# Source code for pde.grids.coordinates.cartesian

```"""
.. 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 CartesianCoordinates(CoordinatesBase):
"""n-dimensional Cartesian coordinates"""

_objs: dict[int, CartesianCoordinates] = {}

def __new__(cls, dim: int):
# cache the instances for each dimension
if dim not in cls._objs:
cls._objs[dim] = super().__new__(cls)
return cls._objs[dim]

def __getnewargs__(self):
return (self.dim,)

def __init__(self, dim: int):
"""
Args:
dim (int):
Dimension of the Cartesian coordinate system
"""
if dim <= 0:
raise ValueError("`dim` must be positive integer")
self.dim = dim
if self.dim <= 3:
self.axes = list("xyz"[: self.dim])
else:
self.axes = [chr(97 + i) for i in range(self.dim)]
self.coordinate_limits = [(-np.inf, np.inf)] * self.dim

def __repr__(self) -> str:
"""return instance as string"""
return f"{self.__class__.__name__}(dim={self.dim})"

def __eq__(self, other):
return self.__class__ is other.__class__ and self.dim == other.dim

def _pos_to_cart(self, points: np.ndarray) -> np.ndarray:
return points

def _pos_from_cart(self, points: np.ndarray) -> np.ndarray:
return points

def _mapping_jacobian(self, points: np.ndarray) -> np.ndarray:
jac = np.zeros((self.dim, self.dim) + points.shape[:-1])
jac[range(self.dim), range(self.dim)] = 1
return jac

def _volume_factor(self, points: np.ndarray) -> ArrayLike:
return np.ones(points.shape[:-1])

def _cell_volume(self, c_low: np.ndarray, c_high: np.ndarray):
return np.prod(c_high - c_low, axis=-1)

def _scale_factors(self, points: np.ndarray) -> np.ndarray:
return np.ones_like(points)

def _basis_rotation(self, points: np.ndarray) -> np.ndarray:
return np.eye(self.dim)

```