw.
!
!***first executable statement dqag
ier = 6
neval = 0
last = 0
result = 0.0d+00
abserr = 0.0d+00
if(limit.lt.1.or.lenw.lt.limit*4) go to 10
!
! prepare call for dqage.
!
l1 = limit+1
l2 = limit+l1
l3 = limit+l2
!
call dqage_2d_outer(f,a,b,g,h,epsabs,epsrel,key,limit, &
result,abserr,neval,ier,work(1),work(l1),work(l2), &
work(l3),iwork,last)
!
! call error handler if necessary.
!
lvl = 0
10 if(ier.eq.6) lvl = 1
! if(ier.ne.0) call xerror(26habnormal return from dqag ,26,ier,lvl)
! we use a simple write for error
if (ier.ne.0) then
write(*,*) "Abnormal return from dqag_2d_outer"
write(*,*) "ier=",ier
end if
return
end subroutine
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