knots Subroutine

subroutine knots ( break, l, kpm, m, t, n )

  !*****************************************************************************80
  !
  !! KNOTS is to be called in COLLOC.
  !
  !  Discussion:
  !
  !    Note that the FORTRAN77 calling sequence has been modified, by
  !    adding the variable M.
  !
  !    From the given breakpoint sequence BREAK, this 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:N+KPM) is equal to BREAK(1) KPM times, then 
  !    BREAK(2) through BREAK(L) each K times, then, finally, BREAK(L+1) 
  !    KPM times.
  !
  !  Modified:
  !
  !    14 February 2007
  !
  !  Author:
  !
  !    Carl DeBoor
  !
  !  Reference:
  !
  !    Carl DeBoor,
  !    A Practical Guide to Splines,
  !    Springer, 2001,
  !    ISBN: 0387953663,
  !    LC: QA1.A647.v27.
  !
  !  Parameters:
  !
  !    Input, real ( kind = 8 ) BREAK(L+1), the breakpoint sequence.
  !
  !    Input, integer ( kind = 4 ) L, the number of intervals or pieces.
  !
  !    Input, integer ( kind = 4 ) KPM, = K+M, the order of the piecewise
  !    polynomial function or spline.
  !
  !    Input, integer ( kind = 4 ) M, the order of the differential equation.
  !
  !    Output, real ( kind = 8 ) T(N+KPM), the knot sequence.
  !
  !    Output, integer ( kind = 4 ) N, = L*K+M = the dimension of SPLINE(K+M,T).
  !
  implicit none

  integer ( kind = 4 ) kpm
  integer ( kind = 4 ) l
  integer ( kind = 4 ) n

  real ( kind = 8 ) break(l+1)
  integer ( kind = 4 ) iside
  integer ( kind = 4 ) j
  integer ( kind = 4 ) jj
  integer ( kind = 4 ) jjj
  integer ( kind = 4 ) k
  integer ( kind = 4 ) ll
  integer ( kind = 4 ) m
  real ( kind = 8 ) t(n+kpm)
  real ( kind = 8 ) xside

  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 subroutine knots