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C/MEMBR ADD NAME=EPSALG,SSI=0
subroutine epsalg(n, epstab, result, abserr, res3la, nres)
c
c based on quadpack routine epsalg
c ******************************************************
c
c purpose
c the routine transforms a given sequence of
c approximations, by means of the epsilon
c algorithm of p. wynn.
c
c an estimate of the absolute error is also given.
c the condensed epsilon table is computed. only those
c elements needed for the computation of the
c next diagonal are preserved.
c
c calling sequence
c call epsalg (n,epstab,result,abserr,res3la,nres)
c
c parameters
c n - epstab(n) contains the new element in the
c first column of the epsilon table.
c
c epstab - one dimensional array containing the
c elements of the two lower diagonals of
c the triangular epsilon table.
c the elements are numbered starting at the
c right-hand corner of the triangle.
c the dimension should be at least n+2.
c
c result - resulting approximation to the integral
c
c abserr - estimate of the absolute error computed from
c result and the 3 previous /results/
c
c res3la - array containing the last 3 /results/
c
c nres - number of calls to the routine
c (should be zero at first call)
c
c ******************************************************
c .. scalar arguments ..
double precision abserr, result
integer n, nres
c .. array arguments ..
double precision epstab(52), res3la(3)
c ..
c .. local scalars ..
double precision delta1, delta2, delta3, e0, e1, e1abs, e2, e3,
* epmach,epsinf, err1, err2, err3, error, oflow, res, ss, tol1,
* tol2,tol3
integer i, ib2, ib, ie, ind, k1, k2, k3, limexp, newelm, num
c .. function references ..
double precision dlamch
c ..
c
c machine dependent constants
c -------------------------
c /limexp/ is the maximum number of elements the epsilon
c table can contain. if this number is reached, the upper
c diagonal of the epsilon table is deleted.
c
data limexp /50/
epmach=dlamch('p')
oflow=dlamch('o')
c
c list of major variables
c -----------------------
c e0 - the 4 elements on which the
c e1 computation of a new element in
c e2 the epsilon table is based
c e3 e0
c e3 e1 new
c e2
c newelm - number of elements to be computed in the new
c diagonal
c error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2)
c result - the element in the new diagonal with least
c error
c
nres = nres + 1
abserr = oflow
result = epstab(n)
if (n.lt.3) go to 200
epstab(n+2) = epstab(n)
newelm = (n-1)/2
epstab(n) = oflow
num = n
k1 = n
do 80 i=1,newelm
k2 = k1 - 1
k3 = k1 - 2
res = epstab(k1+2)
e0 = epstab(k3)
e1 = epstab(k2)
e2 = res
e1abs = abs(e1)
delta2 = e2 - e1
err2 = abs(delta2)
tol2 = max(abs(e2),e1abs)*epmach
delta3 = e1 - e0
err3 = abs(delta3)
tol3 = max(e1abs,abs(e0))*epmach
if (err2.gt.tol2 .or. err3.gt.tol3) go to 20
c
c if e0, e1 and e2 are equal to within machine
c accuracy, convergence is assumed
c result = e2
c abserr = abs(e1-e0)+abs(e2-e1)
c
result = res
abserr = err2 + err3
go to 200
20 e3 = epstab(k1)
epstab(k1) = e1
delta1 = e1 - e3
err1 = abs(delta1)
tol1 = max(e1abs,abs(e3))*epmach
c
c if two elements are very close to each other, omit
c a part of the table by adjusting the value of n
c
if (err1.lt.tol1 .or. err2.lt.tol2 .or. err3.lt.tol3) goto 40
ss = 0.10d+01/delta1 + 0.10d+01/delta2 - 0.10d+01/delta3
epsinf = abs(ss*e1)
c
c test to detect irregular behaviour in the table, and
c eventually omit a part of the table adjusting the value
c of n
c
if (epsinf.gt.0.10d-03) go to 60
40 n = i + i - 1
go to 100
c
c compute a new element and eventually adjust
c the value of result
c
60 res = e1 + 0.10d+01/ss
epstab(k1) = res
k1 = k1 - 2
error = err2 + abs(res-e2) + err3
if (error.gt.abserr) go to 80
abserr = error
result = res
80 continue
c
c shift the table
c
100 if (n.eq.limexp) n = 2*(limexp/2) - 1
ib = 1
if ((num/2)*2.eq.num) ib = 2
ie = newelm + 1
do 120 i=1,ie
ib2 = ib + 2
epstab(ib) = epstab(ib2)
ib = ib2
120 continue
if (num.eq.n) go to 160
ind = num - n + 1
do 140 i=1,n
epstab(i) = epstab(ind)
ind = ind + 1
140 continue
160 if (nres.ge.4) go to 180
res3la(nres) = result
abserr = oflow
go to 200
c
c compute error estimate
c
180 abserr = abs(result-res3la(3)) + abs(result-res3la(2)) +
*abs(result-res3la(1))
res3la(1) = res3la(2)
res3la(2) = res3la(3)
res3la(3) = result
200 abserr = max(abserr,5.0d+00*epmach*abs(result))
return
end
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