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/ colors.py
"""
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 ``'#0f0f0f80'``;
case-insensitive);
* 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 (case-insensitive);
* a name from the `xkcd color survey`_, prefixed with ``'xkcd:'`` (e.g.,
``'xkcd:sky blue'``; case insensitive);
* one of the Tableau Colors from the 'T10' categorical palette (the default
color cycle): ``{'tab:blue', 'tab:orange', 'tab:green', 'tab:red',
'tab:purple', 'tab:brown', 'tab:pink', 'tab:gray', 'tab:olive', 'tab:cyan'}``
(case-insensitive);
* a "CN" color spec, i.e. `'C'` followed by a number, which is an index into
the default property cycle (``matplotlib.rcParams['axes.prop_cycle']``); the
indexing is intended to occur at rendering time, and defaults to black if the
cycle does not include color.
.. _palettable: https://jiffyclub.github.io/palettable/
.. _xkcd color survey: https://xkcd.com/color/rgb/
"""
from collections.abc import Sized
import itertools
import re
import numpy as np
import matplotlib.cbook as cbook
from ._color_data import BASE_COLORS, TABLEAU_COLORS, CSS4_COLORS, XKCD_COLORS
class _ColorMapping(dict):
def __init__(self, mapping):
super().__init__(mapping)
self.cache = {}
def __setitem__(self, key, value):
super().__setitem__(key, value)
self.cache.clear()
def __delitem__(self, key):
super().__delitem__(key)
self.cache.clear()
_colors_full_map = {}
# Set by reverse priority order.
_colors_full_map.update(XKCD_COLORS)
_colors_full_map.update({k.replace('grey', 'gray'): v
for k, v in XKCD_COLORS.items()
if 'grey' in k})
_colors_full_map.update(CSS4_COLORS)
_colors_full_map.update(TABLEAU_COLORS)
_colors_full_map.update({k.replace('gray', 'grey'): v
for k, v in TABLEAU_COLORS.items()
if 'gray' in k})
_colors_full_map.update(BASE_COLORS)
_colors_full_map = _ColorMapping(_colors_full_map)
def get_named_colors_mapping():
"""Return the global mapping of names to named colors."""
return _colors_full_map
def _sanitize_extrema(ex):
if ex is None:
return ex
try:
ret = ex.item()
except AttributeError:
ret = float(ex)
return ret
def _is_nth_color(c):
"""Return whether *c* can be interpreted as an item in the color cycle."""
return isinstance(c, str) and re.match(r"\AC[0-9]+\Z", c)
def is_color_like(c):
"""Return whether *c* can be interpreted as an RGB(A) color."""
# Special-case nth color syntax because it cannot be parsed during setup.
if _is_nth_color(c):
return True
try:
to_rgba(c)
except ValueError:
return False
else:
return True
def same_color(c1, c2):
"""
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()
def to_rgba(c, alpha=None):
"""
Convert *c* to an RGBA color.
Parameters
----------
c : Matplotlib color or ``np.ma.masked``
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.
if _is_nth_color(c):
from matplotlib import rcParams
prop_cycler = rcParams['axes.prop_cycle']
colors = prop_cycler.by_key().get('color', ['k'])
c = colors[int(c[1:]) % len(colors)]
try:
rgba = _colors_full_map.cache[c, alpha]
except (KeyError, TypeError): # Not in cache, or unhashable.
rgba = None
if rgba is None: # Suppress exception chaining of cache lookup failure.
rgba = _to_rgba_no_colorcycle(c, alpha)
try:
_colors_full_map.cache[c, alpha] = rgba
except TypeError:
pass
return rgba
def _to_rgba_no_colorcycle(c, alpha=None):
"""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)``.
"""
orig_c = c
if c is np.ma.masked:
return (0., 0., 0., 0.)
if isinstance(c, str):
if c.lower() == "none":
return (0., 0., 0., 0.)
# Named color.
try:
# This may turn c into a non-string, so we check again below.
c = _colors_full_map[c]
except KeyError:
try:
c = _colors_full_map[c.lower()]
except KeyError:
pass
else:
if len(orig_c) == 1:
cbook.warn_deprecated(
"3.1", message="Support for uppercase "
"single-letter colors is deprecated since Matplotlib "
"%(since)s and will be removed %(removal)s; please "
"use lowercase instead.")
if isinstance(c, str):
# hex color with no alpha.
match = re.match(r"\A#[a-fA-F0-9]{6}\Z", c)
if match:
return (tuple(int(n, 16) / 255
for n in [c[1:3], c[3:5], c[5:7]])
+ (alpha if alpha is not None else 1.,))
# hex color with alpha.
match = re.match(r"\A#[a-fA-F0-9]{8}\Z", c)
if match:
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.
try:
return (float(c),) * 3 + (alpha if alpha is not None else 1.,)
except ValueError:
pass
raise ValueError("Invalid RGBA argument: {!r}".format(orig_c))
# tuple color.
c = np.array(c)
if not np.can_cast(c.dtype, float, "same_kind") or c.ndim != 1:
# 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.
c = tuple(c.astype(float))
if len(c) not in [3, 4]:
raise ValueError("RGBA sequence should have length 3 or 4")
if len(c) == 3 and alpha is None:
alpha = 1
if alpha is not None:
c = c[:3] + (alpha,)
if any(elem < 0 or elem > 1 for elem in c):
raise ValueError("RGBA values should be within 0-1 range")
return c
def to_rgba_array(c, alpha=None):
"""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.
If *c* is a masked array, an ndarray is returned with a (0, 0, 0, 0)
row for each masked value or row in *c*.
"""
# 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.)
if (isinstance(c, np.ndarray) and c.dtype.kind in "if"
and c.ndim == 2 and c.shape[1] in [3, 4]):
mask = c.mask.any(axis=1) if np.ma.is_masked(c) else None
c = np.ma.getdata(c)
if c.shape[1] == 3:
result = np.column_stack([c, np.zeros(len(c))])
result[:, -1] = alpha if alpha is not None else 1.
elif c.shape[1] == 4:
result = c.copy()
if alpha is not None:
result[:, -1] = alpha
if mask is not None:
result[mask] = 0
if np.any((result < 0) | (result > 1)):
raise ValueError("RGBA values should be within 0-1 range")
return result
# 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(!).
if cbook._str_lower_equal(c, "none"):
return np.zeros((0, 4), float)
try:
return np.array([to_rgba(c, alpha)], float)
except (ValueError, TypeError):
pass
# Convert one at a time.
result = np.empty((len(c), 4), float)
for i, cc in enumerate(c):
result[i] = to_rgba(cc, alpha)
return result
def to_rgb(c):
"""Convert *c* to an RGB color, silently dropping the alpha channel."""
return to_rgba(c)[:3]
def to_hex(c, keep_alpha=False):
"""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
cnames = CSS4_COLORS
hexColorPattern = re.compile(r"\A#[a-fA-F0-9]{6}\Z")
rgb2hex = to_hex
hex2color = to_rgb
class ColorConverter(object):
"""
This class is only kept for backwards compatibility.
Its functionality is entirely provided by module-level functions.
"""
colors = _colors_full_map
cache = _colors_full_map.cache
to_rgb = staticmethod(to_rgb)
to_rgba = staticmethod(to_rgba)
to_rgba_array = staticmethod(to_rgba_array)
colorConverter = ColorConverter()
### End of backwards-compatible color-conversion API
def makeMappingArray(N, data, gamma=1.0):
r"""Create an *N* -element 1-d lookup table.
This assumes a mapping :math:`f : [0, 1] \rightarrow [0, 1]`. The returned
data is an array of N values :math:`y = f(x)` where x is sampled from
[0, 1].
By default (*gamma* = 1) x is equidistantly sampled from [0, 1]. The
*gamma* correction factor :math:`\gamma` distorts this equidistant
sampling by :math:`x \rightarrow x^\gamma`.
Parameters
----------
N : int
The number of elements of the created lookup table.
This must be N >= 1.
data : Mx3 array-like or callable
Defines the mapping :math:`f`.
If a Mx3 array-like, the rows define values (x, y0, y1). The x values
must start with x=0, end with x=1, and all x values be in increasing
order.
A value between :math:`x_i` and :math:`x_{i+1}` is mapped to the range
:math:`y^1_{i-1} \ldots y^0_i` by linear interpolation.
For the simple case of a y-continuous mapping, y0 and y1 are identical.
The two values of y are to allow for discontinuous mapping functions.
E.g. a sawtooth with a period of 0.2 and an amplitude of 1 would be::
[(0, 1, 0), (0.2, 1, 0), (0.4, 1, 0), ..., [(1, 1, 0)]
In the special case of ``N == 1``, by convention the returned value
is y0 for x == 1.
If *data* is a callable, it must accept and return numpy arrays::
data(x : ndarray) -> ndarray
and map values between 0 - 1 to 0 - 1.
gamma : float
Gamma correction factor for input distribution x of the mapping.
See also https://en.wikipedia.org/wiki/Gamma_correction.
Returns
-------
lut : array
The lookup table where ``lut[x * (N-1)]`` gives the closest value
for values of x between 0 and 1.
Notes
-----
This function is internally used for `.LinearSegmentedColormaps`.
"""
if callable(data):
xind = np.linspace(0, 1, N) ** gamma
lut = np.clip(np.array(data(xind), dtype=float), 0, 1)
return lut
try:
adata = np.array(data)
except Exception:
raise TypeError("data must be convertible to an array")
shape = adata.shape
if len(shape) != 2 or shape[1] != 3:
raise ValueError("data must be nx3 format")
x = adata[:, 0]
y0 = adata[:, 1]
y1 = adata[:, 2]
if x[0] != 0. or x[-1] != 1.0:
raise ValueError(
"data mapping points must start with x=0 and end with x=1")
if (np.diff(x) < 0).any():
raise ValueError("data mapping points must have x in increasing order")
# begin generation of lookup table
if N == 1:
# convention: use the y = f(x=1) value for a 1-element lookup table
lut = np.array(y0[-1])
else:
x = x * (N - 1)
xind = (N - 1) * np.linspace(0, 1, N) ** gamma
ind = np.searchsorted(x, xind)[1:-1]
distance = (xind[1:-1] - x[ind - 1]) / (x[ind] - x[ind - 1])
lut = np.concatenate([
[y1[0]],
distance * (y0[ind] - y1[ind - 1]) + y1[ind - 1],
[y0[-1]],
])
# ensure that the lut is confined to values between 0 and 1 by clipping it
return np.clip(lut, 0.0, 1.0)
class Colormap(object):
"""
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.
"""
def __init__(self, name, N=256):
"""
Parameters
----------
name : str
The name of the colormap.
N : int
The number of rgb quantization levels.
"""
self.name = name
self.N = int(N) # ensure that N is always int
self._rgba_bad = (0.0, 0.0, 0.0, 0.0) # If bad, don't paint anything.
self._rgba_under = None
self._rgba_over = None
self._i_under = self.N
self._i_over = self.N + 1
self._i_bad = self.N + 2
self._isinit = False
#: 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.
self.colorbar_extend = False
def __call__(self, X, alpha=None, bytes=False):
"""
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.
if not self._isinit:
self._init()
mask_bad = None
if not np.iterable(X):
vtype = 'scalar'
xa = np.array([X])
else:
vtype = 'array'
xma = np.ma.array(X, copy=True) # Copy here to avoid side effects.
mask_bad = xma.mask # Mask will be used below.
xa = xma.filled() # Fill to avoid infs, etc.
del xma
# Calculations with native byteorder are faster, and avoid a
# bug that otherwise can occur with putmask when the last
# argument is a numpy scalar.
if not xa.dtype.isnative:
xa = xa.byteswap().newbyteorder()
if xa.dtype.kind == "f":
xa *= self.N
# Negative values are out of range, but astype(int) would truncate
# them towards zero.
xa[xa < 0] = -1
# xa == 1 (== N after multiplication) is not out of range.
xa[xa == self.N] = self.N - 1
# Avoid converting large positive values to negative integers.
np.clip(xa, -1, self.N, out=xa)
xa = xa.astype(int)
# Set the over-range indices before the under-range;
# otherwise the under-range values get converted to over-range.
xa[xa > self.N - 1] = self._i_over
xa[xa < 0] = self._i_under
if mask_bad is not None:
if mask_bad.shape == xa.shape:
np.copyto(xa, self._i_bad, where=mask_bad)
elif mask_bad:
xa.fill(self._i_bad)
if bytes:
lut = (self._lut * 255).astype(np.uint8)
else:
lut = self._lut.copy() # Don't let alpha modify original _lut.
if alpha is not None:
alpha = np.clip(alpha, 0, 1)
if bytes:
alpha = int(alpha * 255)
if (lut[-1] == 0).all():
lut[:-1, -1] = alpha
# 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.
rgba = lut.take(xa, axis=0, mode='clip')
if vtype == 'scalar':
rgba = tuple(rgba[0, :])
return rgba
def __copy__(self):
"""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
def set_bad(self, color='k', alpha=None):
"""Set color to be used for masked values.
"""
self._rgba_bad = to_rgba(color, alpha)
if self._isinit:
self._set_extremes()
def set_under(self, color='k', alpha=None):
"""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()
def set_over(self, color='k', alpha=None):
"""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()
def _set_extremes(self):
if self._rgba_under:
self._lut[self._i_under] = self._rgba_under
else:
self._lut[self._i_under] = self._lut[0]
if self._rgba_over:
self._lut[self._i_over] = self._rgba_over
else:
self._lut[self._i_over] = self._lut[self.N - 1]
self._lut[self._i_bad] = self._rgba_bad
def _init(self):
"""Generate the lookup table, self._lut"""
raise NotImplementedError("Abstract class only")
def is_gray(self):
if not self._isinit:
self._init()
return (np.all(self._lut[:, 0] == self._lut[:, 1]) and
np.all(self._lut[:, 0] == self._lut[:, 2]))
def _resample(self, lutsize):
"""
Return a new color map with *lutsize* entries.
"""
raise NotImplementedError()
def reversed(self, name=None):
"""
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".
See Also
--------
LinearSegmentedColormap.reversed
ListedColormap.reversed
"""
raise NotImplementedError()
class LinearSegmentedColormap(Colormap):
"""
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.
"""
def __init__(self, name, segmentdata, N=256, gamma=1.0):
"""
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.
See Also
--------
LinearSegmentedColormap.from_list
Static method; factory function for generating a smoothly-varying
LinearSegmentedColormap.
makeMappingArray
For information about making a mapping array.
"""
# True only if all colors in map are identical; needed for contouring.
self.monochrome = False
Colormap.__init__(self, name, N)
self._segmentdata = segmentdata
self._gamma = gamma
def _init(self):
self._lut = np.ones((self.N + 3, 4), float)
self._lut[:-3, 0] = makeMappingArray(
self.N, self._segmentdata['red'], self._gamma)
self._lut[:-3, 1] = makeMappingArray(
self.N, self._segmentdata['green'], self._gamma)
self._lut[:-3, 2] = makeMappingArray(
self.N, self._segmentdata['blue'], self._gamma)
if 'alpha' in self._segmentdata:
self._lut[:-3, 3] = makeMappingArray(
self.N, self._segmentdata['alpha'], 1)
self._isinit = True
self._set_extremes()
def set_gamma(self, gamma):
"""
Set a new gamma value and regenerate color map.
"""
self._gamma = gamma
self._init()
@staticmethod
def from_list(name, colors, N=256, gamma=1.0):
"""
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.
"""
if not np.iterable(colors):
raise ValueError('colors must be iterable')
if (isinstance(colors[0], Sized) and len(colors[0]) == 2
and not isinstance(colors[0], str)):
# List of value, color pairs
vals, colors = zip(*colors)
else:
vals = np.linspace(0, 1, len(colors))
cdict = dict(red=[], green=[], blue=[], alpha=[])
for val, color in zip(vals, colors):
r, g, b, a = to_rgba(color)
cdict['red'].append((val, r, r))
cdict['green'].append((val, g, g))
cdict['blue'].append((val, b, b))
cdict['alpha'].append((val, a, a))
return LinearSegmentedColormap(name, cdict, N, gamma)
def _resample(self, lutsize):
"""
Return a new color map with *lutsize* entries.
"""
return LinearSegmentedColormap(self.name, self._segmentdata, lutsize)
def reversed(self, name=None):
"""
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)
class ListedColormap(Colormap):
"""
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.
Parameters
----------
colors : list, array
List of Matplotlib color specifications, or an equivalent Nx3 or Nx4
floating point array (*N* rgb or rgba values).
name : str, optional
String to identify the colormap.
N : int, optional
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.
"""
def __init__(self, colors, name='from_list', N=None):
self.monochrome = False # True only if all colors in map are
# identical; needed for contouring.
if N is None:
self.colors = colors
N = len(colors)
else:
if isinstance(colors, str):
self.colors = [colors] * N
self.monochrome = True
elif np.iterable(colors):
if len(colors) == 1:
self.monochrome = True
self.colors = list(
itertools.islice(itertools.cycle(colors), N))
else:
try:
gray = float(colors)
except TypeError:
pass
else:
self.colors = [gray] * N
self.monochrome = True
Colormap.__init__(self, name, N)
def _init(self):
self._lut = np.zeros((self.N + 3, 4), float)
self._lut[:-3] = to_rgba_array(self.colors)
self._isinit = True
self._set_extremes()
def _resample(self, lutsize):
"""
Return a new color map with *lutsize* entries.
"""
colors = self(np.linspace(0, 1, lutsize))
return ListedColormap(colors, name=self.name)
def reversed(self, name=None):
"""
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)
class Normalize(object):
"""
A class which, when called, can normalize data into
the ``[0.0, 1.0]`` interval.
"""
def __init__(self, vmin=None, vmax=None, clip=False):
"""
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*.
"""
self.vmin = _sanitize_extrema(vmin)
self.vmax = _sanitize_extrema(vmax)
self.clip = clip
@staticmethod
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.
"""
is_scalar = not np.iterable(value)
if is_scalar:
value = [value]
dtype = np.min_scalar_type(value)
if np.issubdtype(dtype, np.integer) or dtype.type is np.bool_:
# bool_/int8/int16 -> float32; int32/int64 -> float64
dtype = np.promote_types(dtype, np.float32)
# ensure data passed in as an ndarray subclass are interpreted as
# an ndarray. See issue #6622.
mask = np.ma.getmask(value)
data = np.asarray(np.ma.getdata(value))
result = np.ma.array(data, mask=mask, dtype=dtype, copy=True)
return result, is_scalar
def __call__(self, value, clip=None):
"""
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)*.
"""
if clip is None:
clip = self.clip
result, is_scalar = self.process_value(value)
self.autoscale_None(result)
# Convert at least to float, without losing precision.
(vmin,), _ = self.process_value(self.vmin)
(vmax,), _ = self.process_value(self.vmax)
if vmin == vmax:
result.fill(0) # Or should it be all masked? Or 0.5?
elif vmin > vmax:
raise ValueError("minvalue must be less than or equal to maxvalue")
else:
if clip:
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
resdat = result.data
resdat -= vmin
resdat /= (vmax - vmin)
result = np.ma.array(resdat, mask=result.mask, copy=False)
if is_scalar:
result = result[0]
return result
def inverse(self, value):
if not self.scaled():
raise ValueError("Not invertible until scaled")
(vmin,), _ = self.process_value(self.vmin)
(vmax,), _ = self.process_value(self.vmax)
if np.iterable(value):
val = np.ma.asarray(value)
return vmin + val * (vmax - vmin)
else:
return vmin + value * (vmax - vmin)
def autoscale(self, A):
"""Set *vmin*, *vmax* to min, max of *A*."""
A = np.asanyarray(A)
self.vmin = A.min()
self.vmax = A.max()
def autoscale_None(self, A):
"""Autoscale only None-valued vmin or vmax."""
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()
def scaled(self):
"""Return whether vmin and vmax are set."""
return self.vmin is not None and self.vmax is not None
class DivergingNorm(Normalize):
def __init__(self, vcenter, vmin=None, vmax=None):
"""
Normalize data with a set center.
Useful when mapping data with an unequal rates of change around a
conceptual center, e.g., data that range from -2 to 4, with 0 as
the midpoint.
Parameters
----------
vcenter : float
The data value that defines ``0.5`` in the normalization.
vmin : float, optional
The data value that defines ``0.0`` in the normalization.
Defaults to the min value of the dataset.
vmax : float, optional
The data value that defines ``1.0`` in the normalization.
Defaults to the the max value of the dataset.
Examples
--------
This maps data value -4000 to 0., 0 to 0.5, and +10000 to 1.0; data
between is linearly interpolated::
>>> import matplotlib.colors as mcolors
>>> offset = mcolors.DivergingNorm(vmin=-4000.,
vcenter=0., vmax=10000)
>>> data = [-4000., -2000., 0., 2500., 5000., 7500., 10000.]
>>> offset(data)
array([0., 0.25, 0.5, 0.625, 0.75, 0.875, 1.0])
"""
self.vcenter = vcenter
self.vmin = vmin
self.vmax = vmax
if vcenter is not None and vmax is not None and vcenter >= vmax:
raise ValueError('vmin, vcenter, and vmax must be in '
'ascending order')
if vcenter is not None and vmin is not None and vcenter <= vmin:
raise ValueError('vmin, vcenter, and vmax must be in '
'ascending order')
def autoscale_None(self, A):
"""
Get vmin and vmax, and then clip at vcenter
"""
super().autoscale_None(A)
if self.vmin > self.vcenter:
self.vmin = self.vcenter
if self.vmax < self.vcenter:
self.vmax = self.vcenter
def __call__(self, value, clip=None):
"""
Map value to the interval [0, 1]. The clip argument is unused.
"""
result, is_scalar = self.process_value(value)
self.autoscale_None(result) # sets self.vmin, self.vmax if None
if not self.vmin <= self.vcenter <= self.vmax:
raise ValueError("vmin, vcenter, vmax must increase monotonically")
result = np.ma.masked_array(
np.interp(result, [self.vmin, self.vcenter, self.vmax],
[0, 0.5, 1.]), mask=np.ma.getmask(result))
if is_scalar:
result = np.atleast_1d(result)[0]
return result
class LogNorm(Normalize):
"""Normalize a given value to the 0-1 range on a log scale."""
def __call__(self, value, clip=None):
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
def inverse(self, value):
if not self.scaled():
raise ValueError("Not invertible until scaled")
vmin, vmax = self.vmin, self.vmax
if np.iterable(value):
val = np.ma.asarray(value)
return vmin * np.ma.power((vmax / vmin), val)
else:
return vmin * pow((vmax / vmin), value)
def autoscale(self, A):
# docstring inherited.
super().autoscale(np.ma.masked_less_equal(A, 0, copy=False))
def autoscale_None(self, A):
# docstring inherited.
super().autoscale_None(np.ma.masked_less_equal(A, 0, copy=False))
class SymLogNorm(Normalize):
"""
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*).
"""
def __init__(self, linthresh, linscale=1.0,
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()
def __call__(self, value, clip=None):
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
def _transform(self, a):
"""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
def _inv_transform(self, 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
def _transform_vmin_vmax(self):
"""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)
def inverse(self, value):
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)
def autoscale(self, A):
# docstring inherited.
super().autoscale(A)
self._transform_vmin_vmax()
def autoscale_None(self, A):
# docstring inherited.
super().autoscale_None(A)
self._transform_vmin_vmax()
class PowerNorm(Normalize):
"""
Linearly map a given value to the 0-1 range and then apply
a power-law normalization over that range.
"""
def __init__(self, gamma, vmin=None, vmax=None, clip=False):
Normalize.__init__(self, vmin, vmax, clip)
self.gamma = gamma
def __call__(self, value, clip=None):
if clip is None:
clip = self.clip
result, is_scalar = self.process_value(value)
self.autoscale_None(result)
gamma = self.gamma
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)
resdat = result.data
resdat -= vmin
resdat[resdat < 0] = 0
np.power(resdat, gamma, resdat)
resdat /= (vmax - vmin) ** gamma
result = np.ma.array(resdat, mask=result.mask, copy=False)
if is_scalar:
result = result[0]
return result
def inverse(self, value):
if not self.scaled():
raise ValueError("Not invertible until scaled")
gamma = self.gamma
vmin, vmax = self.vmin, self.vmax
if np.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
class BoundaryNorm(Normalize):
"""
Generate a colormap index based on discrete intervals.
Unlike `Normalize` or `LogNorm`, `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.
"""
def __init__(self, boundaries, ncolors, clip=False):
"""
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
def __call__(self, value, clip=None):
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
def inverse(self, value):
"""
Raises
------
ValueError
BoundaryNorm is not invertible, so calling this method will always
raise an error
"""
return ValueError("BoundaryNorm is not invertible")
class NoNorm(Normalize):
"""
Dummy replacement for `Normalize`, for the case where we want to use
indices directly in a `~matplotlib.cm.ScalarMappable`.
"""
def __call__(self, value, clip=None):
return value
def inverse(self, value):
return value
def rgb_to_hsv(arr):
"""
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]
"""
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_shape = arr.shape
arr = np.array(
arr, copy=False,
dtype=np.promote_types(arr.dtype, np.float32), # Don't work on ints.
ndmin=2, # In case input was 1D.
)
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
return out.reshape(in_shape)
def hsv_to_rgb(hsv):
"""
Convert hsv values to rgb.
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))
in_shape = hsv.shape
hsv = np.array(
hsv, copy=False,
dtype=np.promote_types(hsv.dtype, np.float32), # Don't work on ints.
ndmin=2, # In case input was 1D.
)
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)
return rgb.reshape(in_shape)
def _vector_magnitude(arr):
# 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)
class LightSource(object):
"""
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.
"""
def __init__(self, azdeg=315, altdeg=45, hsv_min_val=0, hsv_max_val=1,
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
@property
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)
])
def hillshade(self, elevation, vert_exag=1, dx=1, dy=1, fraction=1.):
"""
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)
def shade_normals(self, normals, fraction=1.):
"""
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)
return intensity
def shade(self, data, cmap, norm=None, blend_mode='overlay', vmin=None,
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
def shade_rgb(self, rgb, elevation, fraction=1., blend_mode='hsv',
vert_exag=1, dx=1, dy=1, **kwargs):
"""
Use this light source to adjust the colors of the *rgb* input array to
give the impression of a shaded relief map with the given `elevation`.
Parameters
----------
rgb : array-like
An (M, N, 3) RGB array, assumed to be in the range of 0 to 1.
elevation : array-like
An (M, N) array 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 (m, n, 3) 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
def blend_hsv(self, rgb, intensity, hsv_max_sat=None, hsv_max_val=None,
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.
np.putmask(hsv[:, :, 1], # i.e. A[mask] = B[mask].
(np.abs(hsv[:, :, 1]) > 1.e-10) & (intensity > 0),
(1 - intensity) * hsv[:, :, 1] + intensity * hsv_max_sat)
np.putmask(hsv[:, :, 2],
intensity > 0,
(1 - intensity) * hsv[:, :, 2] + intensity * hsv_max_val)
np.putmask(hsv[:, :, 1],
(np.abs(hsv[:, :, 1]) > 1.e-10) & (intensity < 0),
(1 + intensity) * hsv[:, :, 1] - intensity * hsv_min_sat)
np.putmask(hsv[:, :, 2],
intensity < 0,
(1 + intensity) * hsv[:, :, 2] - intensity * hsv_min_val)
np.clip(hsv[:, :, 1:], 0, 1, out=hsv[:, :, 1:])
# convert modified hsv back to rgb.
return hsv_to_rgb(hsv)
def blend_soft_light(self, rgb, intensity):
"""
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
def blend_overlay(self, rgb, intensity):
"""
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)
def from_levels_and_colors(levels, colors, extend='neither'):
"""
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`.
Value ``v`` is quantized 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