2015-10-14: There has been an increase in traffic lately! Please feel free to add issues for desired features, and of course, contributions are welcome!
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.
Most 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 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).
To install 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 installNew features are still being added to python-ternary. A stable release is upcoming.
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 a Matplotlib AxesSubplot object:
figure, ax = pyplot.subplots()
tax = ternary.TernaryAxesSubplot(ax=ax)
This is useful if you want to use ternary as 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)
...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.
from matplotlib import pyplot
import ternary
## Boundary and Gridlines
scale = 40
figure, tax = ternary.figure(scale=scale)
# Draw Boundary and Gridlines
tax.boundary(color="black", linewidth=2.0)
tax.gridlines(color="blue", multiple=5) # Every 5th gridline, can be a float
# 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', color="black", linewidth=1)
# Remove default Matplotlib Axes
tax.clear_matplotlib_ticks()
pyplot.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(color="black", 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', color="black", 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(color='black')
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(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(color="black", 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', color="black", linewidth=1, multiple=0.1)
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 heaxagonal regions
The two triangular heatmap styles and the hexagonal heatmap style can be visualized as follows. The dual-triangular style plots the true values on the upright triangles, mapping ternary coordinates to upright triangles otherwise. The triangular style
maps ternary coordinates to vertices and computes the triangle color based on the
values at the vertices.
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.
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
if __name__ == "__main__":
## Heatmaps from data
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(color='black')
tax.set_title("Hexagonal Heatmap from Data")
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, Python-ternary: A python library for ternary plots, 2011-2015, available at: https://github.com/marcharper/python-ternary
- Marc Harper marcharper
- Bryan Weinstein btweinstein: Hexagonal heatmaps, colored trajectory plots
- chebee7i: Docs and figures, triangular heatmapping