splev.f

Go to the documentation of this file.

      subroutine splev(t,n,c,k,x,y,m,ier)
      implicit none
c  subroutine splev evaluates in a number of points x(i),i=1,2,...,m
c  a spline s(x) of degree k, given in its b-spline representation.
c
c  calling sequence:
c     call splev(t,n,c,k,x,y,m,ier)
c
c  input parameters:
c    t    : array,length n, which contains the position of the knots.
c    n    : integer, giving the total number of knots of s(x).
c    c    : array,length n, which contains the b-spline coefficients.
c    k    : integer, giving the degree of s(x).
c    x    : array,length m, which contains the points where s(x) must
c           be evaluated.
c    m    : integer, giving the number of points where s(x) must be
c           evaluated.
c
c  output parameter:
c    y    : array,length m, giving the value of s(x) at the different
c           points.
c    ier  : error flag
c      ier = 0 : normal return
c      ier =10 : invalid input data (see restrictions)
c
c  restrictions:
c    m >= 1
c    t(k+1) <= x(i) <= x(i+1) <= t(n-k) , i=1,2,...,m-1.
c
c  other subroutines required: fpbspl.
c
c  references :
c    de boor c  : on calculating with b-splines, j. approximation theory
c                 6 (1972) 50-62.
c    cox m.g.   : the numerical evaluation of b-splines, j. inst. maths
c                 applics 10 (1972) 134-149.
c    dierckx p. : curve and surface fitting with splines, monographs on
c                 numerical analysis, oxford university press, 1993.
c
c  author :
c    p.dierckx
c    dept. computer science, k.u.leuven
c    celestijnenlaan 200a, b-3001 heverlee, belgium.
c    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
c
c  latest update : march 1987
c
c  ..scalar arguments..
      integer n,k,m,ier
c  ..array arguments..
      real*8 t(n),c(n),x(m),y(m)
c  ..local scalars..
      integer i,j,k1,l,ll,l1,nk1
      real*8 arg,sp,tb,te
c  ..local array..
      real*8 h(6)
c  ..
c  before starting computations a data check is made. if the input data
c  are invalid control is immediately repassed to the calling program.
      ier = 10
      if(m-1) 100,30,10
  10  do 20 i=2,m
        if(x(i).lt.x(i-1)) go to 100
  20  continue
  30  ier = 0
c  fetch tb and te, the boundaries of the approximation interval.
      k1 = k+1
      nk1 = n-k1
      tb = t(k1)
      te = t(nk1+1)
      l = k1
      l1 = l+1
c  main loop for the different points.
      do 80 i=1,m
c  fetch a new x-value arg.
        arg = x(i)
        if(arg.lt.tb) arg = tb
        if(arg.gt.te) arg = te
c  search for knot interval t(l) <= arg < t(l+1)
  40    if(arg.lt.t(l1) .or. l.eq.nk1) go to 50
        l = l1
        l1 = l+1
        go to 40
c  evaluate the non-zero b-splines at arg.
  50    call fpbspl(t,n,k,arg,l,h)
c  find the value of s(x) at x=arg.
        sp = 0.
        ll = l-k1
        do 60 j=1,k1
          ll = ll+1
          sp = sp+c(ll)*h(j)
  60    continue
        y(i) = sp
  80  continue
 100  return
      end