db3val Subroutine

public pure subroutine db3val(xval, yval, zval, idx, idy, idz, tx, ty, tz, nx, ny, nz, kx, ky, kz, bcoef, f, iflag, inbvx, inbvy, inbvz, iloy, iloz, w2, w1, w0, extrap)

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db3ink or one of its derivatives at the point (xval,yval,zval).

To evaluate the interpolant itself, set idx=idy=idz=0, to evaluate the first partial with respect to x, set idx=1,idy=idz=0, and so on.

db3val returns 0.0 if (xval,yval,zval) is out of range. that is,

 xval<tx(1) .or. xval>tx(nx+kx) .or.
 yval<ty(1) .or. yval>ty(ny+ky) .or.
 zval<tz(1) .or. zval>tz(nz+kz)

if the knots tx, ty, and tz were chosen by db3ink, then this is equivalent to

 xval<x(1) .or. xval>x(nx)+epsx .or.
 yval<y(1) .or. yval>y(ny)+epsy .or.
 zval<z(1) .or. zval>z(nz)+epsz

where

 epsx = 0.1*(x(nx)-x(nx-1))
 epsy = 0.1*(y(ny)-y(ny-1))
 epsz = 0.1*(z(nz)-z(nz-1))

The input quantities tx, ty, tz, nx, ny, nz, kx, ky, kz, and bcoef should remain unchanged since the last call of db3ink.

History

  • Boisvert, Ronald, NBS : 25 may 1982 : Author of original routine.
  • JEC : 000330 modified array declarations.
  • Jacob Williams, 2/24/2015 : extensive refactoring of CMLIB routine.

Arguments

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

coordinate of evaluation point.

real(kind=wp), intent(in) :: yval

coordinate of evaluation point.

real(kind=wp), intent(in) :: zval

coordinate of evaluation point.

integer(kind=ip), intent(in) :: idx

derivative of piecewise polynomial to evaluate.

integer(kind=ip), intent(in) :: idy

derivative of piecewise polynomial to evaluate.

integer(kind=ip), intent(in) :: idz

derivative of piecewise polynomial to evaluate.

real(kind=wp), intent(in), dimension(nx+kx) :: tx

sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db3ink)

real(kind=wp), intent(in), dimension(ny+ky) :: ty

sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db3ink)

real(kind=wp), intent(in), dimension(nz+kz) :: tz

sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db3ink)

integer(kind=ip), intent(in) :: nx

the number of interpolation points in . (same as in last call to db3ink)

integer(kind=ip), intent(in) :: ny

the number of interpolation points in . (same as in last call to db3ink)

integer(kind=ip), intent(in) :: nz

the number of interpolation points in . (same as in last call to db3ink)

integer(kind=ip), intent(in) :: kx

order of polynomial pieces in . (same as in last call to db3ink)

integer(kind=ip), intent(in) :: ky

order of polynomial pieces in . (same as in last call to db3ink)

integer(kind=ip), intent(in) :: kz

order of polynomial pieces in . (same as in last call to db3ink)

real(kind=wp), intent(in), dimension(nx,ny,nz) :: bcoef

the b-spline coefficients computed by db3ink.

real(kind=wp), intent(out) :: f

interpolated value

integer(kind=ip), intent(out) :: iflag

status flag:

  • : no errors
  • : error
integer(kind=ip), intent(inout) :: inbvx

initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user.

integer(kind=ip), intent(inout) :: inbvy

initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user.

integer(kind=ip), intent(inout) :: inbvz

initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user.

integer(kind=ip), intent(inout) :: iloy

initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user.

integer(kind=ip), intent(inout) :: iloz

initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user.

real(kind=wp), intent(inout), dimension(ky,kz) :: w2

work array

real(kind=wp), intent(inout), dimension(kz) :: w1

work array

real(kind=wp), intent(inout), dimension(3_ip*max(kx,ky,kz)) :: w0

work array

logical, intent(in), optional :: extrap

if extrapolation is allowed (if not present, default is False)


Calls

proc~~db3val~~CallsGraph proc~db3val bspline_sub_module::db3val proc~check_value bspline_sub_module::check_value proc~db3val->proc~check_value proc~dbvalu bspline_sub_module::dbvalu proc~db3val->proc~dbvalu proc~dintrv bspline_sub_module::dintrv proc~db3val->proc~dintrv proc~dbvalu->proc~dintrv proc~get_temp_x_for_extrap bspline_sub_module::get_temp_x_for_extrap proc~dintrv->proc~get_temp_x_for_extrap

Called by

proc~~db3val~~CalledByGraph proc~db3val bspline_sub_module::db3val proc~evaluate_3d bspline_oo_module::bspline_3d%evaluate_3d proc~evaluate_3d->proc~db3val

Source Code

    pure subroutine db3val(xval,yval,zval,idx,idy,idz,&
                           tx,ty,tz,&
                           nx,ny,nz,kx,ky,kz,bcoef,f,iflag,&
                           inbvx,inbvy,inbvz,iloy,iloz,w2,w1,w0,extrap)

    implicit none

    integer(ip),intent(in)                  :: idx      !! \(x\) derivative of piecewise polynomial to evaluate.
    integer(ip),intent(in)                  :: idy      !! \(y\) derivative of piecewise polynomial to evaluate.
    integer(ip),intent(in)                  :: idz      !! \(z\) derivative of piecewise polynomial to evaluate.
    integer(ip),intent(in)                  :: nx       !! the number of interpolation points in \(x\).
                                                        !! (same as in last call to [[db3ink]])
    integer(ip),intent(in)                  :: ny       !! the number of interpolation points in \(y\).
                                                        !! (same as in last call to [[db3ink]])
    integer(ip),intent(in)                  :: nz       !! the number of interpolation points in \(z\).
                                                        !! (same as in last call to [[db3ink]])
    integer(ip),intent(in)                  :: kx       !! order of polynomial pieces in \(z\).
                                                        !! (same as in last call to [[db3ink]])
    integer(ip),intent(in)                  :: ky       !! order of polynomial pieces in \(y\).
                                                        !! (same as in last call to [[db3ink]])
    integer(ip),intent(in)                  :: kz       !! order of polynomial pieces in \(z\).
                                                        !! (same as in last call to [[db3ink]])
    real(wp),intent(in)                     :: xval     !! \(x\) coordinate of evaluation point.
    real(wp),intent(in)                     :: yval     !! \(y\) coordinate of evaluation point.
    real(wp),intent(in)                     :: zval     !! \(z\) coordinate of evaluation point.
    real(wp),dimension(nx+kx),intent(in)    :: tx       !! sequence of knots defining the piecewise polynomial
                                                        !! in the \(x\) direction. (same as in last call to [[db3ink]])
    real(wp),dimension(ny+ky),intent(in)    :: ty       !! sequence of knots defining the piecewise polynomial
                                                        !! in the \(y\) direction. (same as in last call to [[db3ink]])
    real(wp),dimension(nz+kz),intent(in)    :: tz       !! sequence of knots defining the piecewise polynomial
                                                        !! in the \(z\) direction. (same as in last call to [[db3ink]])
    real(wp),dimension(nx,ny,nz),intent(in) :: bcoef    !! the b-spline coefficients computed by [[db3ink]].
    real(wp),intent(out)                    :: f        !! interpolated value
    integer(ip),intent(out)                 :: iflag    !! status flag:
                                                        !!
                                                        !! * \( = 0 \)   : no errors
                                                        !! * \( \ne 0 \) : error
    integer(ip),intent(inout)               :: inbvx    !! initialization parameter which must be
                                                        !! set to 1 the first time this routine is called,
                                                        !! and must not be changed by the user.
    integer(ip),intent(inout)               :: inbvy    !! initialization parameter which must be
                                                        !! set to 1 the first time this routine is called,
                                                        !! and must not be changed by the user.
    integer(ip),intent(inout)               :: inbvz    !! initialization parameter which must be
                                                        !! set to 1 the first time this routine is called,
                                                        !! and must not be changed by the user.
    integer(ip),intent(inout)               :: iloy     !! initialization parameter which must be
                                                        !! set to 1 the first time this routine is called,
                                                        !! and must not be changed by the user.
    integer(ip),intent(inout)               :: iloz     !! initialization parameter which must be
                                                        !! set to 1 the first time this routine is called,
                                                        !! and must not be changed by the user.
    real(wp),dimension(ky,kz),intent(inout)              :: w2  !! work array
    real(wp),dimension(kz),intent(inout)                 :: w1  !! work array
    real(wp),dimension(3_ip*max(kx,ky,kz)),intent(inout) :: w0  !! work array
    logical,intent(in),optional             :: extrap   !! if extrapolation is allowed
                                                        !! (if not present, default is False)

    integer(ip) :: lefty, leftz, kcoly, kcolz, j, k

    f = 0.0_wp

    iflag = check_value(xval,tx,1_ip,extrap); if (iflag/=0_ip) return
    iflag = check_value(yval,ty,2_ip,extrap); if (iflag/=0_ip) return
    iflag = check_value(zval,tz,3_ip,extrap); if (iflag/=0_ip) return

    call dintrv(ty,ny+ky,yval,iloy,lefty,iflag,extrap); if (iflag/=0_ip) return
    call dintrv(tz,nz+kz,zval,iloz,leftz,iflag,extrap); if (iflag/=0_ip) return

    iflag = 0_ip

    kcolz = leftz - kz
    do k=1_ip,kz
        kcolz = kcolz + 1_ip
        kcoly = lefty - ky
        do j=1_ip,ky
            kcoly = kcoly + 1_ip
            call dbvalu(tx,bcoef(:,kcoly,kcolz),nx,kx,idx,xval,inbvx,w0,iflag,w2(j,k),extrap)
            if (iflag/=0_ip) return
        end do
    end do

    kcoly = lefty - ky + 1_ip
    do k=1_ip,kz
        call dbvalu(ty(kcoly:),w2(:,k),ky,ky,idy,yval,inbvy,w0,iflag,w1(k),extrap)
        if (iflag/=0_ip) return
    end do

    kcolz = leftz - kz + 1_ip
    call dbvalu(tz(kcolz:),w1,kz,kz,idz,zval,inbvz,w0,iflag,f,extrap)

    end subroutine db3val