How to make a ternary contour plot with Python Plotly?

Question

I am trying to plot a function defined on a simplex. Apparently, you can do it very nicely using the Matlab API.

enter image description here

But I cannot figure out how to do this using the Python API. The reference has a section named Ternary Contour Plots in Python but it does not plot a numeric function, but a function mapping the simplex to a given discrete set.

I tried to emulate the Matlab code:

import plotly as py
A = [0, .2, .2, .2, 0, .6, .75, .9, 0, 1, .8, .3]
B = [1, .2, .4, .1, 0, .4, .05, 0, .8, 0, .05, .3]
C = [0, .6, .4, .7, 1, 0, .2, .1, .2, 0, .15, .4]
Z = [.1, .5, .1, .2, 1, .8, .4, 0, .1, .6, 1, .7]
trace = {
 "type": 'scatterternary',
 "carpet": 'scattercontour',
 "a": A,
 "b": B,
 "c": C,
 "z": Z
}
layout = {
 'title': 'Simple Ternary Contour Plot with Python'
}
figure = dict(data=[trace], layout=layout)
py.offline.plot(figure, validate=False)

But I get this plot instead:

enter image description here

Answer 1

If someone is still interested, here is a Jupyter Notebook to see how to generate a Plotly ternary contour plot.

Answer 2

One workaround is possible if you can generate the data whose contours you want to plot for arbitrary proportions. In this case, you can generate the (x, y) data on a mesh, map them to barycentric coordinates, and compute the value z. Then you can use the non-ternary plots like contour or surface.

Here is an example that plots the density function of the Dirichlet distribution:

import plotly as py
import plotly.graph_objs as go
import numpy as np
def compute_in_barycentric_coordinates(a, b, c):
 epsilon = 1e-6
 if 0.0 < a < 1.0 and 0.0 < b < 1.0 and 0.0 < c < 1.0 and abs(a + b + c - 1.0) < epsilon:
 return pow(a, 2) * pow(b, 1.5) * pow(c, 1.8)
 return None
x_data = np.linspace(0, 1, 101)
y_data = np.linspace(0, 1, 101)
z_data = []
f = 1.0 / pow(3.0, 0.5)
for y in y_data:
 next_slice = []
 for x in x_data:
 a = 1 - x - f*y
 b = x - f*y
 c = 2*f*y
 z = compute_in_barycentric_coordinates(a, b, c)
 next_slice.append(z)
 z_data.append(next_slice)
data = [
 go.Contour(
 x=x_data,
 y=y_data,
 z=z_data,
 )
]
py.offline.plot(data)

enter image description here

However, it is still a workaround, so if you have a better idea, I will be very happy to hear from you.