## Plotly asymmetric diverging colorscales adapted to data¶

### Symmetric diverging colorscales¶

Diverging colorscales are recommendend for visualizing data that are symmetric with respect to a reference value, that is the data range is approximately [reference-val, reference+val], where val>0. Such colormaps emphasize the positive and negative deviations from the reference point.

A simplest diverging colormap is defined by two isoiluminant end hues, left color and right color, and a mid color that has a higher luminance than the end colors. The normalized reference point is mapped to the central color of the colorscale defined by these three colors.

Details about Plotly color scales can be found here.

We illustrate below how we can define a custom diverging matplotlib colormap, respectively a Plotly colorscale, starting with a list of three colors (left, mid and right color).

In [3]:
import numpy as np
import pandas as pd
import matplotlib. pyplot as plt
from matplotlib import colors
from matplotlib.colors import LinearSegmentedColormap
%matplotlib inline

In [4]:
def display_cmap(cmap): #Display  a colormap cmap
plt.imshow(np.linspace(0, 100, 256)[None, :],  aspect=25, interpolation='nearest', cmap=cmap)
plt.axis('off')

In [5]:
def colormap_to_colorscale(cmap):
#function that transforms a matplotlib colormap to a Plotly colorscale
return [ [k*0.1, colors.rgb2hex(cmap(k*0.1))] for k in range(11)]


In [6]:
def colorscale_from_list(alist, name):
# Defines a colormap, and the corresponding Plotly colorscale from the list alist
# alist=the list of basic colors
# name is the name of the corresponding matplotlib colormap

cmap = LinearSegmentedColormap.from_list(name, alist)
display_cmap(cmap)
colorscale=colormap_to_colorscale(cmap)
return cmap, colorscale


Let us define a diverging colorscale from a list of three colors. The left color is green, the right is brown and the mid color is a low saturated yellow:

In [7]:
elevation =['#32924c',  '#d7df84', '#91511e']

In [8]:
elev_cmap, elev_cs = colorscale_from_list(elevation, 'elev_cmap')


The elev_cs colorscale, appropriate for elevation data, is explicitly defined by the following list of lists:

In [9]:
elev_cs=[[0.0, '#32924c'],
[0.1, '#52a157'],
[0.2, '#74b162'],
[0.3, '#94c06d'],
[0.4, '#b6d079'],
[0.5, '#d7de84'],
[0.6, '#c9c370'],
[0.7, '#bba65b'],
[0.9, '#9f6d32'],
[1.0, '#91511e']]


Mount Bruno plotted with this colorscale:

From a list of red, low saturated white-yellow and green color we define a diverging colormap and colorscale, that are appropriate for visualizing financial data (see for example here).

In [10]:
redgreen=['#df0101', '#f5f6ce','#31b404']
fin_cmap, fin_cs = colorscale_from_list(redgreen, 'fin_cmap')


The resulted financial-type colorscale is represented by the following list:

In [11]:
fin_cs=[[0.0, u'#df0101'],
[0.1, u'#e33129'],
[0.2, u'#e86353'],
[0.3, u'#ec937b'],
[0.4, u'#f1c5a5'],
[0.5, u'#f4f6cd'],
[0.6, u'#cee9a6'],
[0.7, u'#a6db7c'],
[0.8, u'#7fce55'],
[0.9, u'#57c12c'],
[1.0, u'#31b404']]


Seaborn provides a function for defining custom diverging matplotlib colormaps, that can be transformed in Plotly colorscales:

In [12]:
import seaborn as sns
sns.set(style="white")

In [13]:
sns_cmap = sns.diverging_palette(220, 10, as_cmap=True)
display_cmap(sns_cmap)


The corresponding Plotly colorscale:

In [14]:
sns_cs=colormap_to_colorscale(sns_cmap)
sns_cs

Out[14]:
[[0.0, u'#3f7f93'],
[0.1, u'#6397a7'],
[0.2, u'#88b1bd'],
[0.30000000000000004, u'#acc9d2'],
[0.4, u'#d1e2e7'],
[0.5, u'#f2f2f2'],
[0.6000000000000001, u'#f6cdd0'],
[0.8, u'#e8848b'],
[0.9, u'#e15e68'],
[1.0, u'#da3b46']]

### Asymmetric diverging colorscales adapted to data¶

There are data sets that are asymmetric with respect to a reference value, and it is also of interest to visualize them with a diverging color scale, in order to point out to what extent they exceed the reference value, respectively are under this value.

For example we could be interested in the temperature recorded in an area, each month over many years, that exceeds or is below to 32 Fahrenheit degrees (or 0 Celsius degree).

The above defined elev_cs (elevation) colorscale is destinated for plotting surfaces or contour plots of geographic terrain elevation. A mountain can be green up to some height (reference point) and above it it is brown (no vegetation there).

Symmetric diverging colormaps and colorscales are not appropriate for visualizing such data because they map the mid value of the data range to the color with highest luminance or in this case we are interested in mapping the reference point to that color.

In the following we give a method to associate an asymmetric diverging colorscale to an asymmetric data range with respect to a reference point. Such a colorscale has the maximum luminance at the normalized reference point, and the luminance is decreasing with the same speed toward ends, as in the images inserted in the next cells:

In [15]:
from IPython.display import Image

In [9]:
Image(filename='Data/asym_colorsc1.jpg')

Out[9]:
In [10]:
Image(filename='Data/asym_colorsc2.jpg')

Out[10]:

Given data of range [dmin, dmax], the reference point refp, with dmin<refp<dmax, and a symmetric diverging matplotlib colormap, div_cmap, we define an asymmetric diverging colorscale adapted to this data set.

We discuss the case refp-dmin < dmax-refp. The opposite case can be easily deduced from this one.

Theoretically, the values in the symmetric interval [refp-(dmax-refp), dmax] are normalized and mapped to colors in the chosen symmetric diverging colormap, div_cmap. Then we clip this colormap keeping the colors corresponding to normalized values of the interval [dmin, dmax].

We explain the practical procedure referring to the image below:

In [1]:
from IPython.display import SVG
SVG(filename='Data/asymdiv.svg')

Out[1]:

s is the normalized value of dmin, and repn of the reference point refp.

Starting from repn we divide the interval (s, refpn], respectively (refpn, 1.0), by equally spaced points, with the step size set by default to 0.05. Finally we add the ends, s and 1.0, to the resulted grid. Denote by $T[j]$ a point in this grid.

These grid points are normalized by the linear map $[s, 1]\mapsto [0,1]$.

If T_norm[j]$\in[0,1]$ are their normalized values, then we define a colorscale from the list of lists

[T_norm[j], div_cmap(T[j])], j=0, $\cdots$.

These ideas are implemented below:

In [16]:
def normalize(x,a,b): #maps  the interval [a,b]  to [0,1]
if a>=b:
raise ValueError('(a,b) is not an interval')
return float(x-a)/(b-a)

In [17]:
def asymmetric_colorscale(data,  div_cmap, ref_point=0.0, step=0.05):
#data: data can be a DataFrame, list of equal length lists, np.array, np.ma.array
#div_cmap is the symmetric diverging matplotlib or custom colormap
#ref_point:  reference point
#step:  is step size for t in [0,1] to evaluate the colormap at t

if isinstance(data, pd.DataFrame):
D = data.values
D=np.ma.copy(data)
else:
D=np.asarray(data, dtype=np.float)

dmin=np.nanmin(D)
dmax=np.nanmax(D)
if not (dmin < ref_point < dmax):
raise ValueError('data are not appropriate for a diverging colormap')

if dmax+dmin > 2.0*ref_point:
left=2*ref_point-dmax
right=dmax

s=normalize(dmin, left,right)
refp_norm=normalize(ref_point, left, right)# normalize reference point

T=np.arange(refp_norm, s, -step).tolist()+[s]
T=T[::-1]+np.arange(refp_norm+step, 1, step).tolist()

else:
left=dmin
right=2*ref_point-dmin

s=normalize(dmax, left,right)
refp_norm=normalize(ref_point, left, right)

T=np.arange(refp_norm, 0, -step).tolist()+[0]
T=T[::-1]+np.arange(refp_norm+step, s, step).tolist()+[s]

L=len(T)
T_norm=[normalize(T[k],T[0],T[-1]) for k in range(L)] #normalize T values
return [[T_norm[k], colors.rgb2hex(div_cmap(T[k]))] for k in range(L)]



### Examples¶

a) A heatmap associated to data related to Exchange Traded Funds (ETFs)

Read data from an Excel file:

In [18]:
xl = pd.ExcelFile("Data/ETF-Data.xls")
df = xl.parse("Sheet1")

Out[18]:
Country/ETF-Ticker Aug-09 Sept-09 Change
0 Australia, EWA -0.65% -0.18% 0.47%
1 Austria, EWO 1.99% 0.99% -1.00%
2 Belgium, EWK 0.76% 0.13% -0.63%
3 Brazil, EWZ 1.58% 1.22% -0.36%
4 Canada, EWC 0.88% -0.36% -1.23%
• Define a new Dataframe from the last three columns of df, remove the character '%', and convert strings to float:
In [19]:
df1=df[[ u'Aug-09', u'Sept-09', u' Change']]
tab=df1.values.tolist()
tab=np.array([[float(s.replace('%','')) for s in item] for item in tab])


Our data are asymmetric with respect to $0$, because the min and max values are as follows:

In [20]:
print np.min(tab), np.max(tab)

-22.05 4.57

• Define an asymmetric diverging colorscale associated to our data, with the reference point 0, and the symmetric diverging matplotlib colormap, fin_cmap, defined above:
In [21]:
fin_asymm_cs= asymmetric_colorscale(tab,  fin_cmap, ref_point=0.0, step=0.05)

• Plot the data (tab) Heatmap with the new defined colorscale:
In [22]:
import plotly.plotly as py
from plotly.graph_objs import *

In [23]:
X=['Aug-09', 'Sept-09', 'Change']
Y=list(df[u'Country/ETF-Ticker'])

In [33]:
trace =Heatmap(
z=tab,
x=X,
y=Y,
colorscale=fin_asymm_cs,
colorbar=dict(thickness=20, tickvals=[-20+k*5 for k in range(5)], ticklen=4)
)

width = 400
height =900

layout = Layout(
title='ETFs Data',
font=Font(
family='Balto, sans-serif',
size=12,
color='rgb(68,68,68)'
),
showlegend=False,
xaxis=XAxis(
title='',
showgrid=True,
side='top',
tickangle=45
),
yaxis=YAxis(
title='',
autorange='reversed',
showgrid=True,
autotick=False,
dtick=1
),
autosize=False,
height=height,
width=width,
margin=Margin(
l=135,
r=40,
b=85,
t=170
)
)

fig=Figure(data=Data([trace]), layout=layout)

annotations = Annotations()
alist=list(tab)
for i, row in enumerate(alist):
for j, val in enumerate(row):
annotations.append(
Annotation(
text=str(val)+'%',
x=X[j], y=Y[i],
xref='x1', yref='y1',
font=dict(color= 'rgb(25,25,25)'),
showarrow=False))
fig['layout'].update(annotations=annotations)

In [34]:
import plotly
plotly.offline.init_notebook_mode()