from math import cos, sin, sqrt
import numpy as np
from numba import jit
[docs]
@jit(nopython=True)
def direction(theta_i: float) -> tuple:
"""
Calculate the current direction vector and the normal vector to the current direction.
Args:
theta_i (float): The angle in radians representing the current direction.
Returns:
tuple: A tuple containing the current direction vector (e_i) and the normal vector to the current direction
(e_i_n).
"""
# Current direction vector
e_i = np.array([cos(theta_i), sin(theta_i)])
# Normal vector to current direction
# https://stackoverflow.com/questions/1243614/
e_i_n = np.array([sin(theta_i), -cos(theta_i)])
return e_i, e_i_n
[docs]
@jit(nopython=True)
def projection(e_i_n, e_i_j, s_i_j: float) -> float:
"""
Calculates the projection of vector e_i_j onto vector e_i_n.
Args:
e_i_n (array-like): The vector onto which the projection is made.
e_i_j (array-like): The vector being projected.
s_i_j (float): The magnitude of vector e_i_j.
Returns:
float: The projection of vector e_i_j onto vector e_i_n.
"""
proj = abs(np.dot(e_i_n, e_i_j)) * s_i_j
return proj
[docs]
@jit(nopython=True)
def tangent_dist(theta_i: float, theta_j: float, a_i: float, b_i: float) -> float:
"""
Calculate the tangent distance between two angles.
Args:
theta_i (float): The first angle in radians.
theta_j (float): The second angle in radians.
a_i (float): The value of a_i.
b_i (float): The value of b_i.
Returns:
k_prime (float): The tangent distance between theta_i and theta_j.
"""
if round(cos(theta_j - theta_i), 15) != 0:
c_prime = sin(theta_j - theta_i) / cos(theta_j - theta_i)
d_prime = sqrt(b_i**2 + a_i**2 * c_prime**2)
k_prime = d_prime / sqrt(c_prime**2 + 1)
else:
k_prime = a_i
return k_prime
[docs]
def truncated_rvs(
rng,
size: int,
dist,
x_min: float,
x_max: float,
k,
s: float,
loc: float,
scale: float,
):
"""
Generate truncated random variables.
Args:
rng (object): Random number generator.
size (int): Number of random variables to generate.
dist (object): Probability distribution object.
x_min (float): Minimum value for truncation.
x_max (float): Maximum value for truncation.
k (float): First shape parameter for the distribution.
s (float): Second shape parameter for the distribution.
loc (float): Location parameter for the distribution.
scale (float): Scale parameter for the distribution.
Returns:
numpy.ndarray: Array of truncated random variables.
"""
# https://stackoverflow.com/questions/47933019
if k:
low = dist.cdf(x_min, k, s, loc=loc, scale=scale)
high = dist.cdf(x_max, k, s, loc=loc, scale=scale)
return dist.ppf(
rng.uniform(low=low, high=high, size=size),
k,
s,
loc=0,
scale=scale,
)
else:
low = dist.cdf(x_min, s, loc=loc, scale=scale)
high = dist.cdf(x_max, s, loc=loc, scale=scale)
return dist.ppf(
rng.uniform(low=low, high=high, size=size),
s,
loc=0,
scale=scale,
)