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bspline.f90
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bspline.f90
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! CARACAL - Ring polymer molecular dynamics and rate constant calculations
! on black-box generated potential energy surfaces
!
! Copyright (c) 2023 by Julien Steffen ([email protected])
! Stefan Grimme ([email protected]) (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