!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!   CARACAL - Ring polymer molecular dynamics and rate constant calculations
!             on black-box generated potential energy surfaces
!
!   Copyright (c) 2023 by Julien Steffen (mail@j-steffen.org)
!                         Stefan Grimme (grimme@thch.uni-bonn.de) (QMDFF code)
!
!   Permission is hereby granted, free of charge, to any person obtaining a
!   copy of this software and associated documentation files (the "Software"),
!   to deal in the Software without restriction, including without limitation
!   the rights to use, copy, modify, merge, publish, distribute, sublicense,
!   and/or sell copies of the Software, and to permit persons to whom the
!   Software is furnished to do so, subject to the following conditions:
!
!   The above copyright notice and this permission notice shall be included in
!   all copies or substantial portions of the Software.
!
!   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
!   IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
!   FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
!   THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
!   LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
!   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
!   DEALINGS IN THE SOFTWARE.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!
!     subroutine bspline: calculates the coefficients for an n-th order
!     B-spline approximation
!
!
subroutine bspline (x,n,c)
implicit none
integer i,k,n
real(kind=8)::x,denom
real(kind=8)::c(*)

!
!     initialize the B-spline as the linear case
!
c(1) = 1.0d0 - x
c(2) = x
!
!     compute standard B-spline recursion to n-th order
!
do k = 3, n
   denom = 1.0d0 / dble(k-1)
   c(k) = x * c(k-1) * denom
   do i = 1, k-2
      c(k-i) = ((x+dble(i))*c(k-i-1) &
              &    + (dble(k-i)-x)*c(k-i)) * denom
   end do
   c(1) = (1.0d0-x) * c(1) * denom
end do

return
end subroutine bspline