Bipolar colormap translated from Matlab into Python

readme.md

Rough translation of Bipolar Colormap by Ged Ridgway into Python

Very similar colormap is FireIce by Joseph Kirk

I want to make it smoother and get rid of the prominent bands. Bezier curves work pretty well: https://www.flickr.com/photos/omegatron/8534628384/ https://www.flickr.com/photos/omegatron/8533520357/

bipolar linear.png

bipolar.py

#!/usr/bin/env python

"""
Copyright 2012 endolith at gmail com
Copyright 2009 Ged Ridgway at gmail com

Translation and modification of 
http://www.mathworks.com/matlabcentral/fileexchange/26026-bipolar-colormap

Based on Manja Lehmann's hand-crafted colormap for cortical visualisation
"""

from __future__ import division
import scipy
from matplotlib import cm

def bipolar(lutsize=256, n=0.333, interp=[]):
    """
    Bipolar hot/cold colormap, with neutral central color.
    
    This colormap is meant for visualizing diverging data; positive 
    and negative deviations from a central value.  It is similar to a 
    blackbody colormap for positive values, but with a complementary 
    "cold" colormap for negative values.
    
    Parameters
    ----------
    lutsize : int
        The number of elements in the colormap lookup table. (Default is 256.)
    n : float
        The gray value for the neutral middle of the colormap.  (Default is 
        1/3.)
        The colormap goes from cyan-blue-neutral-red-yellow if neutral 
        is < 0.5, and from blue-cyan-neutral-yellow-red if neutral > 0.5.
        For shaded 3D surfaces, an `n` near 0.5 is better, because it 
        minimizes luminance changes that would otherwise obscure shading cues 
        for determining 3D structure.
        For 2D heat maps, an `n` near the 0 or 1 extremes is better, for 
        maximizing luminance change and showing details of the data.
    interp : str or int, optional
        Specifies the type of interpolation.
        ('linear', 'nearest', 'zero', 'slinear', 'quadratic, 'cubic')
        or as an integer specifying the order of the spline interpolator
        to use. Default is 'linear'.  See `scipy.interpolate.interp1d`.
    
    Returns
    -------
    out : matplotlib.colors.LinearSegmentedColormap
        The resulting colormap object
    
    Notes
    -----
    If neutral is exactly 0.5, then a map which yields a linear increase in
    intensity when converted to grayscale is produced. This colormap should 
    also be reasonably good
    for colorblind viewers, as it avoids green and is predominantly based on
    the purple-yellow pairing which is easily discriminated by the two common
    types of colorblindness. [2]_
     
    Examples
    --------
    >>> from mpl_toolkits.mplot3d import Axes3D
    >>> from matplotlib import cm
    >>> import matplotlib.pyplot as plt
    >>> import numpy as np

    >>> fig = plt.figure()
    >>> ax = fig.gca(projection='3d')
    >>> x = y = np.arange(-4, 4, 0.15)
    >>> x, y = np.meshgrid(x, y)
    >>> z = (1- x/2 + x**5 + y**3)*exp(-x**2-y**2)
    >>> surf = ax.plot_surface(x, y, z, rstride=1, cstride=1, linewidth=0.1, 
    >>>                        vmax=abs(z).max(), vmin=-abs(z).max())
    >>> fig.colorbar(surf)
    >>> plt.show()
    >>> set_cmap(bipolar(201))
    >>> waitforbuttonpress()        
    >>> set_cmap(bipolar(201, 0.1)) # dark gray as neutral
    >>> waitforbuttonpress()
    >>> set_cmap(bipolar(201, 0.9)) # light gray as neutral
    >>> waitforbuttonpress()
    >>> set_cmap(bipolar(201, 0.5)) # grayscale-friendly colormap
    
    References
    ----------
    .. [1] Lehmann Manja, Crutch SJ, Ridgway GR et al. "Cortical thickness 
        and voxel-based morphometry in posterior cortical atrophy and typical 
        Alzheimer's disease", Neurobiology of Aging, 2009,
        doi:10.1016/j.neurobiolaging.2009.08.017
    .. [2] Brewer, Cynthia A., "Guidelines for Selecting Colors for 
        Diverging Schemes on Maps", The Cartographic Journal, Volume 33, 
        Number 2, December 1996, pp. 79-86(8)
        http://www.ingentaconnect.com/content/maney/caj/1996/00000033/00000002/art00002

    """
    if n < 0.5:
        if not interp:
            interp = 'linear' # seems to work well with dark neutral colors  cyan-blue-dark-red-yellow
       
        _data = (
            (0, 1, 1), # cyan
            (0, 0, 1), # blue
            (n, n, n), # dark neutral
            (1, 0, 0), # red
            (1, 1, 0), # yellow
        )
    elif n >= 0.5:
        if not interp:
            interp = 'cubic' # seems to work better with bright neutral colors blue-cyan-light-yellow-red
            # produces bright yellow or cyan rings otherwise

        _data = (
            (0, 0, 1), # blue
            (0, 1, 1), # cyan
            (n, n, n), # light neutral
            (1, 1, 0), # yellow
            (1, 0, 0), # red
        )
    else:
        raise ValueError('n must be 0.0 < n < 1.0')
    
    xi = linspace(0, 1, size(_data, 0))
    cm_interp = scipy.interpolate.interp1d(xi, _data, axis=0, kind=interp)
    xnew = linspace(0, 1, lutsize)
    ynew = cm_interp(xnew)
    
    # No form of interpolation works without this, but that means the interpolations are not working right.
    ynew = clip(ynew, 0, 1)
    
    return cm.colors.LinearSegmentedColormap.from_list('bipolar', ynew, lutsize)

if __name__ == "__main__":
    
    from pylab import *
    
    def func3(x,y):
        return (1- x/2 + x**5 + y**3)*exp(-x**2-y**2)
        
    # make these smaller to increase the resolution
    dx, dy = 0.05, 0.05
    
    x = arange(-3.0, 3.0001, dx)
    y = arange(-3.0, 3.0001, dy)
    X,Y = meshgrid(x, y)
       
    Z = func3(X, Y)
    pcolor(X, Y, Z, cmap=bipolar(n=1./3, interp='linear'), vmax=abs(Z).max(), vmin=-abs(Z).max())
    colorbar()
    axis([-3,3,-3,3])

    show()
    

bipolar_surf_matplotlib.png

color_scale.py

# -*- coding: utf-8 -*-
"""
Created on Thu Feb 28 14:28:50 2013

Translation of
http://www.mathworks.com/matlabcentral/fileexchange/11037-lab-color-scale

Based on https://code.google.com/p/python-colormath/

"""
from __future__ import division
from numpy import pi, linspace, cos, sin, vstack
from colormath.color_objects import LabColor
from matplotlib import cm

def color_scale(n=256, theta=0, r=50, angle_offset=pi/2, dir='cw'):
    if dir == 'cw':
        angle_offset = -angle_offset
    else:
        angle_offset = angle_offset

    theta = pi * theta / 180
    theta_vec = linspace(theta, theta + angle_offset, n)

    a = r * cos(theta_vec)
    b = r * sin(theta_vec)
    L = linspace(0, 100, n)

    rgbs = []

    Lab = vstack([L, a, b])
    for L, a, b in Lab.T:
        rgb = LabColor(L, a, b).convert_to('rgb')
        r = rgb.rgb_r/255.0
        g = rgb.rgb_g/255.0
        b = rgb.rgb_b/255.0
        rgbs.append((r, g, b))

    return cm.colors.LinearSegmentedColormap.from_list('color_scale', rgbs, n)

if __name__ == "__main__":
    
    from pylab import *
    
    dx, dy = 0.01, 0.01
    
    x = arange(-2.0, 2.0001, dx)
    y = arange(-2.0, 2.0001, dy)
    X,Y = meshgrid(x, y)
    Z = X * np.exp(-X**2 - Y**2) # Matplotlib's 2-bump example
    
    figure()
    imshow(Z, vmax=abs(Z).max(), vmin=-abs(Z).max(), 
                 cmap=color_scale(theta = 0, r = 50))
    colorbar()
    show()

colormap_curve.py

# -*- coding: utf-8 -*-
"""
Created on Thu Feb 28 21:13:00 2013
"""

import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from color_scale import color_scale
from bipolar import bipolar

mpl.rcParams['legend.fontsize'] = 10

fig = plt.figure(1)
ax = fig.gca(projection='3d')

#colormap = color_scale(theta = 0, angle_offset=2*pi, r = 50)
#colormap = bipolar(n=0)
colormap = get_cmap('hsv')

lutsize = 256

# Plain lines
#    colors = zeros((lutsize, 3))
#    for i in xrange(0, lutsize):
#        colors[i] = colormap.__call__(i)[:3]
# 
#    r = colors[:,0]
#    g = colors[:,1]
#    b = colors[:,2]
#    
#    ax.plot(r, g, b, label=colormap.name)


# Colored lines
for i in xrange(0, lutsize-1):
    r1, g1, b1 = colormap.__call__(i  )[:3]
    r2, g2, b2 = colormap.__call__(i+1)[:3]

    ax.plot([r1, r2], [g1, g2], [b1, b2], lw=3, color = (r1, g1, b1))

ax.legend()

ax.set_xlim3d(0, 1)
ax.set_ylim3d(0, 1)
ax.set_zlim3d(0, 1)

ax.set_xlabel("red")
ax.set_ylabel("blue")
ax.set_zlabel("green")

plt.show()

license.txt

color_scale.m (Steve Eddins):

Copyright (c) 2009, The MathWorks, Inc.
All rights reserved.

Redistribution and use in source and binary forms, with or without 
modification, are permitted provided that the following conditions are 
met:

    * Redistributions of source code must retain the above copyright 
      notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright 
      notice, this list of conditions and the following disclaimer in 
      the documentation and/or other materials provided with the distribution
    * Neither the name of the The MathWorks, Inc. nor the names 
      of its contributors may be used to endorse or promote products derived 
      from this software without specific prior written permission.
      
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
POSSIBILITY OF SUCH DAMAGE.


bipolar.m:

Copyright (c) 2009, Ged Ridgway
All rights reserved.

Redistribution and use in source and binary forms, with or without 
modification, are permitted provided that the following conditions are 
met:

    * Redistributions of source code must retain the above copyright 
      notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright 
      notice, this list of conditions and the following disclaimer in 
      the documentation and/or other materials provided with the distribution
      
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
POSSIBILITY OF SUCH DAMAGE.

Manja Lehmann example.png

Why did I put the color_scale here though? That's a totally different thing...

I cleaned up the git history and moved it here: https://github.com/endolith/bipolar-colormap

I'm planning to keep the "bipolar" map matching the existing ones, with the RGB cube angles and "halos", and rename the bezier curve version to "hotcold".