This is a plotting library for use with matplotlib to make ternary plots plots in the two dimensional simplex projected onto a two dimensional plane.
The library provides functions for plotting projected lines, curves (trajectories), scatter plots, and heatmaps. There are several examples and a short tutorial below.
From Genetic Drift and Selection in Many-Allele Range Expansions:
See the citations below for more example images.
Have you used python-ternary in a publication? Open a PR or issue to include your citations or example plots!
- Genetic Drift and Selection in Many-Allele Range Expansions by Bryan T. Weinstein, Maxim O. Lavrentovich, Wolfram Möbius, Andrew W. Murray, and David R. Nelson (2017)
- Gibbs Sampler-Based λ-Dynamics and Rao–Blackwell Estimator for Alchemical Free Energy Calculation by Xinqiang Ding, Jonah Z. Vilseck, Ryan L. Hayes, and Charles L. Brooks (2017)
- PREDICTD: PaRallel Epigenomics Data Imputation With Cloud-based Tensor Decomposition by Timothy J Durham, Maxwell W Libbrecht, Jeffry Howbert, Jeffrey Bilmes, William S Noble (2017)
- Kottke, Daniel, et al. Multi-class probabilistic active learning Proc. of the 22nd Europ. Conf. on Artificial Intelligence (ECAI2016). 2016.
- On the origins of three-dimensionality in drug-like molecules by Joshua Meyers, Michael Carter, N Yi Mok, and Nathan Brown (2016)
- Stationary Stability for Evolutionary Dynamics in Finite Populations by Marc Harper and Dashiell Fryer. Entropy 18.9 (2016): 316.
- pyIAST: Ideal adsorbed solution theory (IAST) Python package by Cory Simon (2016)
- Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex by Marc Harper and Dashiell Fryer. Dynamic Games and Applications (2015)
You can install python-ternary with conda:
conda config --add channels conda-forge
conda install python-ternarySee here for more information.
You can install the current release (1.0.1) with pip (you may need to use sudo):
pip install python-ternaryAlternatively you can clone the repository and run setup.py in the usual manner:
git clone git@github.com:marcharper/python-ternary.git
cd python-ternary
sudo python setup.py installThe master branch is kept in a good working state and should be fine for general usage.
You can explore some of these examples with this Jupyter notebook.
The easiest way to use python-ternary is with the wrapper class TernaryAxesSubplot,
which mimics Matplotlib's AxesSubplot. Start with:
figure, tax = ternary.figure()With a ternary axes object tax you can use many of the usual matplotlib
axes object functions:
tax.set_title("Scatter Plot", fontsize=20)
tax.scatter(points, marker='s', color='red', label="Red Squares")
tax.legend()Most drawing functions can take standard matplotlib keyword arguments such as linestyle and linewidth. You can use LaTeX in titles and labels.
If you need to act directly on the underyling matplotlib axes, you can access them:
ax = tax.get_axes()You can also wrap an existing Matplotlib AxesSubplot object:
figure, ax = pyplot.subplots()
tax = ternary.TernaryAxesSubplot(ax=ax)
This is useful if you want to use ternary as a part of another figure, such as
from matplotlib import pyplot, gridspec
pyplot.figure()
gs = gridspec.GridSpec(2,2)
ax = pyplot.subplot(gs[0,0])
figure, tax = ternary.figure(ax=ax)
...Some ternary functions expect the simplex to be partititioned into some number of steps,
determined by the scale parameter. A few functions will do this partitioning automatically
for you, but when working with real data or simulation output, you may have partitioned
already. If you are working with probability distributions, just use scale=1 (the default).
Otherwise the scale parameter effectively controls the resolution of many plot types (e.g. heatmaps).
TernaryAxesSubplot objects keep track of the scale, axes, and other parameters,
supplying them as needed to other functions.
The following code draws a boundary for the simplex and gridlines.
import ternary
## Boundary and Gridlines
scale = 40
figure, tax = ternary.figure(scale=scale)
# Draw Boundary and Gridlines
tax.boundary(linewidth=2.0)
tax.gridlines(color="black", multiple=5)
tax.gridlines(color="blue", multiple=1, linewidth=0.5)
# Set Axis labels and Title
fontsize = 20
tax.set_title("Simplex Boundary and Gridlines", fontsize=fontsize)
tax.left_axis_label("Left label $\\alpha^2$", fontsize=fontsize)
tax.right_axis_label("Right label $\\beta^2$", fontsize=fontsize)
tax.bottom_axis_label("Bottom label $\\Gamma - \\Omega$", fontsize=fontsize)
# Set ticks
tax.ticks(axis='lbr', linewidth=1)
# Remove default Matplotlib Axes
tax.clear_matplotlib_ticks()
ternary.plt.show()
You can draw individual lines between any two points with line and lines parallel to the axes with horizonal_line, left_parallel_line, and right_parallel_line:
import ternary
scale = 40
figure, tax = ternary.figure(scale=scale)
# Draw Boundary and Gridlines
tax.boundary(linewidth=2.0)
tax.gridlines(color="blue", multiple=5)
# Set Axis labels and Title
fontsize = 20
tax.set_title("Various Lines", fontsize=20)
tax.left_axis_label("Left label $\\alpha^2$", fontsize=fontsize)
tax.right_axis_label("Right label $\\beta^2$", fontsize=fontsize)
tax.bottom_axis_label("Bottom label $\\Gamma - \\Omega$", fontsize=fontsize)
# Draw lines parallel to the axes
tax.horizontal_line(16)
tax.left_parallel_line(10, linewidth=2., color='red', linestyle="--")
tax.right_parallel_line(20, linewidth=3., color='blue')
# Draw an arbitrary line, ternary will project the points for you
p1 = (12,8,10)
p2 = (2, 26, 2)
tax.line(p1, p2, linewidth=3., marker='s', color='green', linestyle=":")
tax.ticks(axis='lbr', multiple=5, linewidth=1)
tax.show()The line drawing functions accept the matplotlib keyword arguments of Line2D.
Curves can be plotted by specifying the points of the curve, just like matplotlib's plot. Simply use:
ternary.plot(points)
Points is a list of tuples or numpy arrays, such as [(0.5, 0.25, 0.25), (1./3, 1./3, 1./3)],
import ternary
## Sample trajectory plot
figure, tax = ternary.figure(scale=1.0)
tax.boundary()
tax.gridlines(multiple=0.2, color="black")
tax.set_title("Plotting of sample trajectory data", fontsize=20)
points = []
# Load some data, tuples (x,y,z)
with open("sample_data/curve.txt") as handle:
for line in handle:
points.append(list(map(float, line.split(' '))))
# Plot the data
tax.plot(points, linewidth=2.0, label="Curve")
tax.legend()
tax.show()
There are many more examples in this paper.
You can also color the curves with a Matplotlib heatmap using:
plot_colored_trajectory(points, cmap="hsv", linewidth=2.0)
Similarly, ternary can make scatter plots:
import ternary
### Scatter Plot
scale = 40
figure, tax = ternary.figure(scale=scale)
tax.set_title("Scatter Plot", fontsize=20)
tax.boundary(linewidth=2.0)
tax.gridlines(multiple=5, color="blue")
# Plot a few different styles with a legend
points = random_points(30, scale=scale)
tax.scatter(points, marker='s', color='red', label="Red Squares")
points = random_points(30, scale=scale)
tax.scatter(points, marker='D', color='green', label="Green Diamonds")
tax.legend()
tax.ticks(axis='lbr', linewidth=1, multiple=5)
tax.show()
Ternary can plot heatmaps in two ways and three styles. Given a function, ternary will evaluate the function at the specified number of steps (determined by the scale, expected to be an integer in this case). The simplex can be split up into triangles or hexagons and colored according to one of three styles:
- Triangular --
triangular: coloring triangles by summing the values on the vertices - Dual-triangular --
dual-triangular: mapping (i,j,k) to the upright triangles △ and blending the neigboring triangles for the downward triangles ▽ - Hexagonal --
hexagonal: which does not blend values at all, and divides the simplex up into hexagonal regions
The two triangular heatmap styles and the hexagonal heatmap style can be visualized as follows: left is triangular, right is dual triangular.
Thanks to chebee7i for the above images.
Let's define a function on the simplex for illustration, the Shannon entropy of a probability distribution:
def shannon_entropy(p):
"""Computes the Shannon Entropy at a distribution in the simplex."""
s = 0.
for i in range(len(p)):
try:
s += p[i] * math.log(p[i])
except ValueError:
continue
return -1.*sWe can get a heatmap of this function as follows:
import ternary
scale = 60
figure, tax = ternary.figure(scale=scale)
tax.heatmapf(shannon_entropy, boundary=True, style="triangular")
tax.boundary(linewidth=2.0)
tax.set_title("Shannon Entropy Heatmap")
tax.show()In this case the keyword argument boundary indicates whether you wish to evaluate points on the boundary of the partition (which is sometimes undesirable). Specify style="hexagonal" for hexagons. Large scalings can use a lot of RAM since the number of polygons rendered is O(n^2).
You may specify a matplotlib colormap (an instance or the colormap name) in the cmap argument.
Ternary can also make heatmaps from data. In this case you need to supply a dictionary
mapping (i, j) or (i, j, k) for i + j + k = scale to a float as input for a heatmap. It is not necessary to include k in the dictionary keys since it can be determined from scale, i, and j. This reduces the memory requirements when the partition is very fine (significant when scale is in the hundreds).
Make the heatmap as follows:
ternary.heatmap(data, scale, ax=None, cmap=None)or on a TernaryAxesSubplot object:
tax.heatmap(data, cmap=None)This can produces images such as:
There is a large set of heatmap examples here.
For a given ternary plot there are two valid ways to label the axes ticks
corresponding to the clockwise and counterclockwise orientations. However note
that the axes labels need to be adjusted accordingly, and ternary does not
do so automatically when you pass clockwise=True to tax.ticks().
There is a more detailed discussion on issue #18 (closed).
You can alternatively specify colors as rgba tuples (r,g,b,a) (all between zero and one).
To use this feature, pass colormap=False to heatmap() so that the library will not attempt
to map the tuple to a value with a matplotlib colormap. Note that this disables the
inclusion of a colorbar. Here is an example:
import math
from matplotlib import pyplot
import ternary
def color_point(x, y, z, scale):
w = 255
x_color = x * w / float(scale)
y_color = y * w / float(scale)
z_color = z * w / float(scale)
r = math.fabs(w - y_color) / w
g = math.fabs(w - x_color) / w
b = math.fabs(w - z_color) / w
return (r, g, b, 1.)
def generate_heatmap_data(scale=5):
from ternary.helpers import simplex_iterator
d = dict()
for (i, j, k) in simplex_iterator(scale):
d[(i, j, k)] = color_point(i, j, k, scale)
return d
scale = 80
data = generate_heatmap_data(scale)
figure, tax = ternary.figure(scale=scale, permutation="210")
tax.heatmap(data, style="hexagonal", colormap=False) # Allow colors as rgba tuples
tax.boundary()
tax.set_title("RGBA Heatmap")
pyplot.show()This produces the following image:
You can run the test suite as follows:
python -m unittest discover testsThe included script of examples is intended to act as a series of extended tests.
Contributions are welcome! Please share any nice example plots, contribute features, and add unit tests! Use the pull request and issue systems to contribute.
Please cite as follows:
Marc Harper et al. (2015). python-ternary: Ternary Plots in Python. Zenodo. 10.5281/zenodo.34938
- Marc Harper marcharper
- Bryan Weinstein btweinstein: Hexagonal heatmaps, colored trajectory plots
- chebee7i: Docs and figures, triangular heatmapping
- Cory Simon: Axis Colors, colored heatmap example
There appears to be an issue with anaconda on macs that causes the axes labels not to render. The workaround is to manually call
tax._redraw_labels()
before showing or rendering the image.