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subroutine fpched(x,m,t,n,k,ib,ie,ier)
c subroutine fpched verifies the number and the position of the knots
c t(j),j=1,2,...,n of a spline of degree k,with ib derative constraints
c at x(1) and ie constraints at x(m), in relation to the number and
c the position of the data points x(i),i=1,2,...,m. if all of the
c following conditions are fulfilled, the error parameter ier is set
c to zero. if one of the conditions is violated ier is set to ten.
c 1) k+1 <= n-k-1 <= m + max(0,ib-1) + max(0,ie-1)
c 2) t(1) <= t(2) <= ... <= t(k+1)
c t(n-k) <= t(n-k+1) <= ... <= t(n)
c 3) t(k+1) < t(k+2) < ... < t(n-k)
c 4) t(k+1) <= x(i) <= t(n-k)
c 5) the conditions specified by schoenberg and whitney must hold
c for at least one subset of data points, i.e. there must be a
c subset of data points y(j) such that
c t(j) < y(j) < t(j+k+1), j=1+ib1,2+ib1,...,n-k-1-ie1
c with ib1 = max(0,ib-1), ie1 = max(0,ie-1)
c ..
c ..scalar arguments..
integer m,n,k,ib,ie,ier
c ..array arguments..
real*8 x(m),t(n)
c ..local scalars..
integer i,ib1,ie1,j,jj,k1,k2,l,nk1,nk2,nk3
real*8 tj,tl
c ..
k1 = k+1
k2 = k1+1
nk1 = n-k1
nk2 = nk1+1
ib1 = ib-1
if(ib1.lt.0) ib1 = 0
ie1 = ie-1
if(ie1.lt.0) ie1 = 0
ier = 10
c check condition no 1
if(nk1.lt.k1 .or. nk1.gt.(m+ib1+ie1)) go to 80
c check condition no 2
j = n
do 20 i=1,k
if(t(i).gt.t(i+1)) go to 80
if(t(j).lt.t(j-1)) go to 80
j = j-1
20 continue
c check condition no 3
do 30 i=k2,nk2
if(t(i).le.t(i-1)) go to 80
30 continue
c check condition no 4
if(x(1).lt.t(k1) .or. x(m).gt.t(nk2)) go to 80
c check condition no 5
if(x(1).ge.t(k2) .or. x(m).le.t(nk1)) go to 80
i = 1
jj = 2+ib1
l = jj+k
nk3 = nk1-1-ie1
if(nk3.lt.jj) go to 70
do 60 j=jj,nk3
tj = t(j)
l = l+1
tl = t(l)
40 i = i+1
if(i.ge.m) go to 80
if(x(i).le.tj) go to 40
if(x(i).ge.tl) go to 80
60 continue
70 ier = 0
80 return
end
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