Special histograms in physt

Sometimes, it is necessary to bin values in transformed coordinates (e.g. polar). In principle, it is possible to create histograms from already transformed values (i.e. r and φ). However, this is not always the best way to go as each set of coordinates has its own peculiarities (e.g. the typical range of values for azimuthal angle)

Physt provides a general framework for constructing the transformed histograms (see a dedicated section of this document) and a couple of most frequently used variants:

  • PolarHistogram
  • SphericalHistogram
  • CylindricalHistogram
In [1]:
# Necessary import evil
%matplotlib inline

from physt import cylindrical, polar, spherical
import numpy as np
import matplotlib.pyplot as plt
In [2]:
# Generate some points in the Cartesian coordinates
np.random.seed(42)

x = np.random.rand(1000)  
y = np.random.rand(1000)
z = np.random.rand(1000)

Polar histogram

This histograms maps values to radius (r) and azimuthal angle (φ, ranging from 0 to 2π).

By default (unless you specify the phi_bins parameter), the whole azimuthal range is spanned (even if there are no values that fall in parts of the circle).

In [3]:
# Create a polar histogram with default parameters
hist = polar(x, y)
ax = hist.plot.polar_map()
hist
Out[3]:
PolarHistogram(bins=(10, 16), total=1000, dtype=int64)
In [4]:
hist.bins
Out[4]:
[array([[0.02704268, 0.16306851],
        [0.16306851, 0.29909433],
        [0.29909433, 0.43512015],
        [0.43512015, 0.57114597],
        [0.57114597, 0.7071718 ],
        [0.7071718 , 0.84319762],
        [0.84319762, 0.97922344],
        [0.97922344, 1.11524926],
        [1.11524926, 1.25127509],
        [1.25127509, 1.38730091]]),
 array([[0.        , 0.39269908],
        [0.39269908, 0.78539816],
        [0.78539816, 1.17809725],
        [1.17809725, 1.57079633],
        [1.57079633, 1.96349541],
        [1.96349541, 2.35619449],
        [2.35619449, 2.74889357],
        [2.74889357, 3.14159265],
        [3.14159265, 3.53429174],
        [3.53429174, 3.92699082],
        [3.92699082, 4.3196899 ],
        [4.3196899 , 4.71238898],
        [4.71238898, 5.10508806],
        [5.10508806, 5.49778714],
        [5.49778714, 5.89048623],
        [5.89048623, 6.28318531]])]
In [5]:
# Create a polar histogram with different binning
hist2 = polar(x+.3, y+.3, radial_bins="human", phi_bins="human")
ax = hist2.plot.polar_map(density=True)
In [6]:
# Default axes names
hist.axis_names
Out[6]:
('r', 'phi')

When working with any transformed histograms, you can fill values in the original, or transformed coordinates. All methods working with coordinates understand the parameter transformed which (if True) says that the method parameter are already in the transformed coordinated; otherwise, all values are considered to be in the original coordinates and transformed on inserting (creating, searching).

In [7]:
# Using transformed / untransformed values
print("Non-transformed", hist.find_bin((0.1, 1)))
print("Transformed", hist.find_bin((0.1, 1), transformed=True))

print("Non-transformed", hist.find_bin((0.1, 2.7)))     # Value
print("Transformed", hist.find_bin((0.1, 2.7), transformed=True))
Non-transformed (7, 3)
Transformed (0, 2)
Non-transformed None
Transformed (0, 6)
In [8]:
# Simple plotting, similar to Histogram2D
hist.plot.polar_map(density=True, show_zero=False, cmap="Wistia", lw=0.5, figsize=(5, 5));

Adding new values

In [9]:
# Add a single, untransformed value
hist.fill((-.5, -.5), weight=12)
hist.plot.polar_map(density=True, show_zero=True, cmap="Reds", lw=0.5, figsize=(5, 5));
In [10]:
# Add a couple of values, transformed
data = [[.5, 3.05], [.5, 3.2], [.7, 3.3]]
weights = [1, 5, 20]

hist.fill_n(data, weights=weights, transformed=True)
hist.plot.polar_map(density=True, show_zero=True, cmap="Reds", lw=0.5, figsize=(5, 5));

Projections

The projections are stored using specialized Histogram1D subclasses that keep (in the case of radial) information about the proper bin sizes.

In [11]:
radial = hist.projection("r")
radial.plot(density=True, color="red", alpha=0.5).set_title("Density")
radial.plot(label="absolute", color="blue", alpha=0.5).set_title("Absolute")
radial.plot(label="cumulative", cumulative=True, density=True, color="green", alpha=0.5).set_title("Cumulative")
radial
Out[11]:
RadialHistogram(bins=(10,), total=1026, dtype=int64)
In [12]:
hist.projection("phi").plot(cmap="rainbow")
Out[12]:
<AxesSubplot:xlabel='phi'>

Cylindrical histogram

To be implemented

In [13]:
data = np.random.rand(100, 3)
h = cylindrical(data)
h
Out[13]:
CylindricalHistogram(bins=(10, 16, 10), total=100, dtype=int64)
In [14]:
# %matplotlib qt
proj = h.projection("rho", "phi")
proj.plot.polar_map()
proj
Out[14]:
PolarHistogram(bins=(10, 16), total=100, dtype=int64)
In [15]:
proj = h.projection("phi", "z")
ax = proj.plot.cylinder_map(show_zero=False)
ax.view_init(50, 70)
proj
Out[15]:
CylindricalSurfaceHistogram(bins=(16, 10), total=100, dtype=int64)

Spherical histogram

To be implemented

In [16]:
n = 1000000
data = np.empty((n, 3))
data[:,0] = np.random.normal(0, 1, n)
data[:,1] = np.random.normal(0, 1.3, n)
data[:,2] = np.random.normal(1, 1.2, n)
h = spherical(data)
h
Out[16]:
SphericalHistogram(bins=(10, 16, 16), total=1000000, dtype=int64)
In [17]:
globe = h.projection("theta", "phi")
# globe.plot()
globe.plot.globe_map(density=True, figsize=(7, 7), cmap="rainbow") 
globe.plot.globe_map(density=False, figsize=(7, 7))
globe
Out[17]:
SphericalSurfaceHistogram(bins=(16, 16), total=1000000, dtype=int64)

Implementing custom transformed histogram

TO BE WRITTEN