util.py

from __future__ import unicode_literals, absolute_import
from collections import defaultdict
import traceback

import numpy as np
import param

from ..core import (HoloMap, DynamicMap, CompositeOverlay, Layout,
                    Overlay, GridSpace, NdLayout, Store, NdOverlay)
from ..core.options import Cycle
from ..core.spaces import get_nested_streams
from ..core.util import (match_spec, is_number, wrap_tuple, basestring,
                         get_overlay_spec, unique_iterator)
from ..streams import LinkedStream

def displayable(obj):
    """
    Predicate that returns whether the object is displayable or not
    (i.e whether the object obeys the nesting hierarchy
    """
    if isinstance(obj, Overlay) and any(isinstance(o, (HoloMap, GridSpace))
                                        for o in obj):
        return False
    if isinstance(obj, HoloMap):
        return not (obj.type in [Layout, GridSpace, NdLayout])
    if isinstance(obj, (GridSpace, Layout, NdLayout)):
        for el in obj.values():
            if not displayable(el):
                return False
        return True
    return True


class Warning(param.Parameterized): pass
display_warning = Warning(name='Warning')

def collate(obj):
    if isinstance(obj, Overlay):
        nested_type = [type(o).__name__ for o in obj
                       if isinstance(o, (HoloMap, GridSpace))][0]
        display_warning.warning("Nesting %ss within an Overlay makes it difficult "
                                "to access your data or control how it appears; "
                                "we recommend calling .collate() on the Overlay "
                                "in order to follow the recommended nesting "
                                "structure shown in the Composing Data tutorial"
                                "(http://goo.gl/2YS8LJ)" % nested_type)

        return obj.collate()
    if isinstance(obj, DynamicMap):
        return obj.collate()
    if isinstance(obj, HoloMap):
        display_warning.warning("Nesting {0}s within a {1} makes it difficult "
                                "to access your data or control how it appears; "
                                "we recommend calling .collate() on the {1} "
                                "in order to follow the recommended nesting "
                                "structure shown in the Composing Data tutorial"
                                "(https://goo.gl/2YS8LJ)".format(obj.type.__name__, type(obj).__name__))
        return obj.collate()
    elif isinstance(obj, (Layout, NdLayout)):
        try:
            display_warning.warning(
                "Layout contains HoloMaps which are not nested in the "
                "recommended format for accessing your data; calling "
                ".collate() on these objects will resolve any violations "
                "of the recommended nesting presented in the Composing Data "
                "tutorial (https://goo.gl/2YS8LJ)")
            expanded = []
            for el in obj.values():
                if isinstance(el, HoloMap) and not displayable(el):
                    collated_layout = Layout.from_values(el.collate())
                    expanded.extend(collated_layout.values())
            return Layout(expanded)
        except:
            raise Exception(undisplayable_info(obj))
    else:
        raise Exception(undisplayable_info(obj))


def isoverlay_fn(obj):
    """
    Determines whether object is a DynamicMap returning (Nd)Overlay types.
    """
    return isinstance(obj, DynamicMap) and (isinstance(obj.last, CompositeOverlay))


def overlay_depth(obj):
    """
    Computes the depth of a DynamicMap overlay if it can be determined
    otherwise return None.
    """
    if isinstance(obj, DynamicMap):
        if isinstance(obj.last, CompositeOverlay):
            return len(obj.last)
        elif obj.last is None:
            return None
        return 1
    else:
        return 1


def compute_overlayable_zorders(obj, path=[]):
    """
    Traverses an overlayable composite container to determine which
    objects are associated with specific (Nd)Overlay layers by
    z-order, making sure to take DynamicMap Callables into
    account. Returns a mapping between the zorders of each layer and a
    corresponding lists of objects.

    Used to determine which overlaid subplots should be linked with
    Stream callbacks.
    """
    path = path+[obj]
    zorder_map = defaultdict(list)

    # Process non-dynamic layers
    if not isinstance(obj, DynamicMap):
        if isinstance(obj, CompositeOverlay):
            for z, o in enumerate(obj):
                zorder_map[z] = [o, obj]
        elif isinstance(obj, HoloMap):
            for el in obj.values():
                if isinstance(el, CompositeOverlay):
                    for k, v in compute_overlayable_zorders(el, path).items():
                        zorder_map[k] += v + [obj]
                else:
                    zorder_map[0] += [obj, el]
        else:
            if obj not in zorder_map[0]:
                zorder_map[0].append(obj)
        return zorder_map

    isoverlay = isinstance(obj.last, CompositeOverlay)
    isdynoverlay = obj.callback._is_overlay
    if obj not in zorder_map[0] and not isoverlay:
        zorder_map[0].append(obj)
    depth = overlay_depth(obj)

    # Process the inputs of the DynamicMap callback
    dmap_inputs = obj.callback.inputs if obj.callback.link_inputs else []
    for z, inp in enumerate(dmap_inputs):
        no_zorder_increment = False
        if any(not (isoverlay_fn(p) or p.last is None) for p in path) and isoverlay_fn(inp):
            # If overlay has been collapsed do not increment zorder
            no_zorder_increment = True

        input_depth = overlay_depth(inp)
        if depth is not None and input_depth is not None and depth < input_depth:
            # Skips branch of graph where the number of elements in an
            # overlay has been reduced but still contains more than one layer
            if depth > 1:
                continue
            else:
                no_zorder_increment = True

        # Recurse into DynamicMap.callback.inputs and update zorder_map
        z = z if isdynoverlay else 0
        deep_zorders = compute_overlayable_zorders(inp, path=path)
        offset = max(zorder_map.keys())
        for dz, objs in deep_zorders.items():
            global_z = offset+z if no_zorder_increment else offset+dz+z
            zorder_map[global_z] = list(unique_iterator(zorder_map[global_z]+objs))

    # If object branches but does not declare inputs (e.g. user defined
    # DynamicMaps returning (Nd)Overlay) add the items on the DynamicMap.last
    found = any(isinstance(p, DynamicMap) and p.callback._is_overlay for p in path)
    linked =  any(isinstance(s, LinkedStream) and s.linked for s in obj.streams)
    if (found or linked) and isoverlay and not isdynoverlay:
        offset = max(zorder_map.keys())
        for z, o in enumerate(obj.last):
            if isoverlay and linked:
                zorder_map[offset+z].append(obj)
            if o not in zorder_map[offset+z]:
                zorder_map[offset+z].append(o)
    return zorder_map


def is_dynamic_overlay(dmap):
    """
    Traverses a DynamicMap graph and determines if any components
    were overlaid dynamically (i.e. by * on a DynamicMap).
    """
    if not isinstance(dmap, DynamicMap):
        return False
    elif dmap.callback._is_overlay:
        return True
    else:
        return any(is_dynamic_overlay(dm) for dm in dmap.callback.inputs)


def split_dmap_overlay(obj, depth=0):
    """
    Splits a DynamicMap into the original component layers it was
    constructed from.
    """
    layers = []
    if isinstance(obj, DynamicMap):
        if issubclass(obj.type, NdOverlay) and not depth:
            for v in obj.last.values():
                layers.append(obj)
        elif issubclass(obj.type, Overlay):
            if obj.callback.inputs and is_dynamic_overlay(obj):
                for inp in obj.callback.inputs:
                    layers += split_dmap_overlay(inp, depth+1)
            else:
                for v in obj.last.values():
                    layers.append(obj)
        else:
            layers.append(obj)
        return layers
    if isinstance(obj, Overlay):
        for k, v in obj.items():
            layers.append(v)
    else:
        layers.append(obj)
    return layers


def initialize_dynamic(obj):
    """
    Initializes all DynamicMap objects contained by the object
    """
    dmaps = obj.traverse(lambda x: x, specs=[DynamicMap])
    for dmap in dmaps:
        if dmap.unbounded:
            # Skip initialization until plotting code
            continue
        if not len(dmap):
            dmap[dmap._initial_key()]


def get_plot_frame(map_obj, key_map, cached=False):
    """
    Returns an item in a HoloMap or DynamicMap given a mapping key
    dimensions and their values.
    """
    if map_obj.kdims and len(map_obj.kdims) == 1 and map_obj.kdims[0] == 'Frame':
        # Special handling for static plots
        return map_obj.last
    key = tuple(key_map[kd.name] for kd in map_obj.kdims)
    if key in map_obj.data and cached:
        return map_obj.data[key]
    else:
        try:
            return map_obj[key]
        except KeyError:
            return None
        except StopIteration as e:
            raise e
        except Exception:
            print(traceback.format_exc())
            return None


def undisplayable_info(obj, html=False):
    "Generate helpful message regarding an undisplayable object"

    collate = '<tt>collate</tt>' if html else 'collate'
    info = "For more information, please consult the Composing Data tutorial (http://git.io/vtIQh)"
    if isinstance(obj, HoloMap):
        error = "HoloMap of %s objects cannot be displayed." % obj.type.__name__
        remedy = "Please call the %s method to generate a displayable object" % collate
    elif isinstance(obj, Layout):
        error = "Layout containing HoloMaps of Layout or GridSpace objects cannot be displayed."
        remedy = "Please call the %s method on the appropriate elements." % collate
    elif isinstance(obj, GridSpace):
        error = "GridSpace containing HoloMaps of Layouts cannot be displayed."
        remedy = "Please call the %s method on the appropriate elements." % collate

    if not html:
        return '\n'.join([error, remedy, info])
    else:
        return "<center>{msg}</center>".format(msg=('<br>'.join(
            ['<b>%s</b>' % error, remedy, '<i>%s</i>' % info])))


def compute_sizes(sizes, size_fn, scaling_factor, scaling_method, base_size):
    """
    Scales point sizes according to a scaling factor,
    base size and size_fn, which will be applied before
    scaling.
    """
    if sizes.dtype.kind not in ('i', 'f'):
        return None
    if scaling_method == 'area':
        pass
    elif scaling_method == 'width':
        scaling_factor = scaling_factor**2
    else:
        raise ValueError(
            'Invalid value for argument "scaling_method": "{}". '
            'Valid values are: "width", "area".'.format(scaling_method))
    sizes = size_fn(sizes)
    return (base_size*scaling_factor*sizes)


def get_sideplot_ranges(plot, element, main, ranges):
    """
    Utility to find the range for an adjoined
    plot given the plot, the element, the
    Element the plot is adjoined to and the
    dictionary of ranges.
    """
    key = plot.current_key
    dims = element.dimensions()
    dim = dims[0] if 'frequency' in dims[1].name else dims[1]
    range_item = main
    if isinstance(main, HoloMap):
        if issubclass(main.type, CompositeOverlay):
            range_item = [hm for hm in main.split_overlays()[1]
                          if dim in hm.dimensions('all')][0]
    else:
        range_item = HoloMap({0: main}, kdims=['Frame'])
        ranges = match_spec(range_item.last, ranges)

    if dim.name in ranges:
        main_range = ranges[dim.name]
    else:
        framewise = plot.lookup_options(range_item.last, 'norm').options.get('framewise')
        if framewise and range_item.get(key, False):
            main_range = range_item[key].range(dim)
        else:
            main_range = range_item.range(dim)

    # If .main is an NdOverlay or a HoloMap of Overlays get the correct style
    if isinstance(range_item, HoloMap):
        range_item = range_item.last
    if isinstance(range_item, CompositeOverlay):
        range_item = [ov for ov in range_item
                      if dim in ov.dimensions('all')][0]
    return range_item, main_range, dim


def within_range(range1, range2):
    """Checks whether range1 is within the range specified by range2."""
    range1 = [r if np.isfinite(r) else None for r in range1]
    range2 = [r if np.isfinite(r) else None for r in range2]
    return ((range1[0] is None or range2[0] is None or range1[0] >= range2[0]) and
            (range1[1] is None or range2[1] is None or range1[1] <= range2[1]))


def validate_unbounded_mode(holomaps, dynmaps):
    composite = HoloMap(enumerate(holomaps), kdims=['testing_kdim'])
    holomap_kdims = set(unique_iterator([kd.name for dm in holomaps for kd in dm.kdims]))
    hmranges = {d: composite.range(d) for d in holomap_kdims}
    if any(not set(d.name for d in dm.kdims) <= holomap_kdims
                        for dm in dynmaps):
        raise Exception('DynamicMap that are unbounded must have key dimensions that are a '
                        'subset of dimensions of the HoloMap(s) defining the keys.')
    elif not all(within_range(hmrange, dm.range(d)) for dm in dynmaps
                              for d, hmrange in hmranges.items() if d in dm.kdims):
        raise Exception('HoloMap(s) have keys outside the ranges specified on '
                        'the DynamicMap(s).')


def get_dynamic_mode(composite):
    "Returns the common mode of the dynamic maps in given composite object"
    dynmaps = composite.traverse(lambda x: x, [DynamicMap])
    holomaps = composite.traverse(lambda x: x, ['HoloMap'])
    dynamic_unbounded = any(m.unbounded for m in dynmaps)
    if holomaps:
        validate_unbounded_mode(holomaps, dynmaps)
    elif dynamic_unbounded and not holomaps:
        raise Exception("DynamicMaps in unbounded mode must be displayed alongside "
                        "a HoloMap to define the sampling.")
    return dynmaps and not holomaps, dynamic_unbounded


def initialize_unbounded(obj, dimensions, key):
    """
    Initializes any DynamicMaps in unbounded mode.
    """
    select = dict(zip([d.name for d in dimensions], key))
    try:
        obj.select([DynamicMap], **select)
    except KeyError:
        pass


def save_frames(obj, filename, fmt=None, backend=None, options=None):
    """
    Utility to export object to files frame by frame, numbered individually.
    Will use default backend and figure format by default.
    """
    backend = Store.current_backend if backend is None else backend
    renderer = Store.renderers[backend]
    fmt = renderer.params('fig').objects[0] if fmt is None else fmt
    plot = renderer.get_plot(obj)
    for i in range(len(plot)):
        plot.update(i)
        renderer.save(plot, '%s_%s' % (filename, i), fmt=fmt, options=options)


def dynamic_update(plot, subplot, key, overlay, items):
    """
    Given a plot, subplot and dynamically generated (Nd)Overlay
    find the closest matching Element for that plot.
    """
    match_spec = get_overlay_spec(overlay,
                                  wrap_tuple(key),
                                  subplot.current_frame)
    specs = [(i, get_overlay_spec(overlay, wrap_tuple(k), el))
             for i, (k, el) in enumerate(items)]
    return closest_match(match_spec, specs)


def closest_match(match, specs, depth=0):
    """
    Recursively iterates over type, group, label and overlay key,
    finding the closest matching spec.
    """
    new_specs = []
    match_lengths = []
    for i, spec in specs:
        if spec[0] == match[0]:
            new_specs.append((i, spec[1:]))
        else:
            if is_number(match[0]) and is_number(spec[0]):
                match_length = -abs(match[0]-spec[0])
            elif all(isinstance(s[0], basestring) for s in [spec, match]):
                match_length = max(i for i in range(len(match[0]))
                                   if match[0].startswith(spec[0][:i]))
            else:
                match_length = 0
            match_lengths.append((i, match_length, spec[0]))

    if len(new_specs) == 1:
        return new_specs[0][0]
    elif new_specs:
        depth = depth+1
        return closest_match(match[1:], new_specs, depth)
    else:
        if depth == 0 or not match_lengths:
            return None
        else:
            return sorted(match_lengths, key=lambda x: -x[1])[0][0]


def map_colors(arr, crange, cmap, hex=True):
    """
    Maps an array of values to RGB hex strings, given
    a color range and colormap.
    """
    if isinstance(crange, np.ndarray):
        xsorted = np.argsort(crange)
        ypos = np.searchsorted(crange[xsorted], arr)
        arr = xsorted[ypos]
    else:
        if isinstance(crange, tuple):
            cmin, cmax = crange
        else:
            cmin, cmax = np.nanmin(arr), np.nanmax(arr)
        arr = (arr - cmin) / (cmax-cmin)
        arr = np.ma.array(arr, mask=np.logical_not(np.isfinite(arr)))
    arr = cmap(arr)
    if hex:
        arr *= 255
        return ["#{0:02x}{1:02x}{2:02x}".format(*(int(v) for v in c[:-1]))
                for c in arr]
    else:
        return arr


def mplcmap_to_palette(cmap, ncolors=None):
    """
    Converts a matplotlib colormap to palette of RGB hex strings."
    """
    from matplotlib.colors import Colormap
    if not isinstance(cmap, Colormap):
        import matplotlib.cm as cm
        cmap = cm.get_cmap(cmap) #choose any matplotlib colormap here
    if ncolors:
        return [rgb2hex(cmap(i)) for i in np.linspace(0, 1, ncolors)]
    return [rgb2hex(m) for m in cmap(np.arange(cmap.N))]


def bokeh_palette_to_palette(cmap, ncolors=None):
    from bokeh import palettes
    # Process as bokeh palette
    palette = getattr(palettes, cmap, None)
    if palette is None:
        raise ValueError("Supplied palette %s not found among bokeh palettes" % cmap)
    elif isinstance(palette, dict):
         if ncolors in palette:
             palette = palette[ncolors]
         else:
             palette = sorted(palette.items())[-1][1]
    if ncolors:
        return [palette[i%len(palette)] for i in range(ncolors)]
    return list(palette)


def process_cmap(cmap, ncolors=None):
    """
    Convert valid colormap specifications to a list of colors.
    """
    if isinstance(cmap, Cycle):
        palette = [rgb2hex(c) if isinstance(c, tuple) else c for c in cmap.values]
    elif isinstance(cmap, list):
        palette = cmap
    else:
        try:
            # Process as matplotlib colormap
            palette = mplcmap_to_palette(cmap, ncolors)
        except:
            try:
                palette = bokeh_palette_to_palette(cmap, ncolors)
            except:
                if isinstance(cmap, basestring):
                    raise ValueError("Supplied cmap %s not found among "
                                     "matplotlib or bokeh colormaps." % cmap)
                palette = None
    if not isinstance(palette, list):
        raise TypeError("cmap argument expects a list, Cycle or valid matplotlib "
                        "colormap or bokeh palette, found %s." % cmap)
    if ncolors:
        return [palette[i%len(palette)] for i in range(ncolors)]
    return palette


def dim_axis_label(dimensions, separator=', '):
    """
    Returns an axis label for one or more dimensions.
    """
    if not isinstance(dimensions, list): dimensions = [dimensions]
    return separator.join([d.pprint_label for d in dimensions])


def attach_streams(plot, obj, precedence=1.1):
    """
    Attaches plot refresh to all streams on the object.
    """
    def append_refresh(dmap):
        for stream in get_nested_streams(dmap):
            if plot.refresh not in stream._subscribers:
                stream.add_subscriber(plot.refresh, precedence)
    return obj.traverse(append_refresh, [DynamicMap])


def traverse_setter(obj, attribute, value):
    """
    Traverses the object and sets the supplied attribute on the
    object. Supports Dimensioned and DimensionedPlot types.
    """
    obj.traverse(lambda x: setattr(x, attribute, value))


def get_min_distance(element):
    """
    Gets the minimum sampling distance of the x- and y-coordinates
    in a grid.
    """
    xys = element.array([0, 1]).astype('float64').view(dtype=np.complex128)
    m, n = np.meshgrid(xys, xys)
    distances = np.abs(m-n)
    np.fill_diagonal(distances, np.inf)
    distances = distances[distances>0]
    if len(distances):
        return distances.min()
    return 0


def rgb2hex(rgb):
    """
    Convert RGB(A) tuple to hex.
    """
    if len(rgb) > 3:
        rgb = rgb[:-1]
    return "#{0:02x}{1:02x}{2:02x}".format(*(int(v*255) for v in rgb))


# linear_kryw_0_100_c71 (aka "fire"):
# A perceptually uniform equivalent of matplotlib's "hot" colormap, from
# http://peterkovesi.com/projects/colourmaps

fire_colors = linear_kryw_0_100_c71 = [\
[0,        0,           0         ],  [0.027065, 2.143e-05,   0         ],
[0.052054, 7.4728e-05,  0         ],  [0.071511, 0.00013914,  0         ],
[0.08742,  0.0002088,   0         ],  [0.10109,  0.00028141,  0         ],
[0.11337,  0.000356,    2.4266e-17],  [0.12439,  0.00043134,  3.3615e-17],
[0.13463,  0.00050796,  2.1604e-17],  [0.14411,  0.0005856,   0         ],
[0.15292,  0.00070304,  0         ],  [0.16073,  0.0013432,   0         ],
[0.16871,  0.0014516,   0         ],  [0.17657,  0.0012408,   0         ],
[0.18364,  0.0015336,   0         ],  [0.19052,  0.0017515,   0         ],
[0.19751,  0.0015146,   0         ],  [0.20401,  0.0015249,   0         ],
[0.20994,  0.0019639,   0         ],  [0.21605,  0.002031,    0         ],
[0.22215,  0.0017559,   0         ],  [0.22808,  0.001546,    1.8755e-05],
[0.23378,  0.0016315,   3.5012e-05],  [0.23955,  0.0017194,   3.3352e-05],
[0.24531,  0.0018097,   1.8559e-05],  [0.25113,  0.0019038,   1.9139e-05],
[0.25694,  0.0020015,   3.5308e-05],  [0.26278,  0.0021017,   3.2613e-05],
[0.26864,  0.0022048,   2.0338e-05],  [0.27451,  0.0023119,   2.2453e-05],
[0.28041,  0.0024227,   3.6003e-05],  [0.28633,  0.0025363,   2.9817e-05],
[0.29229,  0.0026532,   1.9559e-05],  [0.29824,  0.0027747,   2.7666e-05],
[0.30423,  0.0028999,   3.5752e-05],  [0.31026,  0.0030279,   2.3231e-05],
[0.31628,  0.0031599,   1.2902e-05],  [0.32232,  0.0032974,   3.2915e-05],
[0.32838,  0.0034379,   3.2803e-05],  [0.33447,  0.0035819,   2.0757e-05],
[0.34057,  0.003731,    2.3831e-05],  [0.34668,  0.0038848,   3.502e-05 ],
[0.35283,  0.0040418,   2.4468e-05],  [0.35897,  0.0042032,   1.1444e-05],
[0.36515,  0.0043708,   3.2793e-05],  [0.37134,  0.0045418,   3.012e-05 ],
[0.37756,  0.0047169,   1.4846e-05],  [0.38379,  0.0048986,   2.796e-05 ],
[0.39003,  0.0050848,   3.2782e-05],  [0.3963,   0.0052751,   1.9244e-05],
[0.40258,  0.0054715,   2.2667e-05],  [0.40888,  0.0056736,   3.3223e-05],
[0.41519,  0.0058798,   2.159e-05 ],  [0.42152,  0.0060922,   1.8214e-05],
[0.42788,  0.0063116,   3.2525e-05],  [0.43424,  0.0065353,   2.2247e-05],
[0.44062,  0.006765,    1.5852e-05],  [0.44702,  0.0070024,   3.1769e-05],
[0.45344,  0.0072442,   2.1245e-05],  [0.45987,  0.0074929,   1.5726e-05],
[0.46631,  0.0077499,   3.0976e-05],  [0.47277,  0.0080108,   1.8722e-05],
[0.47926,  0.0082789,   1.9285e-05],  [0.48574,  0.0085553,   3.0063e-05],
[0.49225,  0.0088392,   1.4313e-05],  [0.49878,  0.0091356,   2.3404e-05],
[0.50531,  0.0094374,   2.8099e-05],  [0.51187,  0.0097365,   6.4695e-06],
[0.51844,  0.010039,    2.5791e-05],  [0.52501,  0.010354,    2.4393e-05],
[0.53162,  0.010689,    1.6037e-05],  [0.53825,  0.011031,    2.7295e-05],
[0.54489,  0.011393,    1.5848e-05],  [0.55154,  0.011789,    2.3111e-05],
[0.55818,  0.012159,    2.5416e-05],  [0.56485,  0.012508,    1.5064e-05],
[0.57154,  0.012881,    2.541e-05 ],  [0.57823,  0.013283,    1.6166e-05],
[0.58494,  0.013701,    2.263e-05 ],  [0.59166,  0.014122,    2.3316e-05],
[0.59839,  0.014551,    1.9432e-05],  [0.60514,  0.014994,    2.4323e-05],
[0.6119,   0.01545,     1.3929e-05],  [0.61868,  0.01592,     2.1615e-05],
[0.62546,  0.016401,    1.5846e-05],  [0.63226,  0.016897,    2.0838e-05],
[0.63907,  0.017407,    1.9549e-05],  [0.64589,  0.017931,    2.0961e-05],
[0.65273,  0.018471,    2.0737e-05],  [0.65958,  0.019026,    2.0621e-05],
[0.66644,  0.019598,    2.0675e-05],  [0.67332,  0.020187,    2.0301e-05],
[0.68019,  0.020793,    2.0029e-05],  [0.68709,  0.021418,    2.0088e-05],
[0.69399,  0.022062,    1.9102e-05],  [0.70092,  0.022727,    1.9662e-05],
[0.70784,  0.023412,    1.7757e-05],  [0.71478,  0.024121,    1.8236e-05],
[0.72173,  0.024852,    1.4944e-05],  [0.7287,   0.025608,    2.0245e-06],
[0.73567,  0.02639,     1.5013e-07],  [0.74266,  0.027199,    0         ],
[0.74964,  0.028038,    0         ],  [0.75665,  0.028906,    0         ],
[0.76365,  0.029806,    0         ],  [0.77068,  0.030743,    0         ],
[0.77771,  0.031711,    0         ],  [0.78474,  0.032732,    0         ],
[0.79179,  0.033741,    0         ],  [0.79886,  0.034936,    0         ],
[0.80593,  0.036031,    0         ],  [0.81299,  0.03723,     0         ],
[0.82007,  0.038493,    0         ],  [0.82715,  0.039819,    0         ],
[0.83423,  0.041236,    0         ],  [0.84131,  0.042647,    0         ],
[0.84838,  0.044235,    0         ],  [0.85545,  0.045857,    0         ],
[0.86252,  0.047645,    0         ],  [0.86958,  0.049578,    0         ],
[0.87661,  0.051541,    0         ],  [0.88365,  0.053735,    0         ],
[0.89064,  0.056168,    0         ],  [0.89761,  0.058852,    0         ],
[0.90451,  0.061777,    0         ],  [0.91131,  0.065281,    0         ],
[0.91796,  0.069448,    0         ],  [0.92445,  0.074684,    0         ],
[0.93061,  0.08131,     0         ],  [0.93648,  0.088878,    0         ],
[0.94205,  0.097336,    0         ],  [0.9473,   0.10665,     0         ],
[0.9522,   0.1166,      0         ],  [0.95674,  0.12716,     0         ],
[0.96094,  0.13824,     0         ],  [0.96479,  0.14963,     0         ],
[0.96829,  0.16128,     0         ],  [0.97147,  0.17303,     0         ],
[0.97436,  0.18489,     0         ],  [0.97698,  0.19672,     0         ],
[0.97934,  0.20846,     0         ],  [0.98148,  0.22013,     0         ],
[0.9834,   0.23167,     0         ],  [0.98515,  0.24301,     0         ],
[0.98672,  0.25425,     0         ],  [0.98815,  0.26525,     0         ],
[0.98944,  0.27614,     0         ],  [0.99061,  0.28679,     0         ],
[0.99167,  0.29731,     0         ],  [0.99263,  0.30764,     0         ],
[0.9935,   0.31781,     0         ],  [0.99428,  0.3278,      0         ],
[0.995,    0.33764,     0         ],  [0.99564,  0.34735,     0         ],
[0.99623,  0.35689,     0         ],  [0.99675,  0.3663,      0         ],
[0.99722,  0.37556,     0         ],  [0.99765,  0.38471,     0         ],
[0.99803,  0.39374,     0         ],  [0.99836,  0.40265,     0         ],
[0.99866,  0.41145,     0         ],  [0.99892,  0.42015,     0         ],
[0.99915,  0.42874,     0         ],  [0.99935,  0.43724,     0         ],
[0.99952,  0.44563,     0         ],  [0.99966,  0.45395,     0         ],
[0.99977,  0.46217,     0         ],  [0.99986,  0.47032,     0         ],
[0.99993,  0.47838,     0         ],  [0.99997,  0.48638,     0         ],
[1,        0.4943,      0         ],  [1,        0.50214,     0         ],
[1,        0.50991,     1.2756e-05],  [1,        0.51761,     4.5388e-05],
[1,        0.52523,     9.6977e-05],  [1,        0.5328,      0.00016858],
[1,        0.54028,     0.0002582 ],  [1,        0.54771,     0.00036528],
[1,        0.55508,     0.00049276],  [1,        0.5624,      0.00063955],
[1,        0.56965,     0.00080443],  [1,        0.57687,     0.00098902],
[1,        0.58402,     0.0011943 ],  [1,        0.59113,     0.0014189 ],
[1,        0.59819,     0.0016626 ],  [1,        0.60521,     0.0019281 ],
[1,        0.61219,     0.0022145 ],  [1,        0.61914,     0.0025213 ],
[1,        0.62603,     0.0028496 ],  [1,        0.6329,      0.0032006 ],
[1,        0.63972,     0.0035741 ],  [1,        0.64651,     0.0039701 ],
[1,        0.65327,     0.0043898 ],  [1,        0.66,        0.0048341 ],
[1,        0.66669,     0.005303  ],  [1,        0.67336,     0.0057969 ],
[1,        0.67999,     0.006317  ],  [1,        0.68661,     0.0068648 ],
[1,        0.69319,     0.0074406 ],  [1,        0.69974,     0.0080433 ],
[1,        0.70628,     0.0086756 ],  [1,        0.71278,     0.0093486 ],
[1,        0.71927,     0.010023  ],  [1,        0.72573,     0.010724  ],
[1,        0.73217,     0.011565  ],  [1,        0.73859,     0.012339  ],
[1,        0.74499,     0.01316   ],  [1,        0.75137,     0.014042  ],
[1,        0.75772,     0.014955  ],  [1,        0.76406,     0.015913  ],
[1,        0.77039,     0.016915  ],  [1,        0.77669,     0.017964  ],
[1,        0.78298,     0.019062  ],  [1,        0.78925,     0.020212  ],
[1,        0.7955,      0.021417  ],  [1,        0.80174,     0.02268   ],
[1,        0.80797,     0.024005  ],  [1,        0.81418,     0.025396  ],
[1,        0.82038,     0.026858  ],  [1,        0.82656,     0.028394  ],
[1,        0.83273,     0.030013  ],  [1,        0.83889,     0.031717  ],
[1,        0.84503,     0.03348   ],  [1,        0.85116,     0.035488  ],
[1,        0.85728,     0.037452  ],  [1,        0.8634,      0.039592  ],
[1,        0.86949,     0.041898  ],  [1,        0.87557,     0.044392  ],
[1,        0.88165,     0.046958  ],  [1,        0.88771,     0.04977   ],
[1,        0.89376,     0.052828  ],  [1,        0.8998,      0.056209  ],
[1,        0.90584,     0.059919  ],  [1,        0.91185,     0.063925  ],
[1,        0.91783,     0.068579  ],  [1,        0.92384,     0.073948  ],
[1,        0.92981,     0.080899  ],  [1,        0.93576,     0.090648  ],
[1,        0.94166,     0.10377   ],  [1,        0.94752,     0.12051   ],
[1,        0.9533,      0.14149   ],  [1,        0.959,       0.1672    ],
[1,        0.96456,     0.19823   ],  [1,        0.96995,     0.23514   ],
[1,        0.9751,      0.2786    ],  [1,        0.97992,     0.32883   ],
[1,        0.98432,     0.38571   ],  [1,        0.9882,      0.44866   ],
[1,        0.9915,      0.51653   ],  [1,        0.99417,     0.58754   ],
[1,        0.99625,     0.65985   ],  [1,        0.99778,     0.73194   ],
[1,        0.99885,     0.80259   ],  [1,        0.99953,     0.87115   ],
[1,        0.99989,     0.93683   ],  [1,        1,           1         ]]

# Bokeh palette
fire = [str('#{0:02x}{1:02x}{2:02x}'.format(int(r*255),int(g*255),int(b*255)))
        for r,g,b in fire_colors]

# Matplotlib colormap
try:
    from matplotlib.colors import LinearSegmentedColormap
    from matplotlib.cm import register_cmap
    fire_cmap   = LinearSegmentedColormap.from_list("fire",   fire_colors, N=len(fire_colors))
    fire_r_cmap = LinearSegmentedColormap.from_list("fire_r", list(reversed(fire_colors)), N=len(fire_colors))
    register_cmap("fire", cmap=fire_cmap)
    register_cmap("fire_r", cmap=fire_r_cmap)
except ImportError:
    pass