dpchdf Function

private function dpchdf(k, x, s, ierr) result(deriv)

Computes divided differences for dpchce and dpchsp

Uses a divided difference formulation to compute a K-point approximation to the derivative at X(K) based on the data in X and S.

Called by dpchce and dpchsp to compute 3- and 4-point boundary derivative approximations.

References

  • Carl de Boor, A Practical Guide to Splines, Springer-Verlag, New York, 1978, pp. 10-16.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: k

is the order of the desired derivative approximation. K must be at least 3 (error return if not).
real(kind=wp), intent(in) :: x(k)

contains the K values of the independent variable. X need not be ordered, but the values MUST be distinct. (Not checked here.)
real(kind=wp), intent(inout) :: s(k)

contains the associated slope values: S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1. (Note that S need only be of length K-1.) Will be destroyed on output.
integer, intent(out) :: ierr

will be set to -1 if K<2 .

Return Value real(kind=wp)

will be set to the desired derivative approximation if IERR=0 or to zero if IERR=-1.


Calls

proc~~dpchdf~~CallsGraph proc~dpchdf pchip_module::dpchdf proc~xermsg pchip_module::xermsg proc~dpchdf->proc~xermsg

Called by

proc~~dpchdf~~CalledByGraph proc~dpchdf pchip_module::dpchdf proc~dpchce pchip_module::dpchce proc~dpchce->proc~dpchdf proc~dpchsp pchip_module::dpchsp proc~dpchsp->proc~dpchdf proc~dpchic pchip_module::dpchic proc~dpchic->proc~dpchce

Source Code

    function dpchdf (k, x, s, ierr) result(deriv)

    integer,intent(in)     :: k    !! is the order of the desired derivative approximation.
                                   !! K must be at least 3 (error return if not).
    real(wp),intent(in)    :: x(k) !! contains the K values of the independent variable.
                                   !! X need not be ordered, but the values **MUST** be
                                   !! distinct.  (Not checked here.)
    real(wp),intent(inout) :: s(k) !! contains the associated slope values:
                                   !! `S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1`.
                                   !! (Note that S need only be of length K-1.)
                                   !! Will be destroyed on output.
    integer,intent(out)    :: ierr !! will be set to -1 if K<2 .
    real(wp) :: deriv  !! will be set to the desired derivative approximation if
                       !! IERR=0 or to zero if IERR=-1.

    integer :: i, j
    real(wp) :: value

    ! check for legal value of k.
    if (k < 3) then
        ierr = -1
        call xermsg ('PCHIP', 'dpchdf', 'k less than three', ierr, 1)
        deriv = zero
    else

        ! compute coefficients of interpolating polynomial.
        do j = 2, k-1
            do  i = 1, k-j
                s(i) = (s(i+1)-s(i))/(x(i+j)-x(i))
            end do
        end do

        ! evaluate derivative at x(k).
        value = s(1)
        do i = 2, k-1
            value = s(i) + value*(x(k)-x(i))
        end do

        ! normal return.
        ierr = 0
        deriv = value

    end if

    end function dpchdf