Introduction to rose diagrams¶

Rose diagrams are useful when comparing a large amount of slopes.

For documentation of the different methods available for the custom rose axes see the SIMPLE documentation.

In [1]:

import matplotlib.pyplot as plt
import numpy as np
import simple

# Generate some random data
rng = np.random.default_rng(seed=46)
n = 10000

x1, y1 = rng.normal(0, 1, n), rng.normal(0, 1, n) # Completely random data
x2, y2 = rng.normal(0, 0.25, n)+1, rng.normal(0, 0.25, n)+2 # random data with a mean slope of 2
x3 = rng.normal(-0.3, 0.6, n); y3 = rng.normal(-2, 0.5, n) * x3

import matplotlib.pyplot as plt import numpy as np import simple # Generate some random data rng = np.random.default_rng(seed=46) n = 10000 x1, y1 = rng.normal(0, 1, n), rng.normal(0, 1, n) # Completely random data x2, y2 = rng.normal(0, 0.25, n)+1, rng.normal(0, 0.25, n)+2 # random data with a mean slope of 2 x3 = rng.normal(-0.3, 0.6, n); y3 = rng.normal(-2, 0.5, n) * x3

Plotting slopes¶

Example where we plot some randomly generated data.

Notice that the normal distribution of Three is distorted. This is because the bin width, in regards to the value of the slope, is bigger towards the vertical (m=infinity) and smaller towards the horizontal (m=0).

In [2]:

# Creates a figure with 2 rectilinear subplots
fig, ax = plt.subplots(1, 2, figsize=(14, 6))

ax[0].scatter(x1, y1, s=1, label='One')
ax[0].scatter(x2, y2, s=1, label='Two')
ax[0].scatter(x3, y3, s=1, label='Three')

ax[0].axline((0,0), slope=2, color='black')
ax[0].axline((0,0), slope=-2, color='black')
ax[0].axline((0,0), slope=-3, color='black', linestyle='--', alpha=0.5)
ax[0].axline((0,0), slope=-1, color='black', linestyle='--', alpha=0.5)

ax[0].set(xlim=(-5, 5), ylim=(-5, 5))
ax[0].legend()
ax[0].grid()

# Replaces the second subplot with a rose plot
ax[1] = simple.create_rose_plot(ax[1])

ax[1].mhist((x1, y1), r=1, label='One', label_kwargs={'color':'white'})
ax[1].mhist((x2, y2), r=2, label='Two')
ax[1].mhist((x3, y3), r=3, label='Three')

ax[1].mline(2, r=3, color='orange', label='Two')
ax[1].axmline(-2, merr=-1, color='green', label='Three')
ax[1].merrorbar(-2, r=4, merr=1, color='green')
ax[1].legend();

# Creates a figure with 2 rectilinear subplots fig, ax = plt.subplots(1, 2, figsize=(14, 6)) ax[0].scatter(x1, y1, s=1, label='One') ax[0].scatter(x2, y2, s=1, label='Two') ax[0].scatter(x3, y3, s=1, label='Three') ax[0].axline((0,0), slope=2, color='black') ax[0].axline((0,0), slope=-2, color='black') ax[0].axline((0,0), slope=-3, color='black', linestyle='--', alpha=0.5) ax[0].axline((0,0), slope=-1, color='black', linestyle='--', alpha=0.5) ax[0].set(xlim=(-5, 5), ylim=(-5, 5)) ax[0].legend() ax[0].grid() # Replaces the second subplot with a rose plot ax[1] = simple.create_rose_plot(ax[1]) ax[1].mhist((x1, y1), r=1, label='One', label_kwargs={'color':'white'}) ax[1].mhist((x2, y2), r=2, label='Two') ax[1].mhist((x3, y3), r=3, label='Three') ax[1].mline(2, r=3, color='orange', label='Two') ax[1].axmline(-2, merr=-1, color='green', label='Three') ax[1].merrorbar(-2, r=4, merr=1, color='green') ax[1].legend();

Changing the scale¶

You can change the scale of the rose diagram which may help reduce the distortion.

Note that this may cause distortion elsewhere like dataset One here.

In [3]:

# Create a figure with 2 rectilinear subplots
fig, ax = plt.subplots(1, 2, figsize=(14, 6))

ax[0].scatter(x1, y1, s=1, label='One')
ax[0].scatter(x2, y2, s=1, label='Two')
ax[0].scatter(x3, y3, s=1, label='Three')

ax[0].axline((0,0), slope=2, color='black')
ax[0].axline((0,0), slope=-2, color='black')
ax[0].axline((0,0), slope=-3, color='black', linestyle='--', alpha=0.5)
ax[0].axline((0,0), slope=-1, color='black', linestyle='--', alpha=0.5)

ax[0].set(xlim=(-5, 5), ylim=(-15, 15))
ax[0].legend()
ax[0].grid()

ax[1] = simple.create_rose_plot(ax[1], yscale=3)

ax[1].mhist((x1, y1), r=1, label='One')
ax[1].mhist((x2, y2), r=2, label='Two')
ax[1].mhist((x3, y3), r=3, label='Three')

ax[1].mline(2, r=3, color='orange', label='Two')
ax[1].axmline(-2, merr=-1, color='green', label='Three')
ax[1].merrorbar(-2, r=4, merr=1, color='green')
ax[1].legend();

# Create a figure with 2 rectilinear subplots fig, ax = plt.subplots(1, 2, figsize=(14, 6)) ax[0].scatter(x1, y1, s=1, label='One') ax[0].scatter(x2, y2, s=1, label='Two') ax[0].scatter(x3, y3, s=1, label='Three') ax[0].axline((0,0), slope=2, color='black') ax[0].axline((0,0), slope=-2, color='black') ax[0].axline((0,0), slope=-3, color='black', linestyle='--', alpha=0.5) ax[0].axline((0,0), slope=-1, color='black', linestyle='--', alpha=0.5) ax[0].set(xlim=(-5, 5), ylim=(-15, 15)) ax[0].legend() ax[0].grid() ax[1] = simple.create_rose_plot(ax[1], yscale=3) ax[1].mhist((x1, y1), r=1, label='One') ax[1].mhist((x2, y2), r=2, label='Two') ax[1].mhist((x3, y3), r=3, label='Three') ax[1].mline(2, r=3, color='orange', label='Two') ax[1].axmline(-2, merr=-1, color='green', label='Three') ax[1].merrorbar(-2, r=4, merr=1, color='green') ax[1].legend();

Antipodal data¶

A slope will intersect a circle at two points, the positive and the negative x coordinates. Here we refer to this type of data as being antipodal.

By default, if (x, y) is passed then the calculated slope is not taken as being antipodal, as seen in the examples above. However, if the slope m is passed then the data is assumed to be antipodal as there is no indication of direction. For histograms this means that each slope will be counted twice, once at the positive x coordinate and once at the negative x coordinate.

In [4]:

ax = simple.create_rose_plot(figsize=(5, 4.5))
ax.mhist(y2/x2, r=2) # Slopes are antipodal by default
ax.mhist((x3, y3), r=3, antipodal=True) # By default, this data would not be antipodal

ax.mline(2, r=3, color='orange', label='Two')
ax.axmline(-2, merr=-1, color='green')

ax = simple.create_rose_plot(figsize=(5, 4.5)) ax.mhist(y2/x2, r=2) # Slopes are antipodal by default ax.mhist((x3, y3), r=3, antipodal=True) # By default, this data would not be antipodal ax.mline(2, r=3, color='orange', label='Two') ax.axmline(-2, merr=-1, color='green')