Complete usage example

This script exercises the main plotting and conversion operations. Plotting calls return figures; save or close them with Matplotlib. Detailed mathematical definitions are in the individual analysis chapters.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
import hilbertplot as hp

# Data plotting: choose a curve by index, label or symbol.
values = np.sin(np.arange(4096) / 20)
fig = hp.plot(values, curve=12, cmap="RdBu_r", vmin=-1, vmax=1)
fig.savefig("data.png", dpi=180)
fig = hp.plot(values, curve="Moore", granularity=4, cmap="RdBu_r")
fig = hp.plot(values, curve="12H", cmap=["navy", "white", "firebrick"])

# Curve geometry, with no measurement data.
fig = hp.plot_curve(0, order=3, color="steelblue")
fig = hp.plot_curve(3, shape=(15, 16), color="darkorchid")
fig = hp.gallery(hp.curves.proper(), order=3, color="steelblue")

# Raw array conversions retain exact integer values and masks.
source = np.arange(100, dtype=np.uint64) + 2**63
grid = hp.data.to_grid(source, curve=12)
recovered = hp.data.from_grid(grid, curve=12, length=source.size)
np.testing.assert_array_equal(recovered, source)

# Read RGB pixels in curve order; retain the full shape to reconstruct.
image = np.arange(16 * 16 * 3, dtype=np.uint16).reshape(16, 16, 3)
sequence = hp.data.from_grid(image, curve=12)
restored = hp.data.to_grid(sequence, curve=12, shape=image.shape)
np.testing.assert_array_equal(restored, image)

# Numerical transforms, with or without rendering.
coarse = hp.data.granulate(values, 4)
spectrum = hp.data.fourier(values, curve=0, window=True)
fig = hp.plot(values, fourier=True, window=True, cmap="magma")
field = hp.curves.difference_map(0, order=6)
fig = hp.plot(values, difference=True, cmap="inferno",
              norm=LogNorm(vmin=1, vmax=field.max()))

# Metadata, direct indexing, and resource controls.
metadata = hp.curves.info(12)
xy = hp.curves.index_to_xy(10**18, order=40, curve=12)
assert hp.curves.xy_to_index(*xy, order=40, curve=12) == 10**18
stats = hp.config.cache_info()
hp.config.clear_cache()
plt.close("all")

For examples where the transforms reveal a specific input structure, see Thue–Morse Fourier maps and periodic-region granularity.