QMCPy logo¶

Generate three lightweight scatter-plot logos from a two-dimensional randomized digital net, deterministic digital net, and lattice transformed to a zero-mean multivariate normal distribution with covariance [[2, 1], [1, 3]]. The deterministic net starts at index 1 because its origin maps to non-finite Gaussian coordinates.

In [1]:

from pathlib import Path

import matplotlib.image as mpimg
import matplotlib.pyplot as plt
import numpy as np
from qmcpy import DigitalNetB2, Gaussian, Lattice

n = 128
seed = 7
covariance = np.array([[2.0, 1.0], [1.0, 3.0]])
assert np.all(np.linalg.eigvalsh(covariance) > 0)

configurations = (
    (DigitalNetB2(dimension=2, seed=seed), "_net", 0),
    (Lattice(dimension=2, seed=seed), "_lattice", 0),
    (DigitalNetB2(dimension=2, randomize=False, order="GRAY"), "_det_net", 1),
)

# Work whether Jupyter starts in the repository root or in demos/.
start = Path.cwd().resolve()
repo_root = None
for path in (start, *start.parents):
    if (path / "pyproject.toml").exists() and (path / "qmcpy").is_dir():
        repo_root = path
        break
if repo_root is None:
    raise RuntimeError(
        "Could not locate repository root (expected pyproject.toml and qmcpy/). Run this notebook from within the QMCSoftware repository."
    )
current_logo = repo_root / "docs" / "assets" / "logos" / "qmcpy_logo.png"

from pathlib import Path import matplotlib.image as mpimg import matplotlib.pyplot as plt import numpy as np from qmcpy import DigitalNetB2, Gaussian, Lattice n = 128 seed = 7 covariance = np.array([[2.0, 1.0], [1.0, 3.0]]) assert np.all(np.linalg.eigvalsh(covariance) > 0) configurations = ( (DigitalNetB2(dimension=2, seed=seed), "_net", 0), (Lattice(dimension=2, seed=seed), "_lattice", 0), (DigitalNetB2(dimension=2, randomize=False, order="GRAY"), "_det_net", 1), ) # Work whether Jupyter starts in the repository root or in demos/. start = Path.cwd().resolve() repo_root = None for path in (start, *start.parents): if (path / "pyproject.toml").exists() and (path / "qmcpy").is_dir(): repo_root = path break if repo_root is None: raise RuntimeError( "Could not locate repository root (expected pyproject.toml and qmcpy/). Run this notebook from within the QMCSoftware repository." ) current_logo = repo_root / "docs" / "assets" / "logos" / "qmcpy_logo.png"

In [2]:

# Read the dominant opaque RGB color from the present logo.
rgba = mpimg.imread(current_logo)
opaque_rgb = rgba[..., :3][rgba[..., 3] > 0.99]
rgb, counts = np.unique(
    np.round(opaque_rgb * 255).astype(np.uint8), axis=0, return_counts=True
)
logo_color = rgb[counts.argmax()] / 255

# Read the dominant opaque RGB color from the present logo. rgba = mpimg.imread(current_logo) opaque_rgb = rgba[..., :3][rgba[..., 3] > 0.99] rgb, counts = np.unique( np.round(opaque_rgb * 255).astype(np.uint8), axis=0, return_counts=True ) logo_color = rgb[counts.argmax()] / 255

In [3]:

for sampler, output_suffix, start_index in configurations:
    normal = Gaussian(sampler, mean=np.zeros(2), covariance=covariance)
    points = normal(n_min=start_index, n_max=start_index + n, warn=False)
    target = repo_root / "docs" / "logos" / f"qmcpy_logo{output_suffix}.png"
    target.parent.mkdir(parents=True, exist_ok=True)

    fig, ax = plt.subplots(figsize=(8, 8), facecolor="none")
    ax.scatter(points[:, 0], points[:, 1], s=150, color=logo_color, edgecolors="none")
    ax.set_aspect("equal")
    center = (points.min(axis=0) + points.max(axis=0)) / 2
    radius = np.ptp(points, axis=0).max() * 0.54
    ax.set_xlim(center[0] - radius, center[0] + radius)
    ax.set_ylim(center[1] - radius, center[1] + radius)
    ax.axis("off")
    fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
    fig.savefig(target, dpi=196, transparent=True)
    saved_logo = mpimg.imread(target)
    print(f"Wrote: {target.relative_to(repo_root)}")

    # Verifty all PNG outputs are transparent 1568 x 1568 RGBA
    assert saved_logo.shape == (1568, 1568, 4)  # Square RGBA image
    assert saved_logo[..., 3].min() == 0  # Has transparent pixels
    assert saved_logo[..., 3].max() == 1  # Has opaque pixels
    plt.show()

for sampler, output_suffix, start_index in configurations: normal = Gaussian(sampler, mean=np.zeros(2), covariance=covariance) points = normal(n_min=start_index, n_max=start_index + n, warn=False) target = repo_root / "docs" / "logos" / f"qmcpy_logo{output_suffix}.png" target.parent.mkdir(parents=True, exist_ok=True) fig, ax = plt.subplots(figsize=(8, 8), facecolor="none") ax.scatter(points[:, 0], points[:, 1], s=150, color=logo_color, edgecolors="none") ax.set_aspect("equal") center = (points.min(axis=0) + points.max(axis=0)) / 2 radius = np.ptp(points, axis=0).max() * 0.54 ax.set_xlim(center[0] - radius, center[0] + radius) ax.set_ylim(center[1] - radius, center[1] + radius) ax.axis("off") fig.subplots_adjust(left=0, right=1, bottom=0, top=1) fig.savefig(target, dpi=196, transparent=True) saved_logo = mpimg.imread(target) print(f"Wrote: {target.relative_to(repo_root)}") # Verifty all PNG outputs are transparent 1568 x 1568 RGBA assert saved_logo.shape == (1568, 1568, 4) # Square RGBA image assert saved_logo[..., 3].min() == 0 # Has transparent pixels assert saved_logo[..., 3].max() == 1 # Has opaque pixels plt.show()

Wrote: docs/logos/qmcpy_logo_net.png

Wrote: docs/logos/qmcpy_logo_lattice.png

Wrote: docs/logos/qmcpy_logo_det_net.png