Ternary Plotting in Python

Let's explore some basic functionality and examples of the ternary library, available at Github.



In [1]:

    
%matplotlib inline

import ternary

print("Version", ternary.__version__)









    



Version 1.0.6



In [2]:

    
# Make images higher resolution and set default size
import matplotlib
matplotlib.rcParams['figure.dpi'] = 200
matplotlib.rcParams['figure.figsize'] = (4, 4)

The ternary library wraps its plotting functions are matplotlib. You can ask ternary for a plotting axes object or wrap an existing matplotlib axes. Our first example draws a ternary boundary and some inner grid lines, as well as some labels (you can use LaTeX just like in matplotlib).

You can use offset parameters to adjust the distances of the axes ticks and labels, which is useful for labels that have unusual symbols or if you otherwise modify the default style significantly.



In [3]:

    
## Boundary and Gridlines
scale = 30
figure, tax = ternary.figure(scale=scale)
# figure.set_size_inches(6, 6)

# Draw Boundary and Gridlines
tax.boundary(linewidth=1.5)
tax.gridlines(color="black", multiple=6)
tax.gridlines(color="blue", multiple=2, linewidth=0.5)

# Set Axis labels and Title
fontsize = 12
tax.set_title("Simplex Boundary and Gridlines\n", fontsize=fontsize)
tax.left_axis_label("Left label $\\alpha^2$", fontsize=fontsize, offset=0.14)
tax.right_axis_label("Right label $\\beta^2$", fontsize=fontsize, offset=0.14)
tax.bottom_axis_label("Bottom label $\\Gamma - \\Omega$", fontsize=fontsize, offset=0.14)

# Set ticks
tax.ticks(axis='lbr', linewidth=1, multiple=5, offset=0.03)

# Remove default Matplotlib Axes
tax.clear_matplotlib_ticks()
tax.get_axes().axis('off')

ternary.plt.show()

Ternary provides functions to plot points and lines, and will do all the necessary projecting for you.



In [4]:

    
import ternary

scale = 40
figure, tax = ternary.figure(scale=scale)
# figure.set_size_inches(10, 10)

# Draw Boundary and Gridlines
tax.boundary(linewidth=2.0)
tax.gridlines(color="blue", multiple=5)

# Set Axis labels and Title
fontsize = 12
offset = 0.14
tax.set_title("Various Lines\n", fontsize=fontsize)
tax.right_corner_label("X", fontsize=fontsize)
tax.top_corner_label("Y", fontsize=fontsize)
tax.left_corner_label("Z", fontsize=fontsize)
tax.left_axis_label("Left label $\\alpha^2$", fontsize=fontsize, offset=offset)
tax.right_axis_label("Right label $\\beta^2$", fontsize=fontsize, offset=offset)
tax.bottom_axis_label("Bottom label $\\Gamma - \\Omega$", fontsize=fontsize, offset=offset)

# 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 = (22, 8, 10)
p2 = (2, 22, 16)
tax.line(p1, p2, linewidth=3., marker='s', color='green', linestyle=":")

tax.ticks(axis='lbr', multiple=5, linewidth=1, offset=0.025)
tax.get_axes().axis('off')
tax.clear_matplotlib_ticks()

tax.show()

You can also plot curves and make scatter plots (ternary will project each point).



In [5]:

    
## Sample trajectory plot
figure, tax = ternary.figure(scale=1.0)
figure.set_size_inches(5, 5)

tax.boundary()
tax.gridlines(multiple=0.2, color="black")
tax.set_title("Plotting of sample trajectory data", fontsize=10)
# Load some data, tuples (x,y,z)
points = []
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.ticks(axis='lbr', multiple=0.2, linewidth=1, tick_formats="%.1f", offset=0.02)

tax.get_axes().axis('off')
tax.clear_matplotlib_ticks()
tax.legend()
tax.show()



In [6]:

    
# Using same points as above

fig, tax = ternary.figure(scale=1.0)
fig.set_size_inches(10, 10)

tax.plot_colored_trajectory(points, linewidth=2.0)

## Shuffle points for additional plot
points = [(y, z, x) for (x, y, z) in points]
tax.plot_colored_trajectory(points, cmap="hsv", linewidth=2.0)

tax.get_axes().axis('off')
tax.clear_matplotlib_ticks()
tax.ticks(axis='lbr', linewidth=1, multiple=0.1, tick_formats="%.1f")
tax.boundary()
tax.set_title("Plotting of sample trajectory data", fontsize=20)
tax.gridlines(multiple=0.2, color="black")
tax.show()



In [7]:

    
## Generate Data
import random

def random_points(num_points=25, scale=40):
    points = []
    for i in range(num_points):
        x = random.randint(1, scale)
        y = random.randint(0, scale - x)
        z = scale - x - y
        points.append((x,y,z))
    return points

# Scatter Plot
scale = 40
figure, tax = ternary.figure(scale=scale)
figure.set_size_inches(10, 10)
# 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.set_title("Scatter Plot", fontsize=20)
tax.boundary(linewidth=2.0)
tax.gridlines(multiple=5, color="blue")
tax.ticks(axis='lbr', linewidth=1, multiple=5)
tax.clear_matplotlib_ticks()
tax.get_axes().axis('off')

tax.show()

Heatmaps

Ternary's most unique feature are its heatmaps, which come in a variety of modes and styles. In the following example, a function is plotted as a heatmap by evaluating on a triangulation of the simplex.



In [8]:

    
import math

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

import ternary
scale = 60

figure, tax = ternary.figure(scale=scale)
figure.set_size_inches(10, 8)
tax.heatmapf(shannon_entropy, boundary=True, style="triangular")
tax.boundary(linewidth=2.0)
tax.set_title("Shannon Entropy Heatmap")
tax.ticks(axis='lbr', linewidth=1, multiple=5)
tax.clear_matplotlib_ticks()
tax.show()

You can also make heatmaps of data by specifying the color of each subtriangle or hexagon.



In [9]:

    
def generate_random_heatmap_data(scale=5):
    from ternary.helpers import simplex_iterator
    d = dict()
    for (i,j,k) in simplex_iterator(scale):
        d[(i,j)] = random.random()
    return d

scale = 20
d = generate_random_heatmap_data(scale)
figure, tax = ternary.figure(scale=scale)
tax.heatmap(d, style="h")
tax.boundary()
tax.set_title("Heatmap Test: Hexagonal")



In [10]:

    
import matplotlib.pyplot as plt

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, colorbar=False)
# Remove default Matplotlib Axes
tax.clear_matplotlib_ticks()
tax.get_axes().axis('off')
tax.boundary()
tax.set_title("RGBA Heatmap")
plt.show()



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