"""
.. codeauthor:: David Zwicker <david.zwicker@ds.mpg.de>
"""
from __future__ import annotations
import numpy as np
from numpy.typing import ArrayLike
from .base import CoordinatesBase
[docs]
class CylindricalCoordinates(CoordinatesBase):
"""n-dimensional Cartesian coordinates"""
_singleton: CylindricalCoordinates | None = None
dim = 3
coordinate_limits = [(0, np.inf), (0, 2 * np.pi), (-np.inf, np.inf)]
axes = ["r", "φ", "z"]
_axes_alt = {"φ": ["phi"]}
def __new__(cls):
# cache the instances for each dimension
if cls._singleton is None:
cls._singleton = super().__new__(cls)
return cls._singleton
def __eq__(self, other):
return self.__class__ is other.__class__
def _pos_to_cart(self, points: np.ndarray) -> np.ndarray:
r, φ, z = points[..., 0], points[..., 1], points[..., 2]
x = r * np.cos(φ)
y = r * np.sin(φ)
return np.stack((x, y, z), axis=-1)
def _pos_from_cart(self, points: np.ndarray) -> np.ndarray:
x, y, z = points[..., 0], points[..., 1], points[..., 2]
r = np.hypot(x, y)
φ = np.arctan2(y, x)
return np.stack((r, φ, z), axis=-1)
def _mapping_jacobian(self, points: np.ndarray) -> np.ndarray:
r, φ = points[..., 0], points[..., 1]
sinφ, cosφ = np.sin(φ), np.cos(φ)
zero = np.zeros_like(r)
return np.array(
[
[cosφ, -r * sinφ, zero],
[sinφ, r * cosφ, zero],
[zero, zero, zero + 1],
]
)
def _volume_factor(self, points: np.ndarray) -> ArrayLike:
return points[..., 0]
def _cell_volume(self, c_low: np.ndarray, c_high: np.ndarray):
r1, φ1, z1 = c_low[..., 0], c_low[..., 1], c_low[..., 2]
r2, φ2, z2 = c_high[..., 0], c_high[..., 1], c_high[..., 2]
return (φ2 - φ1) * (z2 - z1) * (r2**2 - r1**2) / 2
def _scale_factors(self, points: np.ndarray) -> np.ndarray:
r = points[..., 0]
ones = np.ones_like(r)
return np.array([ones, r, ones])
def _basis_rotation(self, points: np.ndarray) -> np.ndarray:
φ = points[..., 1]
sinφ, cosφ = np.sin(φ), np.cos(φ)
zero = np.zeros_like(φ)
return np.array(
[
[cosφ, sinφ, zero],
[-sinφ, cosφ, zero],
[zero, zero, zero + 1],
]
)