dbknot Subroutine

private pure subroutine dbknot(x, n, k, t)

dbknot chooses a knot sequence for interpolation of order k at the data points x(i), i=1,..,n. the n+k knots are placed in the array t. k knots are placed at each endpoint and not-a-knot end conditions are used. the remaining knots are placed at data points if n is even and between data points if n is odd. the rightmost knot is shifted slightly to the right to insure proper interpolation at x(n) (see page 350 of the reference).

History

  • Jacob Williams, 2/24/2015 : Refactored this routine.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in), dimension(:) :: x
integer(kind=ip), intent(in) :: n

dimension of x
integer(kind=ip), intent(in) :: k
real(kind=wp), intent(out), dimension(:) :: t

Called by

proc~~dbknot~~CalledByGraph proc~dbknot bspline_sub_module::dbknot proc~db1ink_default bspline_sub_module::db1ink_default proc~db1ink_default->proc~dbknot proc~db2ink bspline_sub_module::db2ink proc~db2ink->proc~dbknot proc~db3ink bspline_sub_module::db3ink proc~db3ink->proc~dbknot proc~db4ink bspline_sub_module::db4ink proc~db4ink->proc~dbknot proc~db5ink bspline_sub_module::db5ink proc~db5ink->proc~dbknot proc~db6ink bspline_sub_module::db6ink proc~db6ink->proc~dbknot interface~db1ink bspline_sub_module::db1ink interface~db1ink->proc~db1ink_default proc~initialize_2d_auto_knots bspline_oo_module::bspline_2d%initialize_2d_auto_knots proc~initialize_2d_auto_knots->proc~db2ink proc~initialize_2d_specify_knots bspline_oo_module::bspline_2d%initialize_2d_specify_knots proc~initialize_2d_specify_knots->proc~db2ink proc~initialize_3d_auto_knots bspline_oo_module::bspline_3d%initialize_3d_auto_knots proc~initialize_3d_auto_knots->proc~db3ink proc~initialize_3d_specify_knots bspline_oo_module::bspline_3d%initialize_3d_specify_knots proc~initialize_3d_specify_knots->proc~db3ink proc~initialize_4d_auto_knots bspline_oo_module::bspline_4d%initialize_4d_auto_knots proc~initialize_4d_auto_knots->proc~db4ink proc~initialize_4d_specify_knots bspline_oo_module::bspline_4d%initialize_4d_specify_knots proc~initialize_4d_specify_knots->proc~db4ink proc~initialize_5d_auto_knots bspline_oo_module::bspline_5d%initialize_5d_auto_knots proc~initialize_5d_auto_knots->proc~db5ink proc~initialize_5d_specify_knots bspline_oo_module::bspline_5d%initialize_5d_specify_knots proc~initialize_5d_specify_knots->proc~db5ink proc~initialize_6d_auto_knots bspline_oo_module::bspline_6d%initialize_6d_auto_knots proc~initialize_6d_auto_knots->proc~db6ink proc~initialize_6d_specify_knots bspline_oo_module::bspline_6d%initialize_6d_specify_knots proc~initialize_6d_specify_knots->proc~db6ink proc~bspline_2d_constructor_auto_knots bspline_oo_module::bspline_2d_constructor_auto_knots proc~bspline_2d_constructor_auto_knots->proc~initialize_2d_auto_knots proc~bspline_2d_constructor_specify_knots bspline_oo_module::bspline_2d_constructor_specify_knots proc~bspline_2d_constructor_specify_knots->proc~initialize_2d_specify_knots proc~bspline_3d_constructor_auto_knots bspline_oo_module::bspline_3d_constructor_auto_knots proc~bspline_3d_constructor_auto_knots->proc~initialize_3d_auto_knots proc~bspline_3d_constructor_specify_knots bspline_oo_module::bspline_3d_constructor_specify_knots proc~bspline_3d_constructor_specify_knots->proc~initialize_3d_specify_knots proc~bspline_4d_constructor_auto_knots bspline_oo_module::bspline_4d_constructor_auto_knots proc~bspline_4d_constructor_auto_knots->proc~initialize_4d_auto_knots proc~bspline_4d_constructor_specify_knots bspline_oo_module::bspline_4d_constructor_specify_knots proc~bspline_4d_constructor_specify_knots->proc~initialize_4d_specify_knots proc~bspline_5d_constructor_auto_knots bspline_oo_module::bspline_5d_constructor_auto_knots proc~bspline_5d_constructor_auto_knots->proc~initialize_5d_auto_knots proc~bspline_5d_constructor_specify_knots bspline_oo_module::bspline_5d_constructor_specify_knots proc~bspline_5d_constructor_specify_knots->proc~initialize_5d_specify_knots proc~bspline_6d_constructor_auto_knots bspline_oo_module::bspline_6d_constructor_auto_knots proc~bspline_6d_constructor_auto_knots->proc~initialize_6d_auto_knots proc~bspline_6d_constructor_specify_knots bspline_oo_module::bspline_6d_constructor_specify_knots proc~bspline_6d_constructor_specify_knots->proc~initialize_6d_specify_knots proc~initialize_1d_auto_knots bspline_oo_module::bspline_1d%initialize_1d_auto_knots proc~initialize_1d_auto_knots->interface~db1ink proc~initialize_1d_specify_knots bspline_oo_module::bspline_1d%initialize_1d_specify_knots proc~initialize_1d_specify_knots->interface~db1ink interface~bspline_2d bspline_oo_module::bspline_2d interface~bspline_2d->proc~bspline_2d_constructor_auto_knots interface~bspline_2d->proc~bspline_2d_constructor_specify_knots interface~bspline_3d bspline_oo_module::bspline_3d interface~bspline_3d->proc~bspline_3d_constructor_auto_knots interface~bspline_3d->proc~bspline_3d_constructor_specify_knots interface~bspline_4d bspline_oo_module::bspline_4d interface~bspline_4d->proc~bspline_4d_constructor_auto_knots interface~bspline_4d->proc~bspline_4d_constructor_specify_knots interface~bspline_5d bspline_oo_module::bspline_5d interface~bspline_5d->proc~bspline_5d_constructor_auto_knots interface~bspline_5d->proc~bspline_5d_constructor_specify_knots interface~bspline_6d bspline_oo_module::bspline_6d interface~bspline_6d->proc~bspline_6d_constructor_auto_knots interface~bspline_6d->proc~bspline_6d_constructor_specify_knots proc~bspline_1d_constructor_auto_knots bspline_oo_module::bspline_1d_constructor_auto_knots proc~bspline_1d_constructor_auto_knots->proc~initialize_1d_auto_knots proc~bspline_1d_constructor_specify_knots bspline_oo_module::bspline_1d_constructor_specify_knots proc~bspline_1d_constructor_specify_knots->proc~initialize_1d_specify_knots interface~bspline_1d bspline_oo_module::bspline_1d interface~bspline_1d->proc~bspline_1d_constructor_auto_knots interface~bspline_1d->proc~bspline_1d_constructor_specify_knots

Source Code

    pure subroutine dbknot(x,n,k,t)

    implicit none

    integer(ip),intent(in)             :: n  !! dimension of `x`
    integer(ip),intent(in)             :: k
    real(wp),dimension(:),intent(in)   :: x
    real(wp),dimension(:),intent(out)  :: t

    integer(ip) :: i, j, ipj, npj, ip1, jstrt
    real(wp) :: rnot

    !put k knots at each endpoint
    !(shift right endpoints slightly -- see pg 350 of reference)
    rnot = x(n) + 0.1_wp*( x(n)-x(n-1_ip) )
    do j=1_ip,k
        t(j)   = x(1_ip)
        npj    = n + j
        t(npj) = rnot
    end do

    !distribute remaining knots

    if (mod(k,2_ip) == 1_ip)  then

        !case of odd k --  knots between data points

        i = (k-1_ip)/2_ip - k
        ip1 = i + 1_ip
        jstrt = k + 1_ip
        do j=jstrt,n
            ipj = i + j
            t(j) = 0.5_wp*( x(ipj) + x(ipj+1_ip) )
        end do

    else

        !case of even k --  knots at data points

        i = (k/2_ip) - k
        jstrt = k+1_ip
        do j=jstrt,n
            ipj = i + j
            t(j) = x(ipj)
        end do

    end if

    end subroutine dbknot