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spclibs/pppack/spline_hermite_val.f90
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spline_hermite_val.f90
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!>
!> @file spline_hermite_val.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 spline_hermite_val ( ndata, tdata, c, tval, sval )
!*************************************************************************
!
!! SPLINE_HERMITE_VAL evaluates a piecewise cubic Hermite interpolant.
!
! Discussion:
!
! SPLINE_HERMITE_SET must be called first, to set up the
! spline data from the raw function and derivative data.
!
! Modified:
!
! 06 April 1999
!
! Reference:
!
! Conte and de Boor,
! Algorithm PCUBIC,
! Elementary Numerical Analysis,
! 1973, page 234.
!
! Parameters:
!
! Input, integer NDATA, the number of data points.
! NDATA is assumed to 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, real ( kind = 8 ) C(4,NDATA), contains the data computed by
! SPLINE_HERMITE_SET.
!
! Input, real ( kind = 8 ) TVAL, the point where the interpolant is to
! be evaluated.
!
! Output, real ( kind = 8 ) SVAL, the value of the interpolant at TVAL.
!
implicit none
integer ndata
real ( kind = 8 ) c(4,ndata)
real ( kind = 8 ) dt
integer i
integer j
real ( kind = 8 ) sval
real ( kind = 8 ) tdata(ndata)
real ( kind = 8 ) tval
!
! Find the interval J = [ TDATA(J), TDATA(J+1) ] that contains
! or is nearest to TVAL.
!
j = ndata - 1
do i = 1, ndata-2
if ( tval < tdata(i+1) ) then
j = i
exit
end if
end do
!
! Evaluate the cubic polynomial.
!
dt = tval - tdata(j)
sval = c(1,j) + dt * ( c(2,j) + dt * ( c(3,j) + dt * c(4,j) ) )
return
end
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