db1ink_default Subroutine

private pure subroutine db1ink_default(x, nx, fcn, kx, iknot, tx, bcoef, iflag)

Determines the parameters of a function that interpolates the one-dimensional gridded data The interpolating function and its derivatives may subsequently be evaluated by the function db1val.

History

  • Jacob Williams, 10/30/2015 : Created 1D routine.

Arguments

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

(nx) array of abcissae. Must be strictly increasing.
integer(kind=ip), intent(in) :: nx

Number of abcissae
real(kind=wp), intent(in), dimension(:) :: fcn

(nx) array of function values to interpolate. fcn(i) should contain the function value at the point x(i)
integer(kind=ip), intent(in) :: kx

The order of spline pieces in ( ) (order = polynomial degree + 1)
integer(kind=ip), intent(in) :: iknot

knot sequence flag:

  • 0 = knot sequence chosen by db1ink.
  • 1 = knot sequence chosen by user.
real(kind=wp), intent(inout), dimension(:) :: tx

The (nx+kx) knots in the direction for the spline interpolant:

  • If iknot=0 these are chosen by db1ink.
  • If iknot=1 these are specified by the user.

Must be non-decreasing.
real(kind=wp), intent(out), dimension(:) :: bcoef

(nx) array of coefficients of the b-spline interpolant.
integer(kind=ip), intent(out) :: iflag

status flag:

  • 0 = successful execution.
  • 2 = iknot out of range.
  • 3 = nx out of range.
  • 4 = kx out of range.
  • 5 = x not strictly increasing.
  • 6 = tx not non-decreasing.
  • 700 = size(x) size(fcn,1).
  • 706 = size(x) nx.
  • 712 = size(tx) nx+kx.
  • 800 = size(x) size(bcoef,1).

Calls

proc~~db1ink_default~~CallsGraph proc~db1ink_default bspline_sub_module::db1ink_default proc~check_inputs bspline_sub_module::check_inputs proc~db1ink_default->proc~check_inputs proc~dbknot bspline_sub_module::dbknot proc~db1ink_default->proc~dbknot proc~dbtpcf bspline_sub_module::dbtpcf proc~db1ink_default->proc~dbtpcf proc~dbintk bspline_sub_module::dbintk proc~dbtpcf->proc~dbintk proc~dbnslv bspline_sub_module::dbnslv proc~dbtpcf->proc~dbnslv proc~dbintk->proc~dbnslv proc~dbnfac bspline_sub_module::dbnfac proc~dbintk->proc~dbnfac proc~dbspvn bspline_sub_module::dbspvn proc~dbintk->proc~dbspvn

Called by

proc~~db1ink_default~~CalledByGraph proc~db1ink_default bspline_sub_module::db1ink_default interface~db1ink bspline_sub_module::db1ink interface~db1ink->proc~db1ink_default 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 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 db1ink_default(x,nx,fcn,kx,iknot,tx,bcoef,iflag)

    implicit none

    integer(ip),intent(in)                  :: nx     !! Number of \(x\) abcissae
    integer(ip),intent(in)                  :: kx     !! The order of spline pieces in \(x\)
                                                      !! ( \( 2 \le k_x < n_x \) )
                                                      !! (order = polynomial degree + 1)
    real(wp),dimension(:),intent(in)        :: x      !! `(nx)` array of \(x\) abcissae. Must be strictly increasing.
    real(wp),dimension(:),intent(in)        :: fcn    !! `(nx)` array of function values to interpolate. `fcn(i)` should
                                                      !! contain the function value at the point `x(i)`
    integer(ip),intent(in)                  :: iknot  !! knot sequence flag:
                                                      !!
                                                      !! * 0 = knot sequence chosen by [[db1ink]].
                                                      !! * 1 = knot sequence chosen by user.
    real(wp),dimension(:),intent(inout)     :: tx     !! The `(nx+kx)` knots in the \(x\) direction
                                                      !! for the spline interpolant:
                                                      !!
                                                      !! * If `iknot=0` these are chosen by [[db1ink]].
                                                      !! * If `iknot=1` these are specified by the user.
                                                      !!
                                                      !! Must be non-decreasing.
    real(wp),dimension(:),intent(out)       :: bcoef  !! `(nx)` array of coefficients of the b-spline interpolant.
    integer(ip),intent(out)                 :: iflag  !! status flag:
                                                      !!
                                                      !! * 0 = successful execution.
                                                      !! * 2 = `iknot` out of range.
                                                      !! * 3 = `nx` out of range.
                                                      !! * 4 = `kx` out of range.
                                                      !! * 5 = `x` not strictly increasing.
                                                      !! * 6 = `tx` not non-decreasing.
                                                      !! * 700 = `size(x)` \( \ne \) `size(fcn,1)`.
                                                      !! * 706 = `size(x)` \( \ne \) `nx`.
                                                      !! * 712 = `size(tx)` \( \ne \) `nx+kx`.
                                                      !! * 800 = `size(x)` \( \ne \) `size(bcoef,1)`.

    logical :: status_ok
    real(wp),dimension(:),allocatable :: work   !! work array of dimension `2*kx*(nx+1)`

    !check validity of inputs

    call check_inputs(  iknot,&
                        iflag,&
                        nx=nx,&
                        kx=kx,&
                        x=x,&
                        f1=fcn,&
                        bcoef1=bcoef,&
                        tx=tx,&
                        status_ok=status_ok)

    if (status_ok) then

        !choose knots
        if (iknot == 0_ip) then
            call dbknot(x,nx,kx,tx)
        end if

        allocate(work(2_ip*kx*(nx+1_ip)))

        !construct b-spline coefficients
        call dbtpcf(x,nx,fcn,nx,1_ip,tx,kx,bcoef,work,iflag)

        deallocate(work)

    end if

    end subroutine db1ink_default