# Source code for tecplot.data.operate

    from collections.abc import Iterable
    from contextlib import contextmanager

    from ..tecutil import _tecutil
    from ..constant import *
    from ..exception import *
    from .. import layout, tecutil
    from ..tecutil import IndexSet, Index, flatten_args, sv, optional

    @tecutil.lock()
    def execute_equation(equation, zones=None, i_range=None, j_range=None,
                         k_range=None, value_location=None, variable_data_type=None,
                         ignore_divide_by_zero=None):
        """The execute_equation function operates on a data set within the
        |Tecplot Engine| using FORTRAN-like equations.

        Parameters:
            equation (`str`): String containing the equation.
                Multiple equations can be processed by separating each equation
                with a newline. See Section 20 - 1 "Data Alteration through
                Equations" in the |Tecplot User's Manual| for more information on
                using equations. Iterable container of `Zone <data_access>` objects
                to operate on. May be a list, set, tuple, or any iterable
                container. If `None`, the equation will be applied to all zones.

                .. note:: In the equation string, variable names should be enclosed
                    in curly braces. For example, '{X} = {X} + 1'

            zones: (Iterable container of `Zone <data_access>` objects, optional):
                Iterable container of `Zone <data_access>` objects to operate on.
                May be a list, set, tuple, or any iterable container. If `None`,
                the equation will be applied to all zones.
            i_range (`tuple` of `integers <int>`, optional):
                Tuple of integers for I:  (min, max, step). If `None`, then the
                equation will operate on the entire range.
                Not used for finite element nodal data.
            j_range (`tuple` of `integers <int>`, optional):
                Tuple of integers for J:  (min, max, step). If `None`, then the
                equation will operate on the entire range.
                Not used for finite element nodal data.
            k_range (`tuple` of `integers <int>`, optional):
                Tuple of integers for K:  (min, max, step). If `None`, then the
                equation will operate on the entire range.
                Not used for finite element nodal data.
            value_location (`ValueLocation`, optional):
                Variable `ValueLocation` for the variable on the left hand side.
                This is used only if this variable is being created for the first
                time.
                If `None`, |Tecplot Engine| will choose the location for you.
            variable_data_type (`FieldDataType`, optional):
                Data type for the variable on the left hand side.
                This is used only if this variable is being created for the first
                time.
                If `None`, |Tecplot Engine| will choose the type for you.
            ignore_divide_by_zero (`bool`, optional):
                `bool` value which instructs |Tecplot Engine| to ignore
                divide by zero errors. The result is clamped
                such that 0/0 is clamped to zero and (+/-N)/0
                where N != 0 clamps to +/-maximum value for the given type.

        .. warning:: Zero-based Indexing

            It is important to know that all indexing in |PyTecplot| scripts are
            zero-based. This is a departure from the macro language which is
            one-based. This is to keep with the expectations when working in the
            python language. However, |PyTecplot| does not modify strings that are
            passed to the |Tecplot Engine|. This means that one-based indexing
            should be used when running macro commands from python or when using
            `execute_equation() <tecplot.data.operate.execute_equation>`.

        Add one to variable 'X' for zones 'Rectangular' and 'Circular' for every
        data point:

        >>> dataset = tecplot.active_frame().dataset
        >>> execute_equation('{X} = {X} + 1', zones=[dataset.zone('Rectangular'),
        >>>                  dataset.zone('Circular')])

        Create a new, double precision variable called DIST:

        >>> execute_equation('{DIST} = SQRT({X}**2 + {Y}**2)',
        ...                  variable_data_type=FieldDataType.Double)

        Set a variable called **P** to zero along the boundary of an IJ-ordered
        zone:

        >>> execute_equation('{P} = 0', i_range=(0, -1, 0), j_range=(0, -1, 0))

        Using 1-based indexing in equations and 0-based indexing in parameters.
        Zone 4 is subtracted from zone 3 and the result is placed in zone 2:

        >>> execute_equation('{T} = {T}[3]-{T}[4]', zones=[ds.zone(1)])
        """
        if __debug__:
            if not isinstance(equation, str):
                raise TecplotTypeError('Equation must be a string')
            elif len(equation) == 0:
                raise TecplotValueError('Equation can not be empty')
            if not isinstance(value_location, (ValueLocation, type(None))):
                msg = 'value_location must be a ValueLocation'
                raise TecplotTypeError(msg)
            if not isinstance(variable_data_type, (FieldDataType, type(None))):
                msg = 'variable_data_type must be a FieldDataType'
                raise TecplotTypeError(msg)
            if not isinstance(ignore_divide_by_zero, (bool, type(None))):
                raise TecplotTypeError('ignore_divide_by_zero must be a bool')

            # Check that all zones belong to the active dataset
            # (which is currently the only dataset option available)
            if zones:
                def dataset_uid(zone):
                    '''return the dataset uid if zone is a Zone object.'''
                    try:
                        return zone.dataset.uid
                    except AttributeError:
                        return None

                if isinstance(zones, Iterable):
                    # converting generator to list to allow
                    # iterating over it more than once
                    zones = list(zones)
                    parent_ids = map(dataset_uid, zones)
                else:
                    parent_ids = {dataset_uid(zones)}
                parent_ids = set(filter(None, parent_ids))

                active_id = layout.active_frame().dataset.uid
                if parent_ids and parent_ids != {active_id}:
                    msg = 'All zones must have the same parent dataset'
                    raise TecplotValueError(msg)

        with tecutil.ArgList() as arglist:
            arglist[sv.EQUATION] = equation
            with optional(IndexSet, zones) as zoneset:
                arglist[sv.ZONESET] = zoneset

                for dim, rng in zip(['I', 'J', 'K'], [i_range, j_range, k_range]):
                    if rng is not None:
                        rng = tecutil.IndexRange(*rng)
                        if rng.min is not None:
                            arglist[dim + 'MIN'] = Index(rng.min)
                        if rng.max is not None:
                            arglist[dim + 'MAX'] = Index(rng.max)
                        if rng.step is not None:
                            step = int(rng.step)
                            if step > 0:
                                arglist[dim + 'SKIP'] = step
                            elif step < 0:
                                msg = 'Negative step not supported.'
                                raise TecplotLogicError(msg)

                arglist[sv.VALUELOCATION] = value_location
                arglist[sv.VARDATATYPE] = variable_data_type
                arglist[sv.IGNOREDIVIDEBYZERO] = ignore_divide_by_zero

                if not _tecutil.DataAlterX(arglist):
                    raise TecplotSystemError()

    @contextmanager
    def _interpolate_process_args(dest_zone, src_zones, variables, plot):
        if plot is None:
            plot = layout.active_frame().plot()
        if isinstance(dest_zone, int):
            dest_zone = plot.frame.dataset.zone(dest_zone)
        if not isinstance(src_zones, (Iterable, type(None))):
            src_zones = [src_zones]
        if not isinstance(variables, (Iterable, type(None))):
            variables = [variables]

        if __debug__:
            if plot.frame.dataset != dest_zone.dataset:
                msg = 'Plot and destination zone do not share the same dataset.'
                raise TecplotLogicError(msg)
            if src_zones is not None:
                def is_invalid_zone(z):
                    if isinstance(z, int):
                        return z >= plot.frame.dataset.num_zones
                    else:
                        return plot.frame.dataset != z.dataset
                if any(map(is_invalid_zone, src_zones)):
                    msg = 'Source zones are not part of the same dataset.'
                    raise TecplotLogicError(msg)
            if variables is not None:
                def is_invalid_variable(v):
                    if isinstance(v, int):
                        return v >= plot.frame.dataset.num_variables
                    else:
                        return plot.frame.dataset != v.dataset
                if any(map(is_invalid_variable, variables)):
                    msg = 'Variables are not part of the same dataset.'
                    raise TecplotLogicError(msg)

        with plot.activated():
            with optional(IndexSet, src_zones) as src:
                with optional(IndexSet, variables) as varset:
                    dest = dest_zone.index + 1
                    yield src, dest, varset

    @tecutil.lock()
    def interpolate_linear(destination_zone, source_zones=None, variables=None,
                           fill_value=None, plot=None):
        """Linear interpolation onto a destination zone.

        Parameters:
            destination_zone (`zone <data_access>` or `int`): The
                destination zone (or zone index) for interpolation.
            source_zones (`zones <data_access>` or `integers <int>`, optional):
                Zones (or zone indices) used to obtain the field values for
                interpolation. By default, all zones except the *destination_zone*
                will be used. All source zones must be FE-Tetra, FE-Brick or be
                IJK-ordered when doing linear interpolation in 3D.
            variables (`variables <Variable>` or `integers <int>`, optional):
                Variables (or variable indices) to interpolate. By default, all
                variables except those assigned to the axes will be used and is in
                general dependent on the active plot type of the frame.
            fill_value (`float`, optional): Constant value to which all points
                outside the data field are set. By default, the values outside
                the field are preserved.
            plot (:ref:`plot`, optional): The plot to use when interpolating which
                determines the dimensionality and spatial variables. By default,
                the active plot on the active frame will be used.

        .. note:: Cartesian 2D and 3D plots only.

            This interpolation method relies on the coordinates, :math:`(x, y)` for
            2D or :math:`(x, y, z)` for 3D, set for the active (or given) plot
            which must be either Cartesian2D or Cartesian3D.

        The following example loads a 2D dataset and uses interpolation to merge
        information from two independent zones:

        .. code-block:: python

            import os
            import numpy as np
            import tecplot as tp
            from tecplot.constant import *

            # Use interpolation to merge information from two independent zones
            examples_dir = tp.session.tecplot_examples_directory()
            datafile = os.path.join(examples_dir, 'SimpleData', 'RainierElevation.plt')
            dataset = tp.data.load_tecplot(datafile)
            # Get list of source zones to use later
            srczones = list(dataset.zones())

            fr = tp.active_frame()
            plot = fr.plot(PlotType.Cartesian2D)
            plot.activate()
            plot.show_contour = True
            plot.show_edge = True

            # Show two section of the plot independently
            plot.contour(0).legend.show = False
            plot.contour(1).legend.show = False
            plot.contour(1).colormap_name = 'Diverging - Blue/Red'
            for scrzone in srczones:
                plot.fieldmap(scrzone).edge.line_thickness = 0.4
            plot.fieldmap(0).contour.flood_contour_group = plot.contour(1)

            # export image of original data
            tp.export.save_png('interpolate_2d_source.png', 600, supersample=3)

            # use the first zone as the source, and get the range of (x, y)
            xvar = plot.axes.x_axis.variable
            yvar = plot.axes.y_axis.variable
            ymin, xmin = 99999,99999
            ymax, xmax = -99999,-99999
            for scrzone in srczones:
                curxmin, curxmax = scrzone.values(xvar.index).minmax()
                curymin, curymax = scrzone.values(yvar.index).minmax()
                ymin = min(curymin,ymin)
                ymax = max(curymax,ymax)
                xmin = min(curxmin,xmin)
                xmax = max(curxmax,xmax)

            # create new zone with a coarse grid
            # onto which we will interpolate from the source zone
            xpoints = 40
            ypoints = 40
            newzone = dataset.add_ordered_zone('Interpolated', (xpoints, ypoints))

            # setup the (x, y) positions of the new grid
            xx = np.linspace(xmin, xmax, xpoints)
            yy = np.linspace(ymin, ymax, ypoints)
            YY, XX = np.meshgrid(yy, xx, indexing='ij')
            newzone.values(xvar.index)[:] = XX.ravel()
            newzone.values(yvar.index)[:] = YY.ravel()

            # perform linear interpolation from the source to the new zone
            tp.data.operate.interpolate_linear(newzone, source_zones=srczones)

            # show the new zone's data, hide the source
            plot.fieldmap(newzone).show = True
            plot.fieldmap(newzone).contour.show = True
            plot.fieldmap(newzone).contour.flood_contour_group = plot.contour(0)
            plot.fieldmap(newzone).edge.show = True
            plot.fieldmap(newzone).edge.line_thickness = .4
            plot.fieldmap(newzone).edge.color = Color.Orange

            for scrzone in srczones:
                plot.fieldmap(scrzone).show = False

            # export image of interpolated data
            tp.export.save_png('interpolate_linear_2d_dest.png', 600, supersample=3)

        .. figure:: /_static/images/interpolate_2d_source.png
            :width: 300px
            :figwidth: 300px

            Source data.

        .. figure:: /_static/images/interpolate_linear_2d_dest.png
            :width: 300px
            :figwidth: 300px

            Interpolated data.

        """
        with _interpolate_process_args(destination_zone, source_zones, variables,
                                       plot) as (src, dest, varset):
            if fill_value is None:
                interp_const = 0.0
                interp_mode = LinearInterpMode.DontChange
            else:
                interp_const = float(fill_value)
                interp_mode = LinearInterpMode.SetToConst
            if not _tecutil.LinearInterpolate(src, dest, varset, interp_const,
                                              interp_mode.value):
                raise TecplotSystemError()

    @tecutil.lock()
    def interpolate_kriging(destination_zone, source_zones=None, variables=None,
                            krig_range=0.3, zero_value=0.0, drift=Drift.Linear,
                            point_selection=PtSelection.OctantN, num_points=8,
                            plot=None):
        """Kriging interpolation onto a destination zone.

        Parameters:
            destination_zone (`zone <data_access>` or `int`): The
                destination zone (or zone index) for interpolation.
            source_zones (`zones <data_access>` or `integers <int>`, optional):
                Zones (or zone indices) used to obtain the field values for
                interpolation. By default, all zones except the *destination_zone*
                will be used. All source zones must be FE-Tetra, FE-Brick or
                IJK-ordered when doing kriging interpolation in 3D.
            variables (`variables <Variable>` or `integers <int>`, optional):
                Variables (or variable indices) to interpolate. By default, all
                variables except those assigned to the axes will be used and is in
                general dependent on the active plot type of the frame.
            krig_range (`float`, optional): Distance beyond which source points
                become insignificant. Must be between zero and one, inclusive.
                (default: 0.3)
            zero_value (`float`, optional): Semi-variance at each source data point
                on a normalized scale from zero to one. (default: 0.0)
            drift (`Drift`, optional): Overall trend for the data. Possible values:
                `Drift.None_` no trend, `Drift.Linear` (default) linear trend,
                `Drift.Quad` quadratic trend.
            point_selection (`PtSelection`, optional): Method for determining which
                source points to consider for each destination data point. Possible
                values: `PtSelection.OctantN` (default) closest *num_points*
                selected by coordinate-system octants, `PtSelection.NearestN`
                closest *num_points* to the destination point, `PtSelection.All`
                all points in the source zone.
            num_points (`int`, optional): Number of source points to
                consider for each destination data point if *point_selection* is
                `PtSelection.OctantN` or `PtSelection.NearestN`. (default: 8)
            plot (:ref:`plot`, optional): The plot to use when interpolating which
                determines the dimensionality and spatial variables. By default,
                the active plot on the active frame will be used.

        .. note:: Cartesian 2D and 3D plots only.

            This interpolation method relies on the coordinates, :math:`(x, y)` for
            2D or :math:`(x, y, z)` for 3D, set for the active (or given) plot
            which must be either Cartesian2D or Cartesian3D.

        The following example loads a 2D dataset and interpolates the first zone to
        a new one with a larger grid spacing:

        .. code-block:: python
            :emphasize-lines: 58-59

            import os
            import numpy as np
            import tecplot as tp
            from tecplot.constant import *

            # Use interpolation to merge information from two independent zones
            examples_dir = tp.session.tecplot_examples_directory()
            datafile = os.path.join(examples_dir, 'SimpleData',
                                    'RainierElevation.plt')
            dataset = tp.data.load_tecplot(datafile)
            # Get list of source zones to use later
            srczones = list(dataset.zones())

            fr = tp.active_frame()
            plot = fr.plot(PlotType.Cartesian2D)
            plot.activate()
            plot.show_contour = True
            plot.show_edge = True

            # Show two section of the plot independently
            plot.contour(0).legend.show = False
            plot.contour(1).legend.show = False
            plot.contour(1).colormap_name = 'Diverging - Blue/Red'
            for scrzone in srczones:
                plot.fieldmap(scrzone).edge.line_thickness = 0.4
            plot.fieldmap(0).contour.flood_contour_group = plot.contour(1)

            # export image of original data
            tp.export.save_png('interpolate_2d_source.png', 600, supersample=3)

            # use the first zone as the source, and get the range of (x, y)
            xvar = plot.axes.x_axis.variable
            yvar = plot.axes.y_axis.variable
            ymin, xmin = 99999,99999
            ymax, xmax = -99999,-99999
            for scrzone in srczones:
                curxmin, curxmax = scrzone.values(xvar.index).minmax()
                curymin, curymax = scrzone.values(yvar.index).minmax()
                ymin = min(curymin,ymin)
                ymax = max(curymax,ymax)
                xmin = min(curxmin,xmin)
                xmax = max(curxmax,xmax)

            # create new zone with a coarse grid
            # onto which we will interpolate from the source zone
            xpoints = 20
            ypoints = 20
            newzone = dataset.add_ordered_zone('Interpolated', (xpoints, ypoints))

            # setup the (x, y) positions of the new grid
            xx = np.linspace(xmin, xmax, xpoints)
            yy = np.linspace(ymin, ymax, ypoints)
            YY, XX = np.meshgrid(yy, xx, indexing='ij')
            newzone.values(xvar.index)[:] = XX.ravel()
            newzone.values(yvar.index)[:] = YY.ravel()

            # perform linear interpolation from the source to the new zone
            tp.data.operate.interpolate_kriging(newzone, source_zones=srczones,
                                                drift=Drift.None_, num_points=1)

            # show the new zone's data, hide the source
            plot.fieldmap(newzone).show = True
            plot.fieldmap(newzone).contour.show = True
            plot.fieldmap(newzone).contour.flood_contour_group = plot.contour(0)
            plot.fieldmap(newzone).edge.show = True
            plot.fieldmap(newzone).edge.line_thickness = .4
            plot.fieldmap(newzone).edge.color = Color.Orange

            for scrzone in srczones:
                plot.fieldmap(scrzone).show = False

            # export image of interpolated data
            tp.export.save_png('interpolate_krig_2d_dest.png', 600, supersample=3)

        .. figure:: /_static/images/interpolate_2d_source.png
            :width: 300px
            :figwidth: 300px

            Source data.

        .. figure:: /_static/images/interpolate_krig_2d_dest.png
            :width: 300px
            :figwidth: 300px

            Interpolated data.
        """
        with _interpolate_process_args(destination_zone, source_zones, variables,
                                       plot) as (src, dest, varset):
            if not _tecutil.Krig(
                src, dest, varset, krig_range, zero_value, Drift(drift).value,
                    PtSelection(point_selection).value, num_points):
                raise TecplotSystemError()

    @tecutil.lock()
    def interpolate_inverse_distance(destination_zone, source_zones=None,
                                     variables=None, exponent=3.5, min_radius=0.0,
                                     point_selection=PtSelection.OctantN,
                                     num_points=8, plot=None):
        """Inverse-Distance interpolation onto a destination zone.

        Parameters:
            destination_zone (`zone <data_access>` or `int`): The
                destination zone (or zone index) for interpolation.
            source_zones (`zones <data_access>` or `integers <int>`, optional):
                Zones (or zone indices) used to obtain the field values for
                interpolation. By default, all zones except the *destination_zone*
                will be used. All source zones must be FE-Tetra, FE-Brick or be
                IJK-ordered when doing linear interpolation in 3D.
            variables (`variables <Variable>` or `integers <int>`, optional):
                Variables (or variable indices) to interpolate. By default, all
                variables except those assigned to the axes will be used and is in
                general dependent on the active plot type of the frame.
            exponent (`float`, optional): Exponent for the inverse-distance
                weighting. (default: 3.5)
            min_radius (`float`, optional): Minimum distance used for the
                inverse-distance weighting. (default: 0.0)
            point_selection (`PtSelection`, optional): Method for determining which
                source points to consider for each destination data point. Possible
                values: `PtSelection.OctantN` (default) closest *num_points*
                selected by coordinate-system octants, `PtSelection.NearestN`
                closest *num_points* to the destination point, `PtSelection.All`
                all points in the source zone.
            num_points (`int`, optional): Number of source points to
                consider for each destination data point if *point_selection* is
                `PtSelection.OctantN` or `PtSelection.NearestN`. (default: 8)
            plot (:ref:`plot`, optional): The plot to use when interpolating which
                determines the dimensionality and spatial variables. By default,
                the active plot on the active frame will be used.

        .. note:: Cartesian 2D and 3D plots only.

            This interpolation method relies on the coordinates, :math:`(x, y)` for
            2D or :math:`(x, y, z)` for 3D, set for the active (or given) plot
            which must be either Cartesian2D or Cartesian3D.

        The following example loads a 2D dataset and interpolates the first zone to
        a new one with a larger grid spacing:

        .. code-block:: python
            :emphasize-lines: 57

            import os
            import numpy as np
            import tecplot as tp
            from tecplot.constant import *

            # Use interpolation to merge information from two independent zones
            examples_dir = tp.session.tecplot_examples_directory()
            datafile = os.path.join(examples_dir, 'SimpleData', 'RainierElevation.plt')
            dataset = tp.data.load_tecplot(datafile)
            # Get list of source zones to use later
            srczones = list(dataset.zones())

            fr = tp.active_frame()
            plot = fr.plot(PlotType.Cartesian2D)
            plot.activate()
            plot.show_contour = True
            plot.show_edge = True

            # Show two section of the plot independently
            plot.contour(0).legend.show = False
            plot.contour(1).legend.show = False
            plot.contour(1).colormap_name = 'Diverging - Blue/Red'
            for scrzone in srczones:
                plot.fieldmap(scrzone).edge.line_thickness = 0.4
            plot.fieldmap(0).contour.flood_contour_group = plot.contour(1)

            # export image of original data
            tp.export.save_png('interpolate_2d_source.png', 600, supersample=3)

            # use the first zone as the source, and get the range of (x, y)
            xvar = plot.axes.x_axis.variable
            yvar = plot.axes.y_axis.variable
            ymin, xmin = 99999,99999
            ymax, xmax = -99999,-99999
            for scrzone in srczones:
                curxmin, curxmax = scrzone.values(xvar.index).minmax()
                curymin, curymax = scrzone.values(yvar.index).minmax()
                ymin = min(curymin,ymin)
                ymax = max(curymax,ymax)
                xmin = min(curxmin,xmin)
                xmax = max(curxmax,xmax)

            # create new zone with a coarse grid
            # onto which we will interpolate from the source zone
            xpoints = 40
            ypoints = 40
            newzone = dataset.add_ordered_zone('Interpolated', (xpoints, ypoints))

            # setup the (x, y) positions of the new grid
            xx = np.linspace(xmin, xmax, xpoints)
            yy = np.linspace(ymin, ymax, ypoints)
            YY, XX = np.meshgrid(yy, xx, indexing='ij')
            newzone.values(xvar.index)[:] = XX.ravel()
            newzone.values(yvar.index)[:] = YY.ravel()

            # perform linear interpolation from the source to the new zone
            tp.data.operate.interpolate_inverse_distance(newzone, source_zones=srczones)

            # show the new zone's data, hide the source
            plot.fieldmap(newzone).show = True
            plot.fieldmap(newzone).contour.show = True
            plot.fieldmap(newzone).contour.flood_contour_group = plot.contour(0)
            plot.fieldmap(newzone).edge.show = True
            plot.fieldmap(newzone).edge.line_thickness = .4
            plot.fieldmap(newzone).edge.color = Color.Orange

            for scrzone in srczones:
                plot.fieldmap(scrzone).show = False

            # export image of interpolated data
            tp.export.save_png('interpolate_invdst_2d_dest.png', 600, supersample=3)

        .. figure:: /_static/images/interpolate_2d_source.png
            :width: 300px
            :figwidth: 300px

            Source data.

        .. figure:: /_static/images/interpolate_invdst_2d_dest.png
            :width: 300px
            :figwidth: 300px

            Interpolated data.
        """
        with _interpolate_process_args(destination_zone, source_zones, variables,
                                       plot) as (src, dest, varset):
            if not _tecutil.InverseDistInterpolation(
                src, dest, varset, exponent, min_radius,
                    PtSelection(point_selection).value, num_points):
                raise TecplotSystemError()

    @tecutil.lock()
    def smooth(array, num_passes=1, weight=0.8,
               boundary_condition=BoundaryCondition.Fixed, frame=None):
        """Smooth a field data `Array` in the dataset.

        Parameters:
            array (`Array`): The field data to smooth.
            num_passes (`int`, optional): The number of smoothing passes to
                perform. (default: 1)
            weight (`float`, optional):  The relaxation factor for each pass of
                smoothing. Must be a number between zero and one exclusively.
                Higher numbers indicate a greater smoothing effect. (default: 0.8)
            boundary_condition (`BoundaryCondition`, optional): The boundary
                condition by which to smooth. Possible values are
                `BoundaryCondition.Fixed` (default),
                `BoundaryCondition.ZeroGradient` and `BoundaryCondition.Zero2nd`.
            frame (`Frame`, optional): The `Frame` that specifies the spatial
                variables to smooth over via the active plot. By default, the frame
                associated with the input `Array` object will be used.

        The data will be smoothed over the spatial variables set by the plot and is
        dependent on the active plot type of the associated `Frame` (`Cartesian2D`
        or `Cartesian3D`). Example usage::

            >>> tp.data.operate.smooth(dataset.zone('Zone').values('Pressure'))
        """
        frame = frame or array.zone.dataset.frame
        with frame.activated():
            if not _tecutil.Smooth(array.zone.index + 1, array.variable.index + 1,
                                   int(num_passes), float(weight),
                                   BoundaryCondition(boundary_condition).value):
                raise TecplotSystemError()

    def _dataset(*objlists):
        for objs in objlists:
            if objs:
                for obj in objs:
                    if obj and hasattr(obj, 'dataset'):
                        return obj.dataset
        return layout.active_frame().dataset

    @tecutil.lock()
    def transform_polar_to_rectangular(r, theta, x=None, y=None,
                                       angle_units=AngleUnits.Radians, zones=None):
        """Transform all points from polar to rectangular coordinates.

        Parameters:
            r (`Variable`): The radial input variable.
            theta (`Variable`): The angular input variable in **angle_units** from
                the :math:`x`-axis.
            x (`Variable`, optional): The rectangular output :math:`x` variable. By
                default, a new variable will be created. Both **x** and **y** must
                be specified together as either existing variables or as `None`.
            y (`Variable`, optional): The rectangular output :math:`y` variable. By
                default, a new variable will be created. Both **x** and **y** must
                be specified together as either existing variables or as `None`.
            angle_units (`AngleUnits`, optional): The units of the angular
                variables. This may be either `AngleUnits.Radians` (default) or
                `AngleUnits.Degrees`.
            zones (`list` of `Zones <data_access>`, optional): Specific zones to
                transform. By default, all zones are transformed.

        This example will create two new variables in the dataset corresponding to
        the :math:`x` and :math:`y` equivalents of the :math:`r` and :math:`theta`
        variables::

            >>> dataset = tp.active_frame().dataset
            >>> r = dataset.variable('R (m)')
            >>> theta = dataset.variable('Theta (rad)')
            >>> tp.data.operate.transform_polar_to_rectangular(r, theta)
            >>> x, y = dataset.variable(-2), dataset.variable(-1)

        .. warning:: **Source variables must have the same location as the
            destination variables.**

            The variables involved with this transformation must all be either
            nodal or cell-centered.
        """
        dataset = _dataset((r, theta, x, y), zones)
        with tecutil.ArgList() as arglist:
            arglist[sv.TRANSFORMATION] = Transform.PolarToRect
            arglist[sv.RVAR] = dataset.variable(r).index
            arglist[sv.THETAVAR] = dataset.variable(theta).index
            if all(v is None for v in (x, y)):
                arglist[sv.CREATENEWVARIABLES] = True
                arglist[sv.XVAR] = 1
                arglist[sv.YVAR] = 1
            elif all(v is not None for v in (x, y)):
                arglist[sv.CREATENEWVARIABLES] = False
                arglist[sv.XVAR] = dataset.variable(x).index
                arglist[sv.YVAR] = dataset.variable(y).index
            else:
                msg = 'All destination variables must be specified or None.'
                raise TecplotLogicError(msg)
            arglist[sv.ANGLESPEC] = AngleUnits(angle_units)
            with tecutil.optional(tecutil.IndexSet, zones) as zones:
                arglist[sv.ZONELIST] = zones
                if not _tecutil.TransformCoordinatesX(arglist):
                    raise TecplotSystemError()

    @tecutil.lock()
    def transform_rectangular_to_polar(x, y, r=None, theta=None,
                                       angle_units=AngleUnits.Radians, zones=None):
        """Transform all points from rectangular to polar coordinates.

        Parameters:
            x (`Variable`): The rectangular input :math:`x` variable.
            y (`Variable`): The rectangular input :math:`y` variable.
            r (`Variable`, optional): The radial output :math:`r` variable. By
                default, a new variable will be created. Both **r** and **theta**
                must be specified together as either existing variables or as
                `None`.
            theta (`Variable`, optional): The angular output :math:`theta`
                variable. By default, a new variable will be created. Both **r**
                and **theta** must be specified together as either existing
                variables or as `None`.
            angle_units (`AngleUnits`, optional): The units of the angular
                variables. This may be either `AngleUnits.Radians` (default) or
                `AngleUnits.Degrees`.
            zones (`list` of `Zones <data_access>`, optional): Specific zones to
                transform. By default, all zones are transformed.

        This example will create two new variables in the dataset corresponding to
        the :math:`r` and :math:`theta` equivalents of the :math:`x` and :math:`y`
        variables::

            >>> dataset = tp.active_frame().dataset
            >>> x = dataset.variable('X (m)')
            >>> y = dataset.variable('Y (m)')
            >>> tp.data.operate.transform_rectangular_to_polar(x, y)
            >>> theta, r = dataset.variable(-2), dataset.variable(-1)

        .. warning:: **Source variables must have the same location as the
            destination variables.**

            The variables involved with this transformation must all be either
            nodal or cell-centered.
        """
        dataset = _dataset((x, y, r, theta), zones)
        with tecutil.ArgList() as arglist:
            arglist[sv.TRANSFORMATION] = Transform.RectToPolar
            # (x, y) are switched in the SDK for this polar transformation
            arglist[sv.XVAR] = dataset.variable(y).index
            arglist[sv.YVAR] = dataset.variable(x).index
            if all(v is None for v in (r, theta)):
                arglist[sv.CREATENEWVARIABLES] = True
                arglist[sv.RVAR] = 1
                arglist[sv.THETAVAR] = 1
            elif all(v is not None for v in (r, theta)):
                arglist[sv.CREATENEWVARIABLES] = False
                arglist[sv.RVAR] = dataset.variable(r).index
                arglist[sv.THETAVAR] = dataset.variable(theta).index
            else:
                msg = 'All destination variables must be specified or None.'
                raise TecplotLogicError(msg)
            arglist[sv.ANGLESPEC] = AngleUnits(angle_units)
            with tecutil.optional(tecutil.IndexSet, zones) as zones:
                arglist[sv.ZONELIST] = zones
                if not _tecutil.TransformCoordinatesX(arglist):
                    raise TecplotSystemError()

    @tecutil.lock()
    def transform_spherical_to_rectangular(r, theta, psi, x=None, y=None, z=None,
                                       angle_units=AngleUnits.Radians, zones=None):
        """Transform all points from spherical to rectangular coordinates.

        Parameters:
            r (`Variable`): The radial input variable.
            theta (`Variable`): The angular input variable in **angle_units** from
                the :math:`x`-axis.
            psi (`Variable`): The angular input variable in **angle_units** from
                the :math:`z`-axis.
            x (`Variable`, optional): The rectangular output :math:`x` variable. By
                default, a new variable will be created. All of **x**, **y** and
                **z** must be specified together as either existing variables or as
                `None`.
            y (`Variable`, optional): The rectangular output :math:`y` variable. By
                default, a new variable will be created. All of **x**, **y** and
                **z** must be specified together as either existing variables or as
                `None`.
            z (`Variable`, optional): The rectangular output :math:`z` variable. By
                default, a new variable will be created. All of **x**, **y** and
                **z** must be specified together as either existing variables or as
                `None`.
            angle_units (`AngleUnits`, optional): The units of the angular
                variables. This may be either `AngleUnits.Radians` (default) or
                `AngleUnits.Degrees`.
            zones (`list` of `Zones <data_access>`, optional): Specific zones to
                transform. By default, all zones are transformed.

        This example will create three new variables in the dataset corresponding
        to the :math:`(x, y, z)` equivalents of the :math:`(r, theta, psi)`
        variables::

            >>> dataset = tp.active_frame().dataset
            >>> r = dataset.variable('R (m)')
            >>> theta = dataset.variable('Theta (rad)')
            >>> psi = dataset.variable('Psi (rad)')
            >>> tp.data.operate.transform_spherical_to_rectangular(r, theta, psi)
            >>> x = dataset.variable(-3)
            >>> y = dataset.variable(-2)
            >>> z = dataset.variable(-1)

        .. warning:: **Source variables must have the same location as the
            destination variables.**

            The variables involved with this transformation must all be either
            nodal or cell-centered.
        """
        dataset = _dataset((r, theta, psi, x, y, z), zones)
        with tecutil.ArgList() as arglist:
            arglist[sv.TRANSFORMATION] = Transform.SphericalToRect
            arglist[sv.RVAR] = dataset.variable(r).index
            arglist[sv.THETAVAR] = dataset.variable(theta).index
            arglist[sv.PSIVAR] = dataset.variable(psi).index
            if all(v is None for v in (x, y, z)):
                arglist[sv.CREATENEWVARIABLES] = True
                arglist[sv.XVAR] = 1
                arglist[sv.YVAR] = 1
                arglist[sv.ZVAR] = 1
            elif all(v is not None for v in (x, y, z)):
                arglist[sv.CREATENEWVARIABLES] = False
                arglist[sv.XVAR] = dataset.variable(x).index
                arglist[sv.YVAR] = dataset.variable(y).index
                arglist[sv.ZVAR] = dataset.variable(z).index
            else:
                msg = 'All destination variables must be specified or None.'
                raise TecplotLogicError(msg)
            arglist[sv.ANGLESPEC] = AngleUnits(angle_units)
            with tecutil.optional(tecutil.IndexSet, zones) as zones:
                arglist[sv.ZONELIST] = zones
                if not _tecutil.TransformCoordinatesX(arglist):
                    raise TecplotSystemError()

    @tecutil.lock()
    def transform_rectangular_to_spherical(x, y, z, r=None, theta=None, psi=None,
                                       angle_units=AngleUnits.Radians, zones=None):
        """Transform all points from rectangular to spherical coordinates.

        Parameters:
            x (`Variable`): The rectangular input :math:`x` variable.
            y (`Variable`): The rectangular input :math:`y` variable.
            z (`Variable`): The rectangular input :math:`z` variable.
            r (`Variable`, optional): The radial output :math:`r` variable. By
                default, a new variable will be created. All of **r**, **theta**
                and **psi** must be specified together as either existing variables
                or as `None`.
            theta (`Variable`, optional): The angular output :math:`theta` variable
                from the :math:`x`-axis. By default, a new variable will be
                created. All of **r**, **theta** and **psi** must be specified
                together as either existing variables or as `None`.
            psi (`Variable`, optional): The angular output :math:`psi` variable
                from the :math:`z`-axis. By default, a new variable will be
                created. All of **r**, **theta** and **psi** must be specified
                together as either existing variables or as `None`.
            angle_units (`AngleUnits`, optional): The units of the angular
                variables. This may be either `AngleUnits.Radians` (default) or
                `AngleUnits.Degrees`.
            zones (`list` of `Zones <data_access>`, optional): Specific zones to
                transform. By default, all zones are transformed.

        This example will create three new variables in the dataset corresponding
        to the :math:`(r, theta, psi)` equivalents of the :math:`(x, y, z)`
        variables::

            >>> dataset = tp.active_frame().dataset
            >>> x = dataset.variable('X (m)')
            >>> y = dataset.variable('Y (m)')
            >>> z = dataset.variable('Z (m)')
            >>> tp.data.operate.transform_rectangular_to_spherical(x, y, z)
            >>> theta = dataset.variable(-3)
            >>> r = dataset.variable(-2)
            >>> psi = dataset.variable(-1)

        .. warning:: **Source variables must have the same location as the
            destination variables.**

            The variables involved with this transformation must all be either
            nodal or cell-centered.
        """
        dataset = _dataset((x, y, z, r, theta, psi), zones)
        with tecutil.ArgList() as arglist:
            arglist[sv.TRANSFORMATION] = Transform.RectToSpherical
            arglist[sv.XVAR] = dataset.variable(x).index
            arglist[sv.YVAR] = dataset.variable(y).index
            arglist[sv.ZVAR] = dataset.variable(z).index
            if all(v is None for v in (r, theta, psi)):
                arglist[sv.CREATENEWVARIABLES] = True
                arglist[sv.RVAR] = 1
                arglist[sv.THETAVAR] = 1
                arglist[sv.PSIVAR] = 1
            elif all(v is not None for v in (r, theta, psi)):
                arglist[sv.CREATENEWVARIABLES] = False
                arglist[sv.RVAR] = dataset.variable(r).index
                arglist[sv.THETAVAR] = dataset.variable(theta).index
                arglist[sv.PSIVAR] = dataset.variable(psi).index
            else:
                msg = 'All destination variables must be specified or None.'
                raise TecplotLogicError(msg)
            arglist[sv.ANGLESPEC] = AngleUnits(angle_units)
            with tecutil.optional(tecutil.IndexSet, zones) as zones:
                arglist[sv.ZONELIST] = zones
                if not _tecutil.TransformCoordinatesX(arglist):
                    raise TecplotSystemError()