Phasor plot

An introduction to plotting phasor coordinates.

The phasorpy.plot.PhasorPlot class is used to plot phasor coordinates as scattered points, lines, 2D histograms, and contours. The plots are supplemented with universal semicircles, polar grids, polar cursors, component mixture indicators, and manual annotations.

Import required modules, functions, and classes:

import math

import numpy

from phasorpy.plot import PhasorPlot

numpy.random.seed(42)

Empty phasor plot

Create an empty phasor plot, showing the first quadrant and the universal semicircle:

plot = PhasorPlot()
plot.show()

Universal semicircle

Create a phasor plot at a frequency of 80 MHz and custom axis limits. Add a second, transformed universal semicircle:

plot = PhasorPlot(frequency=80.0, xlim=(-0.2, 1.05))
plot.semicircle(polar_reference=(0.9852, 0.5526))
plot.show()

Scatter and line plots

Plot phasor coordinates as scatter and/or lines:

plot = PhasorPlot(frequency=80.0, title='Scatter and line plots')
plot.plot(0.6, 0.4, label='1')
plot.plot([0.2, 0.9], [0.4, 0.3], '.-', label='2')
plot.plot([0.39, 0.4, 0.41], [0.21, 0.19, 0.2], 'x', label='3')
plot.show()

Cursors

Point out certain polar coordinates, and ranges thereof, using phasor coordinates:

plot = PhasorPlot(frequency=80.0, title='Cursors')
plot.cursor(0.4, 0.3)
plot.cursor(0.5, 0.3, 0.8, 0.15)
plot.cursor(0.9, 0.3, radius=0.05)
plot.cursor(0.4, 0.3, radius=0.05, radius_minor=0.1)
plot.cursor(0.1, 0.3, radius=0.05, radius_minor=0.1, align_semicircle=True)
plot.show()

Alternatively, use polar coordinates, here demonstrated with various options:

plot = PhasorPlot(frequency=80.0, title='Polar cursors')
plot.polar_cursor(0.6435, 0.5, linestyle='-')
plot.polar_cursor(0.5236, 0.6, 0.1963, 0.8, linewidth=2)
plot.polar_cursor(0.3233, 0.9482, radius=0.05, color='tab:red')
plot.polar_cursor(
    0.6435,
    0.5,
    radius=0.05,
    radius_minor=0.1,
    color='tab:blue',
    fill=True,
    alpha=0.5,
)
plot.polar_cursor(
    0.6435,
    0.5,
    radius=0.1,
    radius_minor=0.05,
    angle=0.0,
    color='tab:green',
    fill=True,
    alpha=0.5,
)
plot.show()

Component mixtures

Show linear combinations of phasor coordinates or ranges thereof:

real, imag, weights = numpy.array(
    [[0.1, 0.2, 0.5, 0.9], [0.3, 0.4, 0.5, 0.3], [2, 1, 2, 1]]
)

plot = PhasorPlot(frequency=80.0, title='Component mixtures')
plot.components(
    real,
    imag,
    linestyle='',
    marker='o',
    labels=['A', 'B', 'C', 'D'],
    color='tab:blue',
    fill=True,
    facecolor='lightyellow',
    label='components',
)
plot.components(real, imag, weights, marker='o', label='mixture')
plot.show()

2D Histogram

Plot large number of phasor coordinates as a 2D histogram:

real, imag = numpy.random.multivariate_normal(
    (0.6, 0.4), [[3e-3, -1e-3], [-1e-3, 1e-3]], (256, 256)
).T
plot = PhasorPlot(frequency=80.0, title='2D Histogram')
plot.hist2d(real, imag)
plot.show()

Contours

Plot the contours of the density of phasor coordinates:

plot = PhasorPlot(frequency=80.0, title='Contours')
plot.contour(real, imag)
plot.show()

Image

Plot the image of a custom-colored 2D histogram:

plot = PhasorPlot(frequency=80.0, title='Image (not implemented yet)')
# plot.imshow(image)
plot.show()

Combined plots

Multiple plots can be combined:

real2, imag2 = numpy.random.multivariate_normal(
    (0.9, 0.2), [[2e-4, -1e-4], [-1e-4, 2e-4]], 4096
).T

plot = PhasorPlot(
    title='Combined plots', xlim=(0.35, 1.03), ylim=(0.1, 0.59), grid=False
)
plot.hist2d(real, imag, bins=64, cmap='Blues')
plot.contour(real, imag, bins=48, levels=3, cmap='summer_r', norm='log')
plot.hist2d(real2, imag2, bins=64, cmap='Oranges')
plot.plot(0.6, 0.4, '.', color='tab:blue')
plot.plot(0.9, 0.2, '.', color='tab:orange')
plot.cursor(0.9, 0.2, color='tab:orange')
plot.polar_cursor(math.atan2(0.4, 0.6), math.hypot(0.6, 0.4), color='tab:blue')
plot.semicircle(frequency=80.0, color='tab:purple')
plot.show()

All quadrants

Create an empty phasor plot showing all four quadrants:

plot = PhasorPlot(allquadrants=True, title='All quadrants')
plot.show()

Matplotlib axes

The PhasorPlot class can use an existing matlotlib axes. The PhasorPlot.ax attribute provides access to the underlying matplotlib axes, for example, to add annotations:

from matplotlib import pyplot

ax = pyplot.subplot(1, 1, 1)
plot = PhasorPlot(ax=ax, allquadrants=True, title='Matplotlib axes')
plot.hist2d(real, imag, cmap='Blues')
plot.ax.annotate(
    '0.6, 0.4',
    xy=(0.6, 0.4),
    xytext=(0.2, 0.2),
    arrowprops=dict(arrowstyle='->'),
)
pyplot.show()

plot_phasor function

The phasorpy.plot.plot_phasor() function provides a simpler alternative to plot phasor coordinates in a single statement:

from phasorpy.plot import plot_phasor

plot_phasor(real[0, :32], imag[0, :32], marker='.', frequency=80.0)

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