Shamrock 3D unit vector generator

This example shows how to use the unit vector generator

import matplotlib.pyplot as plt  # plots
import numpy as np  # sqrt & arctan2

import shamrock

Pseudo random number generator seed

eng = shamrock.algs.gen_seed(111)

Generate positions

list_pos = []
for i in range(1000000):
    list_pos.append(shamrock.algs.mock_unit_vector_f64_3(eng))

Compute r and theta

r_val = []
for x, y, z in list_pos:
    r = np.sqrt(x**2 + y**2 + z**2)
    r_val.append(r)

for r in r_val:
    if abs(r - 1.0) > 1e-15:
        raise ValueError(f"abs({r} - 1.0) > 1e-15 | delta = {abs(r - 1.0)}")


theta_val = []
for x, y, z in list_pos:
    theta = np.arctan2(y, x)
    theta_val.append(theta)

Radial distribution

hist_r, bins_r = np.histogram(r_val, bins=101, density=True, range=(0, 2))
r = np.linspace(bins_r[0], bins_r[-1], 101)

plt.figure()
plt.bar(bins_r[:-1], hist_r, np.diff(bins_r), alpha=0.5)
plt.xlabel("$r$")
plt.ylabel("$f(r)$")
plt.show()

Angular distribution

hist_theta, bins_theta = np.histogram(theta_val, bins=1000, density=True)
theta = np.linspace(bins_theta[0], bins_theta[-1], 1000)

plt.figure()
plt.plot(theta, [1 / (2 * np.pi) for _ in theta], "r--", lw=2)
plt.bar(bins_theta[:-1], hist_theta, np.diff(bins_theta), alpha=0.5)
plt.xlabel(r"$\theta$")
plt.ylabel(r"$f(\theta)$")

plt.show()

Estimated memory usage: 287 MB