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spclibs/pppack/cubset.f90
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cubset.f90
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!>
!> @file cubset.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 cubset ( tau, c, n, ibcbeg, ibcend )
!*******************************************************************************
!
!! CUBSET sets up a simple cubic spline interpolant.
!
! WARNING: IBCBEG and IBCEND are not set up yet.
!
! A tridiagonal linear system for the unknown slopes S(I) of
! F at TAU(I), I=1,..., N, is generated and then solved by Gauss
! elimination, with S(I) ending up in C(2,I), for all I.
!
! Reference:
!
! Carl DeBoor,
! A Practical Guide to Splines,
! Springer Verlag.
!
! Parameters:
!
! Input, real ( kind = 8 ) TAU(N), the abscissas or X values of
! the data points. The entries of TAU are assumed to be
! strictly increasing.
!
! Input, integer N, the number of data points. N is
! assumed to be at least 2.
!
! Input/output, real ( kind = 8 ) C(4,N).
! On input, if IBCBEG or IBCBEG is 1 or 2, then C(2,1)
! or C(2,N) should have been set to the desired derivative
! values, as described further under IBCBEG and IBCEND.
! On output, C contains the polynomial coefficients of
! the cubic interpolating spline with interior knots
! TAU(2) through TAU(N-1).
! In the interval interval (TAU(I), TAU(I+1)), the spline
! F is given by F(X) =
! C(1,I) +
! C(2,I) * ( X - TAU(I) ) +
! C(3,I) * ( X - TAU(I) )**2 +
! C(4,I) * ( X - TAU(I) )**3
!
! IBCBEG,
! IBCEND Input, integer IBCBEG, IBCEND, boundary condition
! indicators.
!
! IBCBEG=0 means no boundary condition at TAU(1) is given.
! In this case, the "not-a-knot condition" is used. That
! is, the jump in the third derivative across TAU(2) is
! forced to zero. Thus the first and the second cubic
! polynomial pieces are made to coincide.
!
! IBCBEG=1 means that the slope at TAU(1) is to equal the
! input value C(2,1).
!
! IBCBEG=2 means that the second derivative at TAU(1) is
! to equal C(2,1).
!
! IBCEND=0, 1, or 2 has analogous meaning concerning the
! boundary condition at TAU(N), with the additional
! information taken from C(2,N).
!
implicit none
integer n
real ( kind = 8 ) c(4,n)
integer ibcbeg
integer ibcend
real ( kind = 8 ) tau(n)
!
! Solve for the slopes at internal nodes.
!
call cubslo ( tau, c, n )
!
! Now compute the quadratic and cubic coefficients used in the
! piecewise polynomial representation.
!
call spline_hermite_set ( n, tau, c )
return
end
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