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""" A module for converting numbers or color arguments to *RGB* or *RGBA*
*RGB* and *RGBA* are sequences of, respectively, 3 or 4 floats in the range 0-1.
This module includes functions and classes for color specification conversions, and for mapping numbers to colors in a 1-D array of colors called a colormap.
Mapping data onto colors using a colormap typically involves two steps: a data array is first mapped onto the range 0-1 using a subclass of :class:`Normalize`, then this number is mapped to a color using a subclass of :class:`Colormap`. Two are provided here: :class:`LinearSegmentedColormap`, which uses piecewise-linear interpolation to define colormaps, and :class:`ListedColormap`, which makes a colormap from a list of colors.
.. seealso::
:doc:`/tutorials/colors/colormap-manipulation` for examples of how to make colormaps and
:doc:`/tutorials/colors/colormaps` for a list of built-in colormaps.
:doc:`/tutorials/colors/colormapnorms` for more details about data normalization
More colormaps are available at palettable_
The module also provides functions for checking whether an object can be interpreted as a color (:func:`is_color_like`), for converting such an object to an RGBA tuple (:func:`to_rgba`) or to an HTML-like hex string in the `#rrggbb` format (:func:`to_hex`), and a sequence of colors to an `(n, 4)` RGBA array (:func:`to_rgba_array`). Caching is used for efficiency.
Matplotlib recognizes the following formats to specify a color:
* an RGB or RGBA tuple of float values in ``[0, 1]`` (e.g., ``(0.1, 0.2, 0.5)`` or ``(0.1, 0.2, 0.5, 0.3)``); * a hex RGB or RGBA string (e.g., ``'#0F0F0F'`` or ``'#0F0F0F0F'``); * a string representation of a float value in ``[0, 1]`` inclusive for gray level (e.g., ``'0.5'``); * one of ``{'b', 'g', 'r', 'c', 'm', 'y', 'k', 'w'}``; * a X11/CSS4 color name; * a name from the `xkcd color survey <https://xkcd.com/color/rgb/>`__; prefixed with ``'xkcd:'`` (e.g., ``'xkcd:sky blue'``); * one of ``{'tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple', 'tab:brown', 'tab:pink', 'tab:gray', 'tab:olive', 'tab:cyan'}`` which are the Tableau Colors from the 'T10' categorical palette (which is the default color cycle); * a "CN" color spec, i.e. `'C'` followed by a single digit, which is an index into the default property cycle (``matplotlib.rcParams['axes.prop_cycle']``); the indexing occurs at artist creation time and defaults to black if the cycle does not include color.
All string specifications of color, other than "CN", are case-insensitive.
.. _palettable: https://jiffyclub.github.io/palettable/
"""
super().__setitem__(key, value) self.cache.clear()
super().__delitem__(key) self.cache.clear()
# Set by reverse priority order. for k, v in XKCD_COLORS.items() if 'grey' in k}) for k, v in TABLEAU_COLORS.items() if 'gray' in k})
"""Return the global mapping of names to named colors.""" return _colors_full_map
except AttributeError: ret = float(ex)
"""Return whether *c* can be interpreted as an item in the color cycle."""
"""Return whether *c* can be interpreted as an RGB(A) color.""" # Special-case nth color syntax because it cannot be parsed during setup. else:
""" Compare two colors to see if they are the same.
Parameters ---------- c1, c2 : Matplotlib colors
Returns ------- bool ``True`` if *c1* and *c2* are the same color, otherwise ``False``. """ return (to_rgba_array(c1) == to_rgba_array(c2)).all()
""" Convert *c* to an RGBA color.
Parameters ---------- c : Matplotlib color
alpha : scalar, optional If *alpha* is not ``None``, it forces the alpha value, except if *c* is ``"none"`` (case-insensitive), which always maps to ``(0, 0, 0, 0)``.
Returns ------- tuple Tuple of ``(r, g, b, a)`` scalars. """ # Special-case nth color syntax because it should not be cached. except TypeError: pass
"""Convert *c* to an RGBA color, with no support for color-cycle syntax.
If *alpha* is not ``None``, it forces the alpha value, except if *c* is ``"none"`` (case-insensitive), which always maps to ``(0, 0, 0, 0)``. """ # Named color. # This may turn c into a non-string, so we check again below. # hex color with no alpha. for n in [c[1:3], c[3:5], c[5:7]]) + (alpha if alpha is not None else 1.,)) # hex color with alpha. color = [int(n, 16) / 255 for n in [c[1:3], c[3:5], c[5:7], c[7:9]]] if alpha is not None: color[-1] = alpha return tuple(color) # string gray. raise ValueError("Invalid RGBA argument: {!r}".format(orig_c)) # tuple color. # Test the dtype explicitly as `map(float, ...)`, `np.array(..., # float)` and `np.array(...).astype(float)` all convert "0.5" to 0.5. # Test dimensionality to reject single floats. raise ValueError("Invalid RGBA argument: {!r}".format(orig_c)) # Return a tuple to prevent the cached value from being modified. raise ValueError("RGBA sequence should have length 3 or 4") raise ValueError("RGBA values should be within 0-1 range")
"""Convert *c* to a (n, 4) array of RGBA colors.
If *alpha* is not ``None``, it forces the alpha value. If *c* is ``"none"`` (case-insensitive) or an empty list, an empty array is returned. """ # Special-case inputs that are already arrays, for performance. (If the # array has the wrong kind or shape, raise the error during one-at-a-time # conversion.) and c.ndim == 2 and c.shape[1] in [3, 4]): result = np.column_stack([c, np.zeros(len(c))]) result[:, -1] = alpha if alpha is not None else 1. raise ValueError("RGBA values should be within 0-1 range") # Handle single values. # Note that this occurs *after* handling inputs that are already arrays, as # `to_rgba(c, alpha)` (below) is expensive for such inputs, due to the need # to format the array in the ValueError message(!). # Convert one at a time.
"""Convert *c* to an RGB color, silently dropping the alpha channel.""" return to_rgba(c)[:3]
"""Convert *c* to a hex color.
Uses the ``#rrggbb`` format if *keep_alpha* is False (the default), ``#rrggbbaa`` otherwise. """ c = to_rgba(c) if not keep_alpha: c = c[:3] return "#" + "".join(format(int(np.round(val * 255)), "02x") for val in c)
### Backwards-compatible color-conversion API
""" Provides methods for converting color specifications to *RGB* or *RGBA*
Caching is used for more efficient conversion upon repeated calls with the same argument.
Ordinarily only the single instance instantiated in this module, *colorConverter*, is needed. """
def to_rgb(arg): """ Returns an *RGB* tuple of three floats from 0-1.
*arg* can be an *RGB* or *RGBA* sequence or a string in any of several forms:
1) a letter from the set 'rgbcmykw' 2) a hex color string, like '#00FFFF' 3) a standard name, like 'aqua' 4) a string representation of a float, like '0.4', indicating gray on a 0-1 scale
if *arg* is *RGBA*, the *A* will simply be discarded. """ return to_rgb(arg)
""" Returns an *RGBA* tuple of four floats from 0-1.
For acceptable values of *arg*, see :meth:`to_rgb`. In addition, if *arg* is "none" (case-insensitive), then (0,0,0,0) will be returned. If *arg* is an *RGBA* sequence and *alpha* is not *None*, *alpha* will replace the original *A*. """
""" Returns a numpy array of *RGBA* tuples.
Accepts a single mpl color spec or a sequence of specs.
Special case to handle "no color": if *c* is "none" (case-insensitive), then an empty array will be returned. Same for an empty list. """ return to_rgba_array(arg, alpha)
### End of backwards-compatible color-conversion API
"""Create an *N* -element 1-d lookup table
*data* represented by a list of x,y0,y1 mapping correspondences. Each element in this list represents how a value between 0 and 1 (inclusive) represented by x is mapped to a corresponding value between 0 and 1 (inclusive). The two values of y are to allow for discontinuous mapping functions (say as might be found in a sawtooth) where y0 represents the value of y for values of x <= to that given, and y1 is the value to be used for x > than that given). The list must start with x=0, end with x=1, and all values of x must be in increasing order. Values between the given mapping points are determined by simple linear interpolation.
Alternatively, data can be a function mapping values between 0 - 1 to 0 - 1.
The function returns an array "result" where ``result[x*(N-1)]`` gives the closest value for values of x between 0 and 1. """
xind = np.linspace(0, 1, N) ** gamma lut = np.clip(np.array(data(xind), dtype=float), 0, 1) return lut
except Exception: raise TypeError("data must be convertible to an array") raise ValueError("data must be nx3 format")
raise ValueError( "data mapping points must start with x=0 and end with x=1") raise ValueError("data mapping points must have x in increasing order") # begin generation of lookup table
# ensure that the lut is confined to values between 0 and 1 by clipping it
""" Baseclass for all scalar to RGBA mappings.
Typically Colormap instances are used to convert data values (floats) from the interval ``[0, 1]`` to the RGBA color that the respective Colormap represents. For scaling of data into the ``[0, 1]`` interval see :class:`matplotlib.colors.Normalize`. It is worth noting that :class:`matplotlib.cm.ScalarMappable` subclasses make heavy use of this ``data->normalize->map-to-color`` processing chain.
""" """ Parameters ---------- name : str The name of the colormap. N : int The number of rgb quantization levels.
"""
#: When this colormap exists on a scalar mappable and colorbar_extend #: is not False, colorbar creation will pick up ``colorbar_extend`` as #: the default value for the ``extend`` keyword in the #: :class:`matplotlib.colorbar.Colorbar` constructor.
""" Parameters ---------- X : scalar, ndarray The data value(s) to convert to RGBA. For floats, X should be in the interval ``[0.0, 1.0]`` to return the RGBA values ``X*100`` percent along the Colormap line. For integers, X should be in the interval ``[0, Colormap.N)`` to return RGBA values *indexed* from the Colormap with index ``X``. alpha : float, None Alpha must be a scalar between 0 and 1, or None. bytes : bool If False (default), the returned RGBA values will be floats in the interval ``[0, 1]`` otherwise they will be uint8s in the interval ``[0, 255]``.
Returns ------- Tuple of RGBA values if X is scalar, otherwise an array of RGBA values with a shape of ``X.shape + (4, )``.
""" # See class docstring for arg/kwarg documentation. else:
# Calculations with native byteorder are faster, and avoid a # bug that otherwise can occur with putmask when the last # argument is a numpy scalar.
# Negative values are out of range, but astype(int) would truncate # them towards zero. # xa == 1 (== N after multiplication) is not out of range. # Avoid converting large positive values to negative integers. # Set the over-range indices before the under-range; # otherwise the under-range values get converted to over-range. xa.fill(self._i_bad) else:
alpha = int(alpha * 255) # All zeros is taken as a flag for the default bad # color, which is no color--fully transparent. We # don't want to override this. else: lut[:, -1] = alpha # If the bad value is set to have a color, then we # override its alpha just as for any other value.
"""Create new object with the same class, update attributes """ cls = self.__class__ cmapobject = cls.__new__(cls) cmapobject.__dict__.update(self.__dict__) if self._isinit: cmapobject._lut = np.copy(self._lut) return cmapobject
"""Set color to be used for masked values. """ self._rgba_bad = to_rgba(color, alpha) if self._isinit: self._set_extremes()
"""Set color to be used for low out-of-range values. Requires norm.clip = False """ self._rgba_under = to_rgba(color, alpha) if self._isinit: self._set_extremes()
"""Set color to be used for high out-of-range values. Requires norm.clip = False """ self._rgba_over = to_rgba(color, alpha) if self._isinit: self._set_extremes()
self._lut[self._i_under] = self._rgba_under else: self._lut[self._i_over] = self._rgba_over else:
"""Generate the lookup table, self._lut""" raise NotImplementedError("Abstract class only")
if not self._isinit: self._init() return (np.all(self._lut[:, 0] == self._lut[:, 1]) and np.all(self._lut[:, 0] == self._lut[:, 2]))
""" Return a new color map with *lutsize* entries. """ raise NotImplementedError()
""" Make a reversed instance of the Colormap.
.. note :: Function not implemented for base class.
Parameters ---------- name : str, optional The name for the reversed colormap. If it's None the name will be the name of the parent colormap + "_r".
Notes ----- See :meth:`LinearSegmentedColormap.reversed` and :meth:`ListedColormap.reversed` """ raise NotImplementedError()
"""Colormap objects based on lookup tables using linear segments.
The lookup table is generated using linear interpolation for each primary color, with the 0-1 domain divided into any number of segments. """ """Create color map from linear mapping segments
segmentdata argument is a dictionary with a red, green and blue entries. Each entry should be a list of *x*, *y0*, *y1* tuples, forming rows in a table. Entries for alpha are optional.
Example: suppose you want red to increase from 0 to 1 over the bottom half, green to do the same over the middle half, and blue over the top half. Then you would use::
cdict = {'red': [(0.0, 0.0, 0.0), (0.5, 1.0, 1.0), (1.0, 1.0, 1.0)],
'green': [(0.0, 0.0, 0.0), (0.25, 0.0, 0.0), (0.75, 1.0, 1.0), (1.0, 1.0, 1.0)],
'blue': [(0.0, 0.0, 0.0), (0.5, 0.0, 0.0), (1.0, 1.0, 1.0)]}
Each row in the table for a given color is a sequence of *x*, *y0*, *y1* tuples. In each sequence, *x* must increase monotonically from 0 to 1. For any input value *z* falling between *x[i]* and *x[i+1]*, the output value of a given color will be linearly interpolated between *y1[i]* and *y0[i+1]*::
row i: x y0 y1 / / row i+1: x y0 y1
Hence y0 in the first row and y1 in the last row are never used.
.. seealso::
:meth:`LinearSegmentedColormap.from_list` Static method; factory function for generating a smoothly-varying LinearSegmentedColormap.
:func:`makeMappingArray` For information about making a mapping array. """ # True only if all colors in map are identical; needed for contouring.
self.N, self._segmentdata['red'], self._gamma) self.N, self._segmentdata['green'], self._gamma) self.N, self._segmentdata['blue'], self._gamma) self.N, self._segmentdata['alpha'], 1)
""" Set a new gamma value and regenerate color map. """ self._gamma = gamma self._init()
""" Make a linear segmented colormap with *name* from a sequence of *colors* which evenly transitions from colors[0] at val=0 to colors[-1] at val=1. *N* is the number of rgb quantization levels. Alternatively, a list of (value, color) tuples can be given to divide the range unevenly. """
raise ValueError('colors must be iterable')
and not isinstance(colors[0], str)): # List of value, color pairs else:
""" Return a new color map with *lutsize* entries. """ return LinearSegmentedColormap(self.name, self._segmentdata, lutsize)
""" Make a reversed instance of the Colormap.
Parameters ---------- name : str, optional The name for the reversed colormap. If it's None the name will be the name of the parent colormap + "_r".
Returns ------- LinearSegmentedColormap The reversed colormap. """ if name is None: name = self.name + "_r"
# Function factory needed to deal with 'late binding' issue. def factory(dat): def func_r(x): return dat(1.0 - x) return func_r
data_r = {key: (factory(data) if callable(data) else [(1.0 - x, y1, y0) for x, y0, y1 in reversed(data)]) for key, data in self._segmentdata.items()}
return LinearSegmentedColormap(name, data_r, self.N, self._gamma)
"""Colormap object generated from a list of colors.
This may be most useful when indexing directly into a colormap, but it can also be used to generate special colormaps for ordinary mapping. """ """ Make a colormap from a list of colors.
*colors* a list of matplotlib color specifications, or an equivalent Nx3 or Nx4 floating point array (*N* rgb or rgba values) *name* a string to identify the colormap *N* the number of entries in the map. The default is *None*, in which case there is one colormap entry for each element in the list of colors. If::
N < len(colors)
the list will be truncated at *N*. If::
N > len(colors)
the list will be extended by repetition. """ # identical; needed for contouring. else: self.colors = [colors] * N self.monochrome = True itertools.islice(itertools.cycle(colors), N)) else: try: gray = float(colors) except TypeError: pass else: self.colors = [gray] * N self.monochrome = True
""" Return a new color map with *lutsize* entries. """ colors = self(np.linspace(0, 1, lutsize)) return ListedColormap(colors, name=self.name)
""" Make a reversed instance of the Colormap.
Parameters ---------- name : str, optional The name for the reversed colormap. If it's None the name will be the name of the parent colormap + "_r".
Returns ------- ListedColormap A reversed instance of the colormap. """ if name is None: name = self.name + "_r"
colors_r = list(reversed(self.colors)) return ListedColormap(colors_r, name=name, N=self.N)
""" A class which, when called, can normalize data into the ``[0.0, 1.0]`` interval.
""" """ If *vmin* or *vmax* is not given, they are initialized from the minimum and maximum value respectively of the first input processed. That is, *__call__(A)* calls *autoscale_None(A)*. If *clip* is *True* and the given value falls outside the range, the returned value will be 0 or 1, whichever is closer. Returns 0 if::
vmin==vmax
Works with scalars or arrays, including masked arrays. If *clip* is *True*, masked values are set to 1; otherwise they remain masked. Clipping silently defeats the purpose of setting the over, under, and masked colors in the colormap, so it is likely to lead to surprises; therefore the default is *clip* = *False*. """
def process_value(value): """ Homogenize the input *value* for easy and efficient normalization.
*value* can be a scalar or sequence.
Returns *result*, *is_scalar*, where *result* is a masked array matching *value*. Float dtypes are preserved; integer types with two bytes or smaller are converted to np.float32, and larger types are converted to np.float64. Preserving float32 when possible, and using in-place operations, can greatly improve speed for large arrays.
Experimental; we may want to add an option to force the use of float32. """ # bool_/int8/int16 -> float32; int32/int64 -> float64 # ensure data passed in as an ndarray subclass are interpreted as # an ndarray. See issue #6622.
""" Normalize *value* data in the ``[vmin, vmax]`` interval into the ``[0.0, 1.0]`` interval and return it. *clip* defaults to *self.clip* (which defaults to *False*). If not already initialized, *vmin* and *vmax* are initialized using *autoscale_None(value)*. """
# Convert at least to float, without losing precision. result.fill(0) # Or should it be all masked? Or 0.5? raise ValueError("minvalue must be less than or equal to maxvalue") else: mask = np.ma.getmask(result) result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax), mask=mask) # ma division is very slow; we can take a shortcut
raise ValueError("Not invertible until scaled")
else:
""" Set *vmin*, *vmax* to min, max of *A*. """ A = np.asanyarray(A) self.vmin = A.min() self.vmax = A.max()
"""autoscale only None-valued vmin or vmax."""
'return true if vmin and vmax set'
""" Normalize a given value to the 0-1 range on a log scale """ if clip is None: clip = self.clip
result, is_scalar = self.process_value(value)
result = np.ma.masked_less_equal(result, 0, copy=False)
self.autoscale_None(result) vmin, vmax = self.vmin, self.vmax if vmin > vmax: raise ValueError("minvalue must be less than or equal to maxvalue") elif vmin <= 0: raise ValueError("values must all be positive") elif vmin == vmax: result.fill(0) else: if clip: mask = np.ma.getmask(result) result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax), mask=mask) # in-place equivalent of above can be much faster resdat = result.data mask = result.mask if mask is np.ma.nomask: mask = (resdat <= 0) else: mask |= resdat <= 0 np.copyto(resdat, 1, where=mask) np.log(resdat, resdat) resdat -= np.log(vmin) resdat /= (np.log(vmax) - np.log(vmin)) result = np.ma.array(resdat, mask=mask, copy=False) if is_scalar: result = result[0] return result
if not self.scaled(): raise ValueError("Not invertible until scaled") vmin, vmax = self.vmin, self.vmax
if cbook.iterable(value): val = np.ma.asarray(value) return vmin * np.ma.power((vmax / vmin), val) else: return vmin * pow((vmax / vmin), value)
""" Set *vmin*, *vmax* to min, max of *A*. """ A = np.ma.masked_less_equal(A, 0, copy=False) self.vmin = np.ma.min(A) self.vmax = np.ma.max(A)
"""autoscale only None-valued vmin or vmax.""" if self.vmin is not None and self.vmax is not None: return A = np.ma.masked_less_equal(A, 0, copy=False) if self.vmin is None and A.size: self.vmin = A.min() if self.vmax is None and A.size: self.vmax = A.max()
""" The symmetrical logarithmic scale is logarithmic in both the positive and negative directions from the origin.
Since the values close to zero tend toward infinity, there is a need to have a range around zero that is linear. The parameter *linthresh* allows the user to specify the size of this range (-*linthresh*, *linthresh*). """ vmin=None, vmax=None, clip=False): """ *linthresh*: The range within which the plot is linear (to avoid having the plot go to infinity around zero).
*linscale*: This allows the linear range (-*linthresh* to *linthresh*) to be stretched relative to the logarithmic range. Its value is the number of decades to use for each half of the linear range. For example, when *linscale* == 1.0 (the default), the space used for the positive and negative halves of the linear range will be equal to one decade in the logarithmic range. Defaults to 1. """ Normalize.__init__(self, vmin, vmax, clip) self.linthresh = float(linthresh) self._linscale_adj = (linscale / (1.0 - np.e ** -1)) if vmin is not None and vmax is not None: self._transform_vmin_vmax()
if clip is None: clip = self.clip
result, is_scalar = self.process_value(value) self.autoscale_None(result) vmin, vmax = self.vmin, self.vmax
if vmin > vmax: raise ValueError("minvalue must be less than or equal to maxvalue") elif vmin == vmax: result.fill(0) else: if clip: mask = np.ma.getmask(result) result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax), mask=mask) # in-place equivalent of above can be much faster resdat = self._transform(result.data) resdat -= self._lower resdat /= (self._upper - self._lower)
if is_scalar: result = result[0] return result
""" Inplace transformation. """ with np.errstate(invalid="ignore"): masked = np.abs(a) > self.linthresh sign = np.sign(a[masked]) log = (self._linscale_adj + np.log(np.abs(a[masked]) / self.linthresh)) log *= sign * self.linthresh a[masked] = log a[~masked] *= self._linscale_adj return a
""" Inverse inplace Transformation. """ masked = np.abs(a) > (self.linthresh * self._linscale_adj) sign = np.sign(a[masked]) exp = np.exp(sign * a[masked] / self.linthresh - self._linscale_adj) exp *= sign * self.linthresh a[masked] = exp a[~masked] /= self._linscale_adj return a
""" Calculates vmin and vmax in the transformed system. """ vmin, vmax = self.vmin, self.vmax arr = np.array([vmax, vmin]).astype(float) self._upper, self._lower = self._transform(arr)
if not self.scaled(): raise ValueError("Not invertible until scaled") val = np.ma.asarray(value) val = val * (self._upper - self._lower) + self._lower return self._inv_transform(val)
""" Set *vmin*, *vmax* to min, max of *A*. """ self.vmin = np.ma.min(A) self.vmax = np.ma.max(A) self._transform_vmin_vmax()
"""autoscale only None-valued vmin or vmax.""" if self.vmin is not None and self.vmax is not None: pass A = np.asanyarray(A) if self.vmin is None and A.size: self.vmin = A.min() if self.vmax is None and A.size: self.vmax = A.max() self._transform_vmin_vmax()
""" Linearly map a given value to the 0-1 range and then apply a power-law normalization over that range. """
raise ValueError("minvalue must be less than or equal to maxvalue") result.fill(0) else: mask = np.ma.getmask(result) result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax), mask=mask)
if not self.scaled(): raise ValueError("Not invertible until scaled") gamma = self.gamma vmin, vmax = self.vmin, self.vmax
if cbook.iterable(value): val = np.ma.asarray(value) return np.ma.power(val, 1. / gamma) * (vmax - vmin) + vmin else: return pow(value, 1. / gamma) * (vmax - vmin) + vmin
""" Set *vmin*, *vmax* to min, max of *A*. """ self.vmin = np.ma.min(A) self.vmax = np.ma.max(A)
"""autoscale only None-valued vmin or vmax.""" self.vmin = A.min() self.vmax = A.max()
""" Generate a colormap index based on discrete intervals.
Unlike :class:`Normalize` or :class:`LogNorm`, :class:`BoundaryNorm` maps values to integers instead of to the interval 0-1.
Mapping to the 0-1 interval could have been done via piece-wise linear interpolation, but using integers seems simpler, and reduces the number of conversions back and forth between integer and floating point. """ """ Parameters ---------- boundaries : array-like Monotonically increasing sequence of boundaries ncolors : int Number of colors in the colormap to be used clip : bool, optional If clip is ``True``, out of range values are mapped to 0 if they are below ``boundaries[0]`` or mapped to ncolors - 1 if they are above ``boundaries[-1]``.
If clip is ``False``, out of range values are mapped to -1 if they are below ``boundaries[0]`` or mapped to ncolors if they are above ``boundaries[-1]``. These are then converted to valid indices by :meth:`Colormap.__call__`.
Notes ----- *boundaries* defines the edges of bins, and data falling within a bin is mapped to the color with the same index.
If the number of bins doesn't equal *ncolors*, the color is chosen by linear interpolation of the bin number onto color numbers. """ self.clip = clip self.vmin = boundaries[0] self.vmax = boundaries[-1] self.boundaries = np.asarray(boundaries) self.N = len(self.boundaries) self.Ncmap = ncolors if self.N - 1 == self.Ncmap: self._interp = False else: self._interp = True
if clip is None: clip = self.clip
xx, is_scalar = self.process_value(value) mask = np.ma.getmaskarray(xx) xx = np.atleast_1d(xx.filled(self.vmax + 1)) if clip: np.clip(xx, self.vmin, self.vmax, out=xx) max_col = self.Ncmap - 1 else: max_col = self.Ncmap iret = np.zeros(xx.shape, dtype=np.int16) for i, b in enumerate(self.boundaries): iret[xx >= b] = i if self._interp: scalefac = (self.Ncmap - 1) / (self.N - 2) iret = (iret * scalefac).astype(np.int16) iret[xx < self.vmin] = -1 iret[xx >= self.vmax] = max_col ret = np.ma.array(iret, mask=mask) if is_scalar: ret = int(ret[0]) # assume python scalar return ret
""" Raises ------ ValueError BoundaryNorm is not invertible, so calling this method will always raise an error """ return ValueError("BoundaryNorm is not invertible")
""" Dummy replacement for Normalize, for the case where we want to use indices directly in a :class:`~matplotlib.cm.ScalarMappable` . """
return value
""" convert float rgb values (in the range [0, 1]), in a numpy array to hsv values.
Parameters ---------- arr : (..., 3) array-like All values must be in the range [0, 1]
Returns ------- hsv : (..., 3) ndarray Colors converted to hsv values in range [0, 1] """ # make sure it is an ndarray arr = np.asarray(arr)
# check length of the last dimension, should be _some_ sort of rgb if arr.shape[-1] != 3: raise ValueError("Last dimension of input array must be 3; " "shape {} was found.".format(arr.shape))
in_ndim = arr.ndim if arr.ndim == 1: arr = np.array(arr, ndmin=2)
# make sure we don't have an int image arr = arr.astype(np.promote_types(arr.dtype, np.float32))
out = np.zeros_like(arr) arr_max = arr.max(-1) ipos = arr_max > 0 delta = arr.ptp(-1) s = np.zeros_like(delta) s[ipos] = delta[ipos] / arr_max[ipos] ipos = delta > 0 # red is max idx = (arr[..., 0] == arr_max) & ipos out[idx, 0] = (arr[idx, 1] - arr[idx, 2]) / delta[idx] # green is max idx = (arr[..., 1] == arr_max) & ipos out[idx, 0] = 2. + (arr[idx, 2] - arr[idx, 0]) / delta[idx] # blue is max idx = (arr[..., 2] == arr_max) & ipos out[idx, 0] = 4. + (arr[idx, 0] - arr[idx, 1]) / delta[idx]
out[..., 0] = (out[..., 0] / 6.0) % 1.0 out[..., 1] = s out[..., 2] = arr_max
if in_ndim == 1: out.shape = (3,)
return out
""" convert hsv values in a numpy array to rgb values all values assumed to be in range [0, 1]
Parameters ---------- hsv : (..., 3) array-like All values assumed to be in range [0, 1]
Returns ------- rgb : (..., 3) ndarray Colors converted to RGB values in range [0, 1] """ hsv = np.asarray(hsv)
# check length of the last dimension, should be _some_ sort of rgb if hsv.shape[-1] != 3: raise ValueError("Last dimension of input array must be 3; " "shape {shp} was found.".format(shp=hsv.shape))
# if we got passed a 1D array, try to treat as # a single color and reshape as needed in_ndim = hsv.ndim if in_ndim == 1: hsv = np.array(hsv, ndmin=2)
# make sure we don't have an int image hsv = hsv.astype(np.promote_types(hsv.dtype, np.float32))
h = hsv[..., 0] s = hsv[..., 1] v = hsv[..., 2]
r = np.empty_like(h) g = np.empty_like(h) b = np.empty_like(h)
i = (h * 6.0).astype(int) f = (h * 6.0) - i p = v * (1.0 - s) q = v * (1.0 - s * f) t = v * (1.0 - s * (1.0 - f))
idx = i % 6 == 0 r[idx] = v[idx] g[idx] = t[idx] b[idx] = p[idx]
idx = i == 1 r[idx] = q[idx] g[idx] = v[idx] b[idx] = p[idx]
idx = i == 2 r[idx] = p[idx] g[idx] = v[idx] b[idx] = t[idx]
idx = i == 3 r[idx] = p[idx] g[idx] = q[idx] b[idx] = v[idx]
idx = i == 4 r[idx] = t[idx] g[idx] = p[idx] b[idx] = v[idx]
idx = i == 5 r[idx] = v[idx] g[idx] = p[idx] b[idx] = q[idx]
idx = s == 0 r[idx] = v[idx] g[idx] = v[idx] b[idx] = v[idx]
rgb = np.stack([r, g, b], axis=-1)
if in_ndim == 1: rgb.shape = (3,)
return rgb
# things that don't work here: # * np.linalg.norm # - doesn't broadcast in numpy 1.7 # - drops the mask from ma.array # * using keepdims - broken on ma.array until 1.11.2 # * using sum - discards mask on ma.array unless entire vector is masked
sum_sq = 0 for i in range(arr.shape[-1]): sum_sq += np.square(arr[..., i, np.newaxis]) return np.sqrt(sum_sq)
""" Create a light source coming from the specified azimuth and elevation. Angles are in degrees, with the azimuth measured clockwise from north and elevation up from the zero plane of the surface.
The :meth:`shade` is used to produce "shaded" rgb values for a data array. :meth:`shade_rgb` can be used to combine an rgb image with The :meth:`shade_rgb` The :meth:`hillshade` produces an illumination map of a surface. """ hsv_min_sat=1, hsv_max_sat=0): """ Specify the azimuth (measured clockwise from south) and altitude (measured up from the plane of the surface) of the light source in degrees.
Parameters ---------- azdeg : number, optional The azimuth (0-360, degrees clockwise from North) of the light source. Defaults to 315 degrees (from the northwest). altdeg : number, optional The altitude (0-90, degrees up from horizontal) of the light source. Defaults to 45 degrees from horizontal.
Notes ----- For backwards compatibility, the parameters *hsv_min_val*, *hsv_max_val*, *hsv_min_sat*, and *hsv_max_sat* may be supplied at initialization as well. However, these parameters will only be used if "blend_mode='hsv'" is passed into :meth:`shade` or :meth:`shade_rgb`. See the documentation for :meth:`blend_hsv` for more details. """ self.azdeg = azdeg self.altdeg = altdeg self.hsv_min_val = hsv_min_val self.hsv_max_val = hsv_max_val self.hsv_min_sat = hsv_min_sat self.hsv_max_sat = hsv_max_sat
def direction(self): """ The unit vector direction towards the light source """
# Azimuth is in degrees clockwise from North. Convert to radians # counterclockwise from East (mathematical notation). az = np.radians(90 - self.azdeg) alt = np.radians(self.altdeg)
return np.array([ np.cos(az) * np.cos(alt), np.sin(az) * np.cos(alt), np.sin(alt) ])
""" Calculates the illumination intensity for a surface using the defined azimuth and elevation for the light source.
This computes the normal vectors for the surface, and then passes them on to `shade_normals`
Parameters ---------- elevation : array-like A 2d array (or equivalent) of the height values used to generate an illumination map vert_exag : number, optional The amount to exaggerate the elevation values by when calculating illumination. This can be used either to correct for differences in units between the x-y coordinate system and the elevation coordinate system (e.g. decimal degrees vs meters) or to exaggerate or de-emphasize topographic effects. dx : number, optional The x-spacing (columns) of the input *elevation* grid. dy : number, optional The y-spacing (rows) of the input *elevation* grid. fraction : number, optional Increases or decreases the contrast of the hillshade. Values greater than one will cause intermediate values to move closer to full illumination or shadow (and clipping any values that move beyond 0 or 1). Note that this is not visually or mathematically the same as vertical exaggeration. Returns ------- intensity : ndarray A 2d array of illumination values between 0-1, where 0 is completely in shadow and 1 is completely illuminated. """
# Because most image and raster GIS data has the first row in the array # as the "top" of the image, dy is implicitly negative. This is # consistent to what `imshow` assumes, as well. dy = -dy
# compute the normal vectors from the partial derivatives e_dy, e_dx = np.gradient(vert_exag * elevation, dy, dx)
# .view is to keep subclasses normal = np.empty(elevation.shape + (3,)).view(type(elevation)) normal[..., 0] = -e_dx normal[..., 1] = -e_dy normal[..., 2] = 1 normal /= _vector_magnitude(normal)
return self.shade_normals(normal, fraction)
""" Calculates the illumination intensity for the normal vectors of a surface using the defined azimuth and elevation for the light source.
Imagine an artificial sun placed at infinity in some azimuth and elevation position illuminating our surface. The parts of the surface that slope toward the sun should brighten while those sides facing away should become darker.
Parameters ---------- fraction : number, optional Increases or decreases the contrast of the hillshade. Values greater than one will cause intermediate values to move closer to full illumination or shadow (and clipping any values that move beyond 0 or 1). Note that this is not visually or mathematically the same as vertical exaggeration.
Returns ------- intensity : ndarray A 2d array of illumination values between 0-1, where 0 is completely in shadow and 1 is completely illuminated. """
intensity = normals.dot(self.direction)
# Apply contrast stretch imin, imax = intensity.min(), intensity.max() intensity *= fraction
# Rescale to 0-1, keeping range before contrast stretch # If constant slope, keep relative scaling (i.e. flat should be 0.5, # fully occluded 0, etc.) if (imax - imin) > 1e-6: # Strictly speaking, this is incorrect. Negative values should be # clipped to 0 because they're fully occluded. However, rescaling # in this manner is consistent with the previous implementation and # visually appears better than a "hard" clip. intensity -= imin intensity /= (imax - imin) intensity = np.clip(intensity, 0, 1, intensity)
return intensity
vmax=None, vert_exag=1, dx=1, dy=1, fraction=1, **kwargs): """ Combine colormapped data values with an illumination intensity map (a.k.a. "hillshade") of the values.
Parameters ---------- data : array-like A 2d array (or equivalent) of the height values used to generate a shaded map. cmap : `~matplotlib.colors.Colormap` instance The colormap used to color the *data* array. Note that this must be a `~matplotlib.colors.Colormap` instance. For example, rather than passing in `cmap='gist_earth'`, use `cmap=plt.get_cmap('gist_earth')` instead. norm : `~matplotlib.colors.Normalize` instance, optional The normalization used to scale values before colormapping. If None, the input will be linearly scaled between its min and max. blend_mode : {'hsv', 'overlay', 'soft'} or callable, optional The type of blending used to combine the colormapped data values with the illumination intensity. Default is "overlay". Note that for most topographic surfaces, "overlay" or "soft" appear more visually realistic. If a user-defined function is supplied, it is expected to combine an MxNx3 RGB array of floats (ranging 0 to 1) with an MxNx1 hillshade array (also 0 to 1). (Call signature `func(rgb, illum, **kwargs)`) Additional kwargs supplied to this function will be passed on to the *blend_mode* function. vmin : scalar or None, optional The minimum value used in colormapping *data*. If *None* the minimum value in *data* is used. If *norm* is specified, then this argument will be ignored. vmax : scalar or None, optional The maximum value used in colormapping *data*. If *None* the maximum value in *data* is used. If *norm* is specified, then this argument will be ignored. vert_exag : number, optional The amount to exaggerate the elevation values by when calculating illumination. This can be used either to correct for differences in units between the x-y coordinate system and the elevation coordinate system (e.g. decimal degrees vs meters) or to exaggerate or de-emphasize topography. dx : number, optional The x-spacing (columns) of the input *elevation* grid. dy : number, optional The y-spacing (rows) of the input *elevation* grid. fraction : number, optional Increases or decreases the contrast of the hillshade. Values greater than one will cause intermediate values to move closer to full illumination or shadow (and clipping any values that move beyond 0 or 1). Note that this is not visually or mathematically the same as vertical exaggeration. Additional kwargs are passed on to the *blend_mode* function.
Returns ------- rgba : ndarray An MxNx4 array of floats ranging between 0-1. """ if vmin is None: vmin = data.min() if vmax is None: vmax = data.max() if norm is None: norm = Normalize(vmin=vmin, vmax=vmax)
rgb0 = cmap(norm(data)) rgb1 = self.shade_rgb(rgb0, elevation=data, blend_mode=blend_mode, vert_exag=vert_exag, dx=dx, dy=dy, fraction=fraction, **kwargs) # Don't overwrite the alpha channel, if present. rgb0[..., :3] = rgb1[..., :3] return rgb0
vert_exag=1, dx=1, dy=1, **kwargs): """ Take the input RGB array (ny*nx*3) adjust their color values to given the impression of a shaded relief map with a specified light source using the elevation (ny*nx). A new RGB array ((ny*nx*3)) is returned.
Parameters ---------- rgb : array-like An MxNx3 RGB array, assumed to be in the range of 0 to 1. elevation : array-like A 2d array (or equivalent) of the height values used to generate a shaded map. fraction : number Increases or decreases the contrast of the hillshade. Values greater than one will cause intermediate values to move closer to full illumination or shadow (and clipping any values that move beyond 0 or 1). Note that this is not visually or mathematically the same as vertical exaggeration. blend_mode : {'hsv', 'overlay', 'soft'} or callable, optional The type of blending used to combine the colormapped data values with the illumination intensity. For backwards compatibility, this defaults to "hsv". Note that for most topographic surfaces, "overlay" or "soft" appear more visually realistic. If a user-defined function is supplied, it is expected to combine an MxNx3 RGB array of floats (ranging 0 to 1) with an MxNx1 hillshade array (also 0 to 1). (Call signature `func(rgb, illum, **kwargs)`) Additional kwargs supplied to this function will be passed on to the *blend_mode* function. vert_exag : number, optional The amount to exaggerate the elevation values by when calculating illumination. This can be used either to correct for differences in units between the x-y coordinate system and the elevation coordinate system (e.g. decimal degrees vs meters) or to exaggerate or de-emphasize topography. dx : number, optional The x-spacing (columns) of the input *elevation* grid. dy : number, optional The y-spacing (rows) of the input *elevation* grid. Additional kwargs are passed on to the *blend_mode* function.
Returns ------- shaded_rgb : ndarray An MxNx3 array of floats ranging between 0-1. """ # Calculate the "hillshade" intensity. intensity = self.hillshade(elevation, vert_exag, dx, dy, fraction) intensity = intensity[..., np.newaxis]
# Blend the hillshade and rgb data using the specified mode lookup = { 'hsv': self.blend_hsv, 'soft': self.blend_soft_light, 'overlay': self.blend_overlay, } if blend_mode in lookup: blend = lookup[blend_mode](rgb, intensity, **kwargs) else: try: blend = blend_mode(rgb, intensity, **kwargs) except TypeError: raise ValueError('"blend_mode" must be callable or one of {}' .format(lookup.keys))
# Only apply result where hillshade intensity isn't masked if hasattr(intensity, 'mask'): mask = intensity.mask[..., 0] for i in range(3): blend[..., i][mask] = rgb[..., i][mask]
return blend
hsv_min_val=None, hsv_min_sat=None): """ Take the input data array, convert to HSV values in the given colormap, then adjust those color values to give the impression of a shaded relief map with a specified light source. RGBA values are returned, which can then be used to plot the shaded image with imshow.
The color of the resulting image will be darkened by moving the (s,v) values (in hsv colorspace) toward (hsv_min_sat, hsv_min_val) in the shaded regions, or lightened by sliding (s,v) toward (hsv_max_sat hsv_max_val) in regions that are illuminated. The default extremes are chose so that completely shaded points are nearly black (s = 1, v = 0) and completely illuminated points are nearly white (s = 0, v = 1).
Parameters ---------- rgb : ndarray An MxNx3 RGB array of floats ranging from 0 to 1 (color image). intensity : ndarray An MxNx1 array of floats ranging from 0 to 1 (grayscale image). hsv_max_sat : number, optional The maximum saturation value that the *intensity* map can shift the output image to. Defaults to 1. hsv_min_sat : number, optional The minimum saturation value that the *intensity* map can shift the output image to. Defaults to 0. hsv_max_val : number, optional The maximum value ("v" in "hsv") that the *intensity* map can shift the output image to. Defaults to 1. hsv_min_val: number, optional The minimum value ("v" in "hsv") that the *intensity* map can shift the output image to. Defaults to 0.
Returns ------- rgb : ndarray An MxNx3 RGB array representing the combined images. """ # Backward compatibility... if hsv_max_sat is None: hsv_max_sat = self.hsv_max_sat if hsv_max_val is None: hsv_max_val = self.hsv_max_val if hsv_min_sat is None: hsv_min_sat = self.hsv_min_sat if hsv_min_val is None: hsv_min_val = self.hsv_min_val
# Expects a 2D intensity array scaled between -1 to 1... intensity = intensity[..., 0] intensity = 2 * intensity - 1
# convert to rgb, then rgb to hsv hsv = rgb_to_hsv(rgb[:, :, 0:3])
# modify hsv values to simulate illumination. hsv[:, :, 1] = np.where(np.logical_and(np.abs(hsv[:, :, 1]) > 1.e-10, intensity > 0), ((1. - intensity) * hsv[:, :, 1] + intensity * hsv_max_sat), hsv[:, :, 1])
hsv[:, :, 2] = np.where(intensity > 0, ((1. - intensity) * hsv[:, :, 2] + intensity * hsv_max_val), hsv[:, :, 2])
hsv[:, :, 1] = np.where(np.logical_and(np.abs(hsv[:, :, 1]) > 1.e-10, intensity < 0), ((1. + intensity) * hsv[:, :, 1] - intensity * hsv_min_sat), hsv[:, :, 1]) hsv[:, :, 2] = np.where(intensity < 0, ((1. + intensity) * hsv[:, :, 2] - intensity * hsv_min_val), hsv[:, :, 2]) hsv[:, :, 1:] = np.where(hsv[:, :, 1:] < 0., 0, hsv[:, :, 1:]) hsv[:, :, 1:] = np.where(hsv[:, :, 1:] > 1., 1, hsv[:, :, 1:]) # convert modified hsv back to rgb. return hsv_to_rgb(hsv)
""" Combines an rgb image with an intensity map using "soft light" blending. Uses the "pegtop" formula.
Parameters ---------- rgb : ndarray An MxNx3 RGB array of floats ranging from 0 to 1 (color image). intensity : ndarray An MxNx1 array of floats ranging from 0 to 1 (grayscale image).
Returns ------- rgb : ndarray An MxNx3 RGB array representing the combined images. """ return 2 * intensity * rgb + (1 - 2 * intensity) * rgb**2
""" Combines an rgb image with an intensity map using "overlay" blending.
Parameters ---------- rgb : ndarray An MxNx3 RGB array of floats ranging from 0 to 1 (color image). intensity : ndarray An MxNx1 array of floats ranging from 0 to 1 (grayscale image).
Returns ------- rgb : ndarray An MxNx3 RGB array representing the combined images. """ low = 2 * intensity * rgb high = 1 - 2 * (1 - intensity) * (1 - rgb) return np.where(rgb <= 0.5, low, high)
""" A helper routine to generate a cmap and a norm instance which behave similar to contourf's levels and colors arguments.
Parameters ---------- levels : sequence of numbers The quantization levels used to construct the :class:`BoundaryNorm`. Values ``v`` are quantizized to level ``i`` if ``lev[i] <= v < lev[i+1]``. colors : sequence of colors The fill color to use for each level. If `extend` is "neither" there must be ``n_level - 1`` colors. For an `extend` of "min" or "max" add one extra color, and for an `extend` of "both" add two colors. extend : {'neither', 'min', 'max', 'both'}, optional The behaviour when a value falls out of range of the given levels. See :func:`~matplotlib.pyplot.contourf` for details.
Returns ------- (cmap, norm) : tuple containing a :class:`Colormap` and a \ :class:`Normalize` instance """ colors_i0 = 0 colors_i1 = None
if extend == 'both': colors_i0 = 1 colors_i1 = -1 extra_colors = 2 elif extend == 'min': colors_i0 = 1 extra_colors = 1 elif extend == 'max': colors_i1 = -1 extra_colors = 1 elif extend == 'neither': extra_colors = 0 else: raise ValueError('Unexpected value for extend: {0!r}'.format(extend))
n_data_colors = len(levels) - 1 n_expected_colors = n_data_colors + extra_colors if len(colors) != n_expected_colors: raise ValueError('With extend == {0!r} and n_levels == {1!r} expected' ' n_colors == {2!r}. Got {3!r}.' ''.format(extend, len(levels), n_expected_colors, len(colors)))
cmap = ListedColormap(colors[colors_i0:colors_i1], N=n_data_colors)
if extend in ['min', 'both']: cmap.set_under(colors[0]) else: cmap.set_under('none')
if extend in ['max', 'both']: cmap.set_over(colors[-1]) else: cmap.set_over('none')
cmap.colorbar_extend = extend
norm = BoundaryNorm(levels, ncolors=n_data_colors) return cmap, norm |