class_docstr: Linear Elliptical Slice Sampler.
  
  Ideas:
  - Add batch support, broadcasting over parallel chains.
  - Optimize computations if possible, potentially with torch.compile.
  - Extend fixed features constraint to general linear equality constraints.
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docstr: Determine location on ellipsoid in cartesian coordinates.
  
  Args:
      nu: A `d x 1`-dim tensor (the "new" direction, drawn from N(0, I)).
      theta: A `k`-dim tensor of angles.
  
  Returns:
      A `d x k`-dim tensor of samples from the domain in cartesian coordinates.
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code: def _get_cart_coords(self, nu: Tensor, theta: Tensor) -> Tensor:
      r"""Determine location on ellipsoid in cartesian coordinates.
  
      Args:
          nu: A `d x 1`-dim tensor (the "new" direction, drawn from N(0, I)).
          theta: A `k`-dim tensor of angles.
  
      Returns:
          A `d x k`-dim tensor of samples from the domain in cartesian coordinates.
      """
      return self._z * torch.cos(theta) + nu * torch.sin(theta)
  
imports: from __future__ import annotations
  import math
  from typing import List, Optional, Tuple, Union
  import torch
  from botorch.utils.sampling import PolytopeSampler
  from torch import Tensor
label_desc: Use image node_id 8 for calling the LinearEllipticalSliceSampler obj's underlying member method code with example usage: obj._get_cart_coords(nu, theta) and returns: unknown