@@ -758,8 +758,12 @@ class gridmatrix(param.ParameterizedFunction):
         for d1, d2 in permuted_dims:
             if d1 == d2:
                 if p.diagonal_type is not None:
-                    values = element.dimension_values(d1)
-                    el = p.diagonal_type(values, vdims=[d1])
+                    if p.diagonal_type._1d:
+                        values = element.dimension_values(d1)
+                        el = p.diagonal_type(values, vdims=[d1])
+                    else:
+                        el = p.diagonal_type(el_data, kdims=[d1], vdims=[d2],
+                                             datatype=['dataframe', 'dictionary'])
                 elif p.diagonal_operation is histogram or isinstance(p.diagonal_operation, histogram):
                     bin_range = ranges.get(d1.name, element.range(d1))
                     opts = dict(axiswise=True, framewise=True)
"""
Collection of either extremely generic or simple ElementOperation
examples.
"""

import numpy as np

import param
from param import _is_number

from ..core import (ElementOperation, NdOverlay, Overlay, GridMatrix,
                    HoloMap, Dataset, Element, Collator)
from ..core.data import ArrayInterface, DictInterface
from ..core.util import find_minmax, group_sanitizer, label_sanitizer, pd
from ..element.chart import Histogram, Scatter
from ..element.raster import Raster, Image, RGB, QuadMesh
from ..element.path import Contours, Polygons
from ..element.util import categorical_aggregate2d
from ..streams import RangeXY

column_interfaces = [ArrayInterface, DictInterface]
if pd:
    from ..core.data import PandasInterface
    column_interfaces.append(PandasInterface)


def identity(x,k): return x

class operation(ElementOperation):
    """
    The most generic operation that wraps any callable into an
    ElementOperation. The callable needs to accept an HoloViews
    component and a key (that may be ignored) and must return a new
    HoloViews component.

    This class may be useful for turning a HoloViews method into an
    operation to define as compositor operation. For instance, the
    following definition:

    operation.instance(op=lambda x, k: x.collapse(np.subtract))

    Could be used to implement a collapse operation to subtracts the
    data between Rasters in an Overlay.
    """

    output_type = param.Parameter(None, doc="""
       The output element type which may be None to disable type
       checking.

       May be used to declare useful information to other code in
       HoloViews e.g required for tab-completion support of operations
       registered with compositors.""")

    group = param.String(default='Operation', doc="""
        The group assigned to the result after having applied the
        operator.""")

    op = param.Callable(default=identity, doc="""
        The operation used to generate a new HoloViews object returned
        by the operation. By default, the identity operation is
        applied.""")

    def _process(self, view, key=None):
        retval = self.p.op(view, key)
        if (self.p.output_type is not None):
            assert isinstance(retval, self.p.output_type), \
                              "Return value does not match the declared output type."
        return retval.relabel(group=self.p.group)


class factory(ElementOperation):
    """
    Simple operation that constructs any element that accepts some
    other element as input. For instance, RGB and HSV elements can be
    created from overlays of Image elements.
    """

    output_type = param.Parameter(RGB, doc="""
        The output type of the factor operation.

        By default, if three overlaid Images elements are supplied,
        the corresponding RGB element will be returned. """)

    def _process(self, view, key=None):
        return self.p.output_type(view)


class chain(ElementOperation):
    """
    Defining an ElementOperation chain is an easy way to define a new
    ElementOperation from a series of existing ones. The argument is a
    list of ElementOperation (or ElementOperation instances) that are
    called in sequence to generate the returned element.

    chain(operations=[gradient, threshold.instance(level=2)])

    This operation can accept an Image instance and would first
    compute the gradient before thresholding the result at a level of
    2.0.

    Instances are only required when arguments need to be passed to
    individual operations so the resulting object is a function over a
    single argument.
    """

    output_type = param.Parameter(Image, doc="""
        The output type of the chain operation. Must be supplied if
        the chain is to be used as a channel operation.""")

    group = param.String(default='Chain', doc="""
        The group assigned to the result after having applied the chain.""")


    operations = param.List(default=[], class_=ElementOperation, doc="""
       A list of ElementOperations (or ElementOperation instances)
       that are applied on the input from left to right..""")

    def _process(self, view, key=None):
        processed = view
        for operation in self.p.operations:
            processed = operation.process_element(processed, key,
                                                  input_ranges=self.p.input_ranges)

        return processed.clone(group=self.p.group)


class transform(ElementOperation):
    """
    Generic ElementOperation to transform an input Image or RGBA
    element into an output Image. The transformation is defined by
    the supplied callable that accepts the data of the input Image
    (typically a numpy array) and returns the transformed data of the
    output Image.

    This operator is extremely versatile; for instance, you could
    implement an alternative to the explict threshold operator with:

    operator=lambda x: np.clip(x, 0, 0.5)

    Alternatively, you can implement a transform computing the 2D
    autocorrelation using the scipy library with:

    operator=lambda x: scipy.signal.correlate2d(x, x)
    """

    output_type = Image

    group = param.String(default='Transform', doc="""
        The group assigned to the result after applying the
        transform.""")

    operator = param.Callable(doc="""
       Function of one argument that transforms the data in the input
       Image to the data in the output Image. By default, acts as
       the identity function such that the output matches the input.""")

    def _process(self, matrix, key=None):
        processed = (matrix.data if not self.p.operator
                     else self.p.operator(matrix.data))
        return Image(processed, matrix.bounds, group=self.p.group)



class image_overlay(ElementOperation):
    """
    Operation to build a overlay of images to a specification from a
    subset of the required elements.

    This is useful for reordering the elements of an overlay,
    duplicating layers of an overlay or creating blank image elements
    in the appropriate positions.

    For instance, image_overlay may build a three layered input
    suitable for the RGB factory operation even if supplied with one
    or two of the required channels (creating blank channels for the
    missing elements).

    Note that if there is any ambiguity regarding the match, the
    strongest match will be used. In the case of a tie in match
    strength, the first layer in the input is used. One successful
    match is always required.
    """

    output_type = Overlay

    spec = param.String(doc="""
       Specification of the output Overlay structure. For instance:

       Image.R * Image.G * Image.B

       Will ensure an overlay of this structure is created even if
       (for instance) only (Image.R * Image.B) is supplied.

       Elements in the input overlay that match are placed in the
       appropriate positions and unavailable specification elements
       are created with the specified fill group.""")

    fill = param.Number(default=0)

    default_range = param.Tuple(default=(0,1), doc="""
        The default range that will be set on the value_dimension of
        any automatically created blank image elements.""")

    group = param.String(default='Transform', doc="""
        The group assigned to the resulting overlay.""")


    @classmethod
    def _match(cls, el, spec):
        "Return the strength of the match (None if no match)"
        spec_dict = dict(zip(['type', 'group', 'label'], spec.split('.')))
        if not isinstance(el, Image) or spec_dict['type'] != 'Image':
            raise NotImplementedError("Only Image currently supported")

        sanitizers = {'group':group_sanitizer, 'label':label_sanitizer}
        strength = 1
        for key in ['group', 'label']:
            attr_value = sanitizers[key](getattr(el, key))
            if key in spec_dict:
                if spec_dict[key] != attr_value: return None
                strength += 1
        return strength


    def _match_overlay(self, raster, overlay_spec):
        """
        Given a raster or input overlay, generate a list of matched
        elements (None if no match) and corresponding tuple of match
        strength values.
        """
        ordering = [None]*len(overlay_spec) # Elements to overlay
        strengths = [0]*len(overlay_spec)   # Match strengths

        elements = raster.values() if isinstance(raster, Overlay) else [raster]

        for el in elements:
            for pos in range(len(overlay_spec)):
                strength = self._match(el, overlay_spec[pos])
                if strength is None:               continue  # No match
                elif (strength <= strengths[pos]): continue  # Weaker match
                else:                                        # Stronger match
                    ordering[pos] = el
                    strengths[pos] = strength
        return ordering, strengths


    def _process(self, raster, key=None):
        specs = tuple(el.strip() for el in self.p.spec.split('*'))
        ordering, strengths = self._match_overlay(raster, specs)
        if all(el is None for el in ordering):
            raise Exception("The image_overlay operation requires at least one match")

        completed = []
        strongest = ordering[np.argmax(strengths)]
        for el, spec in zip(ordering, specs):
            if el is None:
                spec_dict = dict(zip(['type', 'group', 'label'], spec.split('.')))
                el = Image(np.ones(strongest.data.shape) * self.p.fill,
                            group=spec_dict.get('group','Image'),
                            label=spec_dict.get('label',''))
                el.vdims[0].range = self.p.default_range
            completed.append(el)
        return np.prod(completed)



class threshold(ElementOperation):
    """
    Threshold a given Image whereby all values higher than a given
    level map to the specified high value and all values lower than
    that level map to the specified low value.
    """
    output_type = Image

    level = param.Number(default=0.5, doc="""
       The value at which the threshold is applied. Values lower than
       the threshold map to the 'low' value and values above map to
       the 'high' value.""")

    high = param.Number(default=1.0, doc="""
      The value given to elements greater than (or equal to) the
      threshold.""")

    low = param.Number(default=0.0, doc="""
      The value given to elements below the threshold.""")

    group = param.String(default='Threshold', doc="""
       The group assigned to the thresholded output.""")

    def _process(self, matrix, key=None):

        if not isinstance(matrix, Image):
            raise TypeError("The threshold operation requires a Image as input.")

        arr = matrix.data
        high = np.ones(arr.shape) * self.p.high
        low = np.ones(arr.shape) * self.p.low
        thresholded = np.where(arr > self.p.level, high, low)

        return matrix.clone(thresholded, group=self.p.group)



class gradient(ElementOperation):
    """
    Compute the gradient plot of the supplied Image.

    If the Image value dimension is cyclic, the smallest step is taken
    considered the cyclic range
    """

    output_type = Image

    group = param.String(default='Gradient', doc="""
    The group assigned to the output gradient matrix.""")

    def _process(self, matrix, key=None):

        if len(matrix.vdims) != 1:
            raise ValueError("Input matrix to gradient operation must "
                             "have single value dimension.")

        matrix_dim = matrix.vdims[0]

        data = matrix.data
        r, c = data.shape

        if  matrix_dim.cyclic and (None in matrix_dim.range):
            raise Exception("Cyclic range must be specified to compute "
                            "the gradient of cyclic quantities")
        cyclic_range = None if not matrix_dim.cyclic else np.diff(matrix_dim.range)
        if cyclic_range is not None:
            # shift values such that wrapping works ok
            data = data - matrix_dim.range[0]

        dx = np.diff(data, 1, axis=1)[0:r-1, 0:c-1]
        dy = np.diff(data, 1, axis=0)[0:r-1, 0:c-1]

        if cyclic_range is not None: # Wrap into the specified range
            # Convert negative differences to an equivalent positive value
            dx = dx % cyclic_range
            dy = dy % cyclic_range
            #
            # Prefer small jumps
            dx_negatives = dx - cyclic_range
            dy_negatives = dy - cyclic_range
            dx = np.where(np.abs(dx_negatives)<dx, dx_negatives, dx)
            dy = np.where(np.abs(dy_negatives)<dy, dy_negatives, dy)

        return Image(np.sqrt(dx * dx + dy * dy), matrix.bounds, group=self.p.group)



class convolve(ElementOperation):
    """
    Apply a convolution to an overlay using the top layer as the
    kernel for convolving the bottom layer. Both Image elements in
    the input overlay should have a single value dimension.
    """

    output_type = Image

    group = param.String(default='Convolution', doc="""
        The group assigned to the convolved output.""")

    kernel_roi = param.NumericTuple(default=(0,0,0,0), length=4, doc="""
        A 2-dimensional slice of the kernel layer to use in the
        convolution in lbrt (left, bottom, right, top) format. By
        default, no slicing is applied.""")

    def _process(self, overlay, key=None):
        if len(overlay) != 2:
            raise Exception("Overlay must contain at least to items.")

        [target, kernel] = overlay.get(0), overlay.get(1)

        if len(target.vdims) != 1:
            raise Exception("Convolution requires inputs with single value dimensions.")

        xslice = slice(self.p.kernel_roi[0], self.p.kernel_roi[2])
        yslice = slice(self.p.kernel_roi[1], self.p.kernel_roi[3])

        k = kernel.data if self.p.kernel_roi == (0,0,0,0) else kernel[xslice, yslice].data

        fft1 = np.fft.fft2(target.data)
        fft2 = np.fft.fft2(k, s= target.data.shape)
        convolved_raw = np.fft.ifft2(fft1 * fft2).real

        k_rows, k_cols = k.shape
        rolled = np.roll(np.roll(convolved_raw, -(k_cols//2), axis=-1), -(k_rows//2), axis=-2)
        convolved = rolled / float(k.sum())

        return Image(convolved, bounds=target.bounds, group=self.p.group)



class contours(ElementOperation):
    """
    Given a Image with a single channel, annotate it with contour
    lines for a given set of contour levels.

    The return is an NdOverlay with a Contours layer for each given
    level, overlaid on top of the input Image.
    """

    output_type = Overlay

    levels = param.NumericTuple(default=(0.5,), doc="""
        A list of scalar values used to specify the contour levels.""")

    group = param.String(default='Level', doc="""
        The group assigned to the output contours.""")

    filled = param.Boolean(default=False, doc="""
        Whether to generate filled contours""")

    overlaid = param.Boolean(default=True, doc="""
        Whether to overlay the contour on the supplied Element.""")

    def _process(self, element, key=None):
        try:
            from matplotlib import pyplot as plt
        except ImportError:
            raise ImportError("contours operation requires matplotlib.")
        figure_handle = plt.figure()
        extent = element.range(0) + element.range(1)[::-1]
        if self.p.filled:
            contour_fn = plt.contourf
            contour_type = Polygons
        else:
            contour_fn = plt.contour
            contour_type = Contours
        if type(element) is Raster:
            data = [np.flipud(element.data)]
        elif isinstance(element, Raster):
            data = [element.data]
        
        elif isinstance(element, QuadMesh):
            data = (element.dimension_values(0, False),
                    element.dimension_values(1, False),
                    element.data[2])
        contour_set = contour_fn(*data, extent=extent,
                                 levels=self.p.levels)

        contours = NdOverlay(None, kdims=['Levels'])
        for level, cset in zip(self.p.levels, contour_set.collections):
            paths = []
            for path in cset.get_paths():
                paths.extend(np.split(path.vertices, np.where(path.codes==1)[0][1:]))
            contours[level] = contour_type(paths, level=level, group=self.p.group,
                                           label=element.label, kdims=element.kdims,
                                           vdims=element.vdims)

        plt.close(figure_handle)
        if self.p.overlaid:
            contours = element * contours
        return contours


class histogram(ElementOperation):
    """
    Returns a Histogram of the input element data, binned into
    num_bins over the bin_range (if specified) along the specified
    dimension.
    """

    bin_range = param.NumericTuple(default=None, length=2,  doc="""
      Specifies the range within which to compute the bins.""")

    dimension = param.String(default=None, doc="""
      Along which dimension of the Element to compute the histogram.""")

    individually = param.Boolean(default=True, doc="""
      Specifies whether the histogram will be rescaled for each Element in a UniformNdMapping.""")

    log = param.Boolean(default=False, doc="""
      Whether to use base 10 logarithmic samples for the bin edges.""")

    mean_weighted = param.Boolean(default=False, doc="""
      Whether the weighted frequencies are averaged.""")

    normed = param.Boolean(default=True, doc="""
      Whether the histogram frequencies are normalized.""")

    nonzero = param.Boolean(default=False, doc="""
      Whether to use only nonzero values when computing the histogram""")

    num_bins = param.Integer(default=20, doc="""
      Number of bins in the histogram .""")

    weight_dimension = param.String(default=None, doc="""
       Name of the dimension the weighting should be drawn from""")

    style_prefix = param.String(default=None, allow_None=None, doc="""
      Used for setting a common style for histograms in a HoloMap or AdjointLayout.""")

    def _process(self, view, key=None):
        if self.p.dimension:
            selected_dim = self.p.dimension
        else:
            selected_dim = [d.name for d in view.vdims + view.kdims][0]
        data = np.array(view.dimension_values(selected_dim))
        if self.p.nonzero:
            mask = data > 0
            data = data[mask]
        if self.p.weight_dimension:
            weights = np.array(view.dimension_values(self.p.weight_dimension))
            if self.p.nonzero:
                weights = weights[mask]
        else:
            weights = None
        hist_range = find_minmax((np.nanmin(data), np.nanmax(data)), (0, -float('inf')))\
            if self.p.bin_range is None else self.p.bin_range

        # Avoids range issues including zero bin range and empty bins
        if hist_range == (0, 0):
            hist_range = (0, 1)
        data = data[np.invert(np.isnan(data))]
        if self.p.log:
            bin_min = max([abs(hist_range[0]), data[data>0].min()])
            edges = np.logspace(np.log10(bin_min), np.log10(hist_range[1]),
                                self.p.num_bins+1)
        else:
            edges = np.linspace(hist_range[0], hist_range[1], self.p.num_bins + 1)
        normed = False if self.p.mean_weighted and self.p.weight_dimension else self.p.normed
        try:
            hist, edges = np.histogram(data[np.isfinite(data)], normed=normed,
                                       range=hist_range, weights=weights, bins=edges)
            if not normed and self.p.weight_dimension and self.p.mean_weighted:
                hist_mean, _ = np.histogram(data[np.isfinite(data)], normed=normed,
                                            range=hist_range, bins=self.p.num_bins)
                hist /= hist_mean
        except:
            hist = np.zeros(self.p.num_bins)

        hist[np.isnan(hist)] = 0

        params = {}
        if self.p.weight_dimension:
            params['vdims'] = [view.get_dimension(self.p.weight_dimension)]
        if view.group != view.__class__.__name__:
            params['group'] = view.group

        return Histogram(hist, edges, kdims=[view.get_dimension(selected_dim)],
                         label=view.label, **params)



class decimate(ElementOperation):
    """
    Decimates any column based Element to a specified number of random
    rows if the current view defined by the x_range and y_range
    contains more than max_samples. By default the operation returns a
    DynamicMap with a RangeXY stream allowing dynamic downsampling.
    """

    dynamic = param.Boolean(default=True, doc="""
       Enables dynamic processing by default.""")

    max_samples = param.Integer(default=5000, doc="""
        Maximum number of samples to display at the same time.""")

    random_seed = param.Integer(default=42, doc="""
        Seed used to initialize randomization.""")

    streams = param.List(default=[RangeXY], doc="""
        List of streams that are applied if dynamic=True, allowing
        for dynamic interaction with the plot.""")

    x_range  = param.NumericTuple(default=None, length=2, doc="""
       The x_range as a tuple of min and max x-value. Auto-ranges
       if set to None.""")

    y_range  = param.NumericTuple(default=None, length=2, doc="""
       The x_range as a tuple of min and max y-value. Auto-ranges
       if set to None.""")

    def _process_layer(self, element, key=None):
        if not isinstance(element, Dataset):
            raise ValueError("Cannot downsample non-Dataset types.")
        if element.interface not in column_interfaces:
            element = plot.current_frame.clone(datatype=['dataframe', 'dictionary'])

        xstart, xend = self.p.x_range if self.p.x_range else element.range(0)
        ystart, yend = self.p.y_range if self.p.y_range else element.range(1)

        # Slice element to current ranges
        xdim, ydim = element.dimensions(label=True)[0:2]
        sliced = element.select(**{xdim: (xstart, xend),
                                   ydim: (ystart, yend)})

        if len(sliced) > self.p.max_samples:
            prng = np.random.RandomState(self.p.random_seed)
            length = len(sliced)
            if element.interface is PandasInterface:
                data = sliced.data.sample(self.p.max_samples,
                                          random_state=prng)
            else:
                inds = prng.choice(length, self.p.max_samples, False)
                if isinstance(element.interface, DictInterface):
                    data = {k: v[inds] for k, v in sliced.data.items()}
                else:
                    data = sliced.data[inds, :]
            sliced = element.clone(data)
        return sliced

    def _process(self, element, key=None):
        return element.map(self._process_layer, Element)


class interpolate_curve(ElementOperation):
    """
    Resamples a Curve using the defined interpolation method, e.g.
    to represent changes in y-values as steps.
    """

    interpolation = param.ObjectSelector(objects=['steps-pre', 'steps-mid',
                                                  'steps-post', 'linear'],
                                         default='steps-mid', doc="""
       Controls the transition point of the step along the x-axis.""")

    @classmethod
    def pts_to_prestep(cls, x, y):
        steps = np.zeros((2, 2 * len(x) - 1))
        steps[0, 0::2] = x
        steps[0, 1::2] = steps[0, 0:-2:2]
        steps[1:, 0::2] = y
        steps[1:, 1::2] = steps[1:, 2::2]
        return steps

    @classmethod
    def pts_to_midstep(cls, x, y):
        steps = np.zeros((2, 2 * len(x)))
        x = np.asanyarray(x)
        steps[0, 1:-1:2] = steps[0, 2::2] = (x[:-1] + x[1:]) / 2
        steps[0, 0], steps[0, -1] = x[0], x[-1]
        steps[1:, 0::2] = y
        steps[1:, 1::2] = steps[1:, 0::2]
        return steps

    @classmethod
    def pts_to_poststep(cls, x, y):
        steps = np.zeros((2, 2 * len(x) - 1))
        steps[0, 0::2] = x
        steps[0, 1::2] = steps[0, 2::2]
        steps[1:, 0::2] = y
        steps[1:, 1::2] = steps[1:, 0:-2:2]
        return steps

    def _process_layer(self, element, key=None):
        INTERPOLATE_FUNCS = {'steps-pre': self.pts_to_prestep,
                             'steps-mid': self.pts_to_midstep,
                             'steps-post': self.pts_to_poststep}
        if self.p.interpolation not in INTERPOLATE_FUNCS:
            return element
        x, y = element.dimension_values(0), element.dimension_values(1)
        array = INTERPOLATE_FUNCS[self.p.interpolation](x, y)
        dvals = tuple(element.dimension_values(d) for d in element.dimensions()[2:])
        return element.clone((array[0, :], array[1, :])+dvals)

    def _process(self, element, key=None):
        return element.map(self._process_layer, Element)


#==================#
# Other operations #
#==================#


class collapse(ElementOperation):
    """
    Given an overlay of Element types, collapse into single Element
    object using supplied function. Collapsing aggregates over the
    key dimensions of each object applying the supplied fn to each group.

    This is an example of an ElementOperation that does not involve
    any Raster types.
    """

    fn = param.Callable(default=np.mean, doc="""
        The function that is used to collapse the curve y-values for
        each x-value.""")

    def _process(self, overlay, key=None):
        if isinstance(overlay, NdOverlay):
            collapse_map = HoloMap(overlay)
        else:
            collapse_map = HoloMap({i: el for i, el in enumerate(overlay)})
        return collapse_map.collapse(function=self.p.fn)


class gridmatrix(param.ParameterizedFunction):
    """
    The gridmatrix operation takes an Element or HoloMap
    of Elements as input and creates a GridMatrix object,
    which plots each dimension in the Element against
    each other dimension. This provides a very useful
    overview of high-dimensional data and is inspired
    by pandas and seaborn scatter_matrix implementations.
    """

    chart_type = param.Parameter(default=Scatter, doc="""
        The Element type used to display bivariate distributions
        of the data.""")

    diagonal_type = param.Parameter(default=None, doc="""
       The Element type along the diagonal, may be a Histogram or any
       other plot type which can visualize a univariate distribution.
       This parameter overrides diagonal_operation.""")

    diagonal_operation = param.Parameter(default=histogram, doc="""
       The operation applied along the diagonal, may be a histogram-operation
       or any other function which returns a viewable element.""")

    overlay_dims = param.List(default=[], doc="""
       If a HoloMap is supplied this will allow overlaying one or
       more of it's key dimensions.""")

    def __call__(self, data, **params):
        p = param.ParamOverrides(self, params)

        if isinstance(data, (HoloMap, NdOverlay)):
            ranges = {d.name: data.range(d) for d in data.dimensions()}
            data = data.clone({k: GridMatrix(self._process(p, v, ranges))
                               for k, v in data.items()})
            data = Collator(data, merge_type=type(data))()
            if p.overlay_dims:
                data = data.map(lambda x: x.overlay(p.overlay_dims), (HoloMap,))
            return data
        elif isinstance(data, Element):
            data = self._process(p, data)
            return GridMatrix(data)


    def _process(self, p, element, ranges={}):
        # Creates a unified Dataset.data attribute
        # to draw the data from
        if isinstance(element.data, np.ndarray):
            if 'dataframe' in Dataset.datatype:
                el_data = element.table('dataframe')
            else:
                el_data = element.table('dictionary')
        else:
            el_data = element.data

        # Get dimensions to plot against each other
        dims = [d for d in element.dimensions()
                if _is_number(element.range(d)[0])]
        permuted_dims = [(d1, d2) for d1 in dims
                         for d2 in dims[::-1]]

        # Convert Histogram type to operation to avoid one case in the if below.
        if p.diagonal_type is Histogram:
            p.diagonal_type = None
            p.diagonal_operation = histogram

        data = {}
        for d1, d2 in permuted_dims:
            if d1 == d2:
                if p.diagonal_type is not None:
                    values = element.dimension_values(d1)
                    el = p.diagonal_type(values, vdims=[d1])
                elif p.diagonal_operation is histogram or isinstance(p.diagonal_operation, histogram):
                    bin_range = ranges.get(d1.name, element.range(d1))
                    opts = dict(axiswise=True, framewise=True)
                    el = p.diagonal_operation(element,
                                              dimension=d1.name,
                                              bin_range=bin_range)(norm=opts)
                else:
                    el = p.diagonal_operation(element, dimension=d1.name)
            else:
                el = p.chart_type(el_data, kdims=[d1],
                                  vdims=[d2], datatype=['dataframe', 'dictionary'])
            data[(d1.name, d2.name)] = el
        return data


What is this ``_1d`` attribute on elements?