## Pascal Triangle¶

In this IPython Notebook we insert a truncated Pascal triangle, with base containing $n$ elements (n an odd integer), in a masked numpy array and plot it as a Plotly Heatmap.

In [1]:
import numpy as np

In [4]:
def Pascal_array(n):# insert the Pascal triangle in a numpy array (m,n)
if not n%2:
raise ValueError('n must be an odd integer')
m=(n-1)/2+1
T=np.zeros((m,n), int)
c=m-1
T[0][c]=1
T[1][c-1]=T[1][c+1]=1

for i in range(2, m-1):
for j in range(c-i, c+i+1):
T[i][j]=T[i-1][j-1]+T[i-1][j+1]
i=m-1
T[i][0]=T[i][n-1]=1

for j in range(2, n-2):
T[i][j]=T[i-1][j-1]+T[i-1][j+1]
return T

In [5]:
T=Pascal_array(21)
n=T.shape[1]

In [6]:
Ttext=[]
m=T.shape[0]
for k in range(m):
Ttext.append(['' if item==0 else str(item) for item in T[k]])# convert values to strings in order to annotate the heatmap cells


In [7]:
T= np.ma.masked_equal(T, 0)

In [8]:
X=range(n)
Y=range(m)


The colorscale to plot the Pascal triangle as a heatmap is defined as:

In [10]:
colorsc=[[0.0, 'rgb(77.400000000000006, 58.0, 57.800000000000004)'],
[0.33333333, 'rgb(164.19999999999996, 105.99999999999999, 105.40000000000001)'],
[0.66666, 'rgb(207.59999999999999, 130.0, 129.20000000000002)'],
[1.0, 'rgb(251.0, 154.0, 153.0)']]

In [19]:
import plotly.plotly as py
from plotly.graph_objs import *

axisx=dict(showgrid=False,
zeroline=False,
showline=False,
ticks='',
showticklabels=False)
dy=dict(autorange='reversed')

data = Data([
Heatmap(
z=T,
colorscale=colorsc,
reversescale=True,
connectgaps=False,
)
])
layout = Layout(
title="Pascal Triangle",
showlegend=False,
autosize=True,
width=800,
height=450,
xaxis=XAxis(axisx),
yaxis=YAxis(dict(axisx, **dy)),# concatenate the two dicts

margin=Margin(
l=40,
r=20,
b=30,
t=60,

),
)

fig = Figure(data=data, layout=layout)
annotations = Annotations([
Annotation(
showarrow=False,
text="Pascal triangle: <a href='https://en.wikipedia.org/wiki/Pascal%27s_triangle'> [1]</a>",
xref='paper',
yref='paper',
x=0,
y=-0.09,
xanchor='left',
yanchor='bottom',
font=Font(
size=0 )
)
])

#Insert  text from Ttext in the corresponding cells
for i, row in enumerate(Ttext):
for j, s in enumerate(row):
annotations.append(
Annotation(
text=s,
x=X[j], y=Y[i],
xref='x1', yref='y1',
font=dict(color='white' if T[i][j]>35 else 'rgb(25,25,25)'),
showarrow=False)
)

fig['layout'].update(
annotations=annotations
)
py.sign_in('empet', 'my_api_key')
py.iplot(fig, filename='Pascal-triangle', width=1000)

Out[19]:
In [20]:
from IPython.core.display import HTML
def  css_styling():