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fitpack/splint.f

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+      recursive function splint(t,n,c,nc,k,a,b,wrk) result(splint_res)
+      implicit none
+      real*8 :: splint_res
+c  function splint calculates the integral of a spline function s(x)
+c  of degree k, which is given in its normalized b-spline representation
+c
+c  calling sequence:
+c     aint = splint(t,n,c,k,a,b,wrk)
+c
+c  input parameters:
+c    t    : array,length n,which contains the position of the knots
+c           of s(x).
+c    n    : integer, giving the total number of knots of s(x).
+c    c    : array,length nc, containing the b-spline coefficients.
+c           the length of the array, nc >= n - k -1.
+c           further coefficients are ignored.
+c    k    : integer, giving the degree of s(x).
+c    a,b  : real values, containing the end points of the integration
+c           interval. s(x) is considered to be identically zero outside
+c           the interval (t(k+1),t(n-k)).
+c
+c  output parameter:
+c    aint : real, containing the integral of s(x) between a and b.
+c    wrk  : real array, length n.  used as working space
+c           on output, wrk will contain the integrals of the normalized
+c           b-splines defined on the set of knots.
+c
+c  other subroutines required: fpintb.
+c
+c  references :
+c    gaffney p.w. : the calculation of indefinite integrals of b-splines
+c                   j. inst. maths applics 17 (1976) 37-41.
+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..
+      real*8 a,b
+      integer n,k, nc
+c  ..array arguments..
+      real*8 t(n),c(nc),wrk(n)
+c  ..local scalars..
+      integer i,nk1
+c  ..
+      nk1 = n-k-1
+c  calculate the integrals wrk(i) of the normalized b-splines
+c  ni,k+1(x), i=1,2,...nk1.
+      call fpintb(t,n,wrk,nk1,a,b)
+c  calculate the integral of s(x).
+      splint_res = 0.0d0
+      do 10 i=1,nk1
+        splint_res = splint_res+c(i)*wrk(i)
+  10  continue
+      return
+      end