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+chapter xii, example 2. cubic spline interpolation with good knots
+c  from  * a practical guide to splines *  by c. de boor
+calls  cubspl, newnot
+c     parameter nmax=20
+      integer i,istep,iter,itermx,j,n,nhigh,nlow,nm1
+c     real algerp,aloger,decay,dx,errmax,c(4,nmax),g,h,pnatx
+c    *	  ,scrtch(2,nmax),step,tau(nmax),taunew(nmax)
+      real algerp,aloger,decay,dx,errmax,c(4,20),g,h,pnatx
+     *	  ,scrtch(2,20),step,tau(20),taunew(20),x
+c     istep and step = float(istep) specify point density for error det-
+c     ermination.
+      data step, istep /20., 20/
+c				the function  g  is to be interpolated .
+      g(x) = sqrt(x+1.)
+      decay = 0.
+c      read in the number of iterations to be carried out and the lower
+c      and upper limit for the number  n  of data points to be used.
+      read 500,itermx,nlow,nhigh
+  500 format(3i3)
+      print 600, itermx
+  600 format(i4,22h cycles through newnot//
+     *	    28h  n   max.error	 decay exp./)
+c				  loop over  n = number of data points .
+      do 40 n=nlow,nhigh,2
+c					 knots are initially equispaced.
+	 nm1 = n-1
+	 h = 2./float(nm1)
+	 do 10 i=1,n
+   10	    tau(i) = float(i-1)*h - 1.
+	 iter = 1
+c		construct cubic spline interpolant. then, itermx  times,
+c		 determine new knots from it and find a new interpolant.
+   11	    do 15 i=1,n
+   15	       c(1,i) = g(tau(i))
+	    call cubspl ( tau, c, n, 0, 0 )
+	    if (iter .gt. itermx)	go to 19
+	    iter = iter+1
+	    call newnot(tau,c,nm1,4,taunew,nm1,scrtch)
+	    do 18 i=1,n
+   18	       tau(i) = taunew(i)
+					go to 11
+   19	 continue
+c			     estimate max.interpolation error on (-1,1).
+	 errmax = 0.
+c			    loop over polynomial pieces of interpolant .
+	 do 30 i=1,nm1
+	    dx = (tau(i+1)-tau(i))/step
+c		 interpolation error is calculated at  istep  points per
+c		     polynomial piece .
+	    do 30 j=1,istep
+	       h = float(j)*dx
+	       pnatx = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+   30	    errmax = amax1(errmax,abs(g(tau(i)+h)-pnatx))
+c					      calculate decay exponent .
+	 aloger = alog(errmax)
+	 if (n .gt. nlow)  decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+c
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end