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spclibs/pppack/spline_hermite_set.f90
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spline_hermite_set.f90
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!>
!> @file spline_hermite_set.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/>.
!>
!> @authors
!> (in alphabetical order)
!> @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
!>
subroutine spline_hermite_set ( ndata, tdata, c )
!*************************************************************************
!
!! SPLINE_HERMITE_SET sets up a piecewise cubic Hermite interpolant.
!
! Modified:
!
! 06 April 1999
!
! Reference:
!
! Conte and de Boor,
! Algorithm CALCCF,
! Elementary Numerical Analysis,
! 1973, page 235.
!
! Parameters:
!
! Input, integer NDATA, the number of data points.
! NDATA must be at least 2.
!
! Input, real ( kind = 8 ) TDATA(NDATA), the abscissas of the data points.
! The entries of TDATA are assumed to be strictly increasing.
!
! Input/output, real ( kind = 8 ) C(4,NDATA).
! On input, C(1,I) and C(2,I) should contain the value of the
! function and its derivative at TDATA(I), for I = 1 to NDATA.
! These values will not be changed by this routine.
! On output, C(3,I) and C(4,I) contain the quadratic
! and cubic coefficients of the Hermite polynomial
! in the interval (TDATA(I), TDATA(I+1)), for I=1 to NDATA-1.
! C(3,NDATA) and C(4,NDATA) are set to 0.
! In the interval (TDATA(I), TDATA(I+1)), the interpolating Hermite
! polynomial is given by
!
! SVAL(TVAL) = C(1,I)
! + ( TVAL - TDATA(I) ) * ( C(2,I)
! + ( TVAL - TDATA(I) ) * ( C(3,I)
! + ( TVAL - TDATA(I) ) * C(4,I) ) )
!
implicit none
integer ndata
real ( kind = 8 ) c(4,ndata)
real ( kind = 8 ) divdif1
real ( kind = 8 ) divdif3
real ( kind = 8 ) dt
integer i
real ( kind = 8 ) tdata(ndata)
do i = 1, ndata-1
dt = tdata(i+1) - tdata(i)
divdif1 = ( c(1,i+1) - c(1,i) ) / dt
divdif3 = c(2,i) + c(2,i+1) - 2.0D+00 * divdif1
c(3,i) = ( divdif1 - c(2,i) - divdif3 ) / dt
c(4,i) = divdif3 / ( dt * dt )
end do
c(3,ndata) = 0.0D+00
c(4,ndata) = 0.0D+00
return
end
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