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spclibs/pppack/ppvalu.f90
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ppvalu.f90
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!>
!> @file ppvalu.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 ppvalu ( break, coef, l, k, x, jderiv, value )
!*******************************************************************************
!
!! PPVALU evaluates a piecewise polynomial function or its derivative.
!
! Discussion:
!
! PPVALU calculates the value at X of the JDERIV-th derivative of
! the piecewise polynomial function F from its piecewise
! polynomial representation.
!
! The interval index I, appropriate for X, is found through a
! call to INTERV. The formula for the JDERIV-th derivative
! of F is then evaluated by nested multiplication.
!
! The J-th derivative of F is given by:
!
! (d**j)f(x) =
! coef(j+1,i) + h * (
! coef(j+2,i) + h * (
! ...
! coef(k-1,i) + h * (
! coef(k,i) / (k-j-1) ) / (k-j-2) ... ) / 2 ) / 1
!
! with
!
! H=X-BREAK(I)
!
! and
!
! i = max( 1 , max( j , break(j) <= x , 1 <= j <= l ) ).
!
! Reference:
!
! Carl DeBoor,
! A Practical Guide to Splines,
! Springer Verlag.
!
! Parameters:
!
! Input, real ( kind = 8 ) BREAK(L+1), real COEF(*), integer L, for
! piecewise polynomial representation of the function F to
! be evaluated.
!
! Input, integer K, the order of the polynomial pieces
! that make up the function F. The usual value for
! K is 4, signifying a piecewise cubic polynomial.
!
! Input, real ( kind = 8 ) X, the point at which to evaluate F or
! of its derivatives.
!
! Input, integer JDERIV, the order of the derivative to be
! evaluated. If JDERIV is 0, then F itself is evaluated,
! which is actually the most common case. It is assumed
! that JDERIV is zero or positive.
!
! Output, real ( kind = 8 ) VALUE, the value of the JDERIV-th
! derivative of F at X.
!
implicit none
integer k
integer l
real ( kind = 8 ) break(l+1)
real ( kind = 8 ) coef(k,l)
real ( kind = 8 ) fmmjdr
real ( kind = 8 ) h
integer i
integer jderiv
integer m
integer ndummy
real ( kind = 8 ) value
real ( kind = 8 ) x
value = 0.0D+00
fmmjdr = k - jderiv
!
! Derivatives of order K or higher are identically zero.
!
if ( k <= jderiv ) then
return
end if
!
! Find the index I of the largest breakpoint to the left of X.
!
call interv ( break, l+1, x, i, ndummy )
!
! Evaluate the JDERIV-th derivative of the I-th polynomial piece at X.
!
h = x - break(i)
m = k
do
value = ( value / fmmjdr ) * h + coef(m,i)
m = m - 1
fmmjdr = fmmjdr - 1.0D+00
if ( fmmjdr <= 0.0D+00 ) then
exit
end if
end do
return
end
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