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