The library provides functions for plotting projected lines, curves (trajectories), scatter plots, and heatmaps. There are several examples and a short tutorial below.
Last image from: Genetic Drift and Selection in Many-Allele Range Expansions.
See the citations below for more example images.
Citations and Recent Usage in Publications
Have you used python-ternary in a publication? Open a PR or issue to include your citations or example plots!
You can install python-ternary with conda:
conda config --add channels conda-forge conda install python-ternary
See here for more information.
You can install the current release (1.0.4) with pip (you may need to use sudo):
pip install python-ternary
Alternatively you can clone the repository and run
setup.py in the usual manner:
git clone firstname.lastname@example.org:marcharper/python-ternary.git cd python-ternary sudo python setup.py install
The master branch is kept in a good working state and should be fine for general usage.
Usage, Examples, Plotting Functions
You can explore some of these examples with this Jupyter notebook.
The easiest way to use python-ternary is with the wrapper class
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.
Simplex Boundary and Gridlines
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
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:
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.*s
We 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
(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
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
This can produces images such as:
Axes Ticks and Orientations
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
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
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 as plt 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) tax.heatmap(data, style="hexagonal", use_rgba=True) tax.boundary() tax.set_title("RGBA Heatmap") plt.show()
This produces the following image:
You can run the test suite as follows:
python -m unittest discover tests
The 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.
- 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
before showing or rendering the image.