!>
!> @file knots.f90
!>
!> @brief
!>
!> @copyright
!> Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
!> SPC (Swiss Plasma Center)
!>
!> SPClibs is free software: you can redistribute it and/or modify it under
!> the terms of the GNU Lesser General Public License as published by the Free
!> Software Foundation, either version 3 of the License, or (at your option)
!> any later version.
!>
!> SPClibs is distributed in the hope that it will be useful, but WITHOUT ANY
!> WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
!> FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!>
!> You should have received a copy of the GNU Lesser General Public License
!> along with this program. If not, see <https://www.gnu.org/licenses/>.
!>
!> @author
!> (in alphabetical order)
!> @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
!>
subroutine knots ( break, l, kpm, t, n )

!*************************************************************************
!
!! KNOTS is to be called in COLLOC.
!
!  Discussion:
!
!    From the given breakpoint sequence BREAK the routine constructs the
!    knot sequence T so that
!
!      SPLINE(K+M,T) = PP(K+M,BREAK)
!
!    with M-1 continuous derivatives.  This means that
!
!      t(1),...,t(n+kpm) = break(1) kpm times, then break(2),...,
!        break(l) each  k  times, then, finally, break(l+1) kpm times.
!
!  Reference:
!
!    Carl DeBoor,
!    A Practical Guide to Splines,
!    Springer Verlag.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) BREAK(L+1), the breakpoint sequence.
!
!    Input, integer L, the number of intervals or pieces.
!
!    Input, integer KPM, = K+M, the order of the piecewise polynomial
!    function or spline.
!
!    Output, real ( kind = 8 ) T(N+KPM), the knot sequence.
!
!    Output, integer N, = L*K+M = the dimension of SPLINE(K+M,T).
!
  implicit none

  integer kpm
  integer l
  integer n

  real ( kind = 8 ) break(l+1)
  integer iside
  integer j
  integer jj
  integer jjj
  integer k
  integer ll
  integer m
  real ( kind = 8 ) t(*)
  real ( kind = 8 ) xside

  common /side/ m,iside,xside(10)

  k = kpm-m
  n = l*k+m
  jj = n+kpm
  jjj = l+1

  do ll = 1, kpm
    t(jj) = break(jjj)
    jj = jj-1
  end do

  do j = 1, l
    jjj = jjj-1
    do ll = 1, k
      t(jj) = break(jjj)
      jj = jj-1
    end do
  end do

  t(1:kpm) = break(1)

  return
end