splint Function

      real(RKIND) function splint(t,n,c,k,a,b,wrk) result(integral)

      !  calling sequence:
      !     aint = splint(t,n,c,k,a,b,wrk)
      !
      !  input parameters:
      !    t    : array,length n,which contains the position of the knots of s(x).
      !    n    : integer, giving the total number of knots of s(x).
      !    c    : array,length n, containing the b-spline coefficients.
      !    k    : integer, giving the degree of s(x).
      !    a,b  : real values, containing the end points of the integration interval. s(x) is considered to be identically
      !           zero outside the interval (t(k+1),t(n-k)).
      !
      !  output parameter:
      !    aint : real, containing the integral of s(x) between a and b.
      !    wrk  : real array, length n, used as working space. on output, wrk will contain the integrals of the normalized
      !           b-splines defined on the set of knots.
      !
      !  other subroutines required: fpintb.
      !
      !  references :
      !    gaffney p.w. : the calculation of indefinite integrals of b-splines. j. inst. maths applics 17 (1976) 37-41.
      !    dierckx p. : curve and surface fitting with splines, monographs on numerical analysis, oxford university press, 1993.
      !
      !  author :
      !    p.dierckx
      !    dept. computer science, k.u.leuven
      !    celestijnenlaan 200a, b-3001 heverlee, belgium.
      !    e-mail : Paul.Dierckx@cs.kuleuven.ac.be
      !
      !  ..scalar arguments..
      real(RKIND), intent(in) :: a,b
      integer    , intent(in) :: n,k
      !  ..array arguments..
      real(RKIND), intent(in)    :: t(n),c(n)
      real(RKIND), intent(inout) :: wrk(n)

      !  ..local scalars..
      integer :: nk1

      nk1 = n-k-1

      !  calculate the integrals wrk(i) of the normalized b-splines ni,k+1(x), i=1,2,...nk1.
      call fpintb(t,n,wrk,nk1,a,b)

      !  calculate the integral of s(x).
      integral = dot_product(c(1:nk1),wrk(1:nk1))
      return
      end function splint