code: def gen_one_shot_kg_initial_conditions(
      acq_function: qKnowledgeGradient,
      bounds: Tensor,
      q: int,
      num_restarts: int,
      raw_samples: int,
      fixed_features: Optional[Dict[int, float]] = None,
      options: Optional[Dict[str, Union[bool, float, int]]] = None,
      inequality_constraints: Optional[
          List[Tuple[Tensor, Tensor, float]]
      ] = None,
      equality_constraints: Optional[
          List[Tuple[Tensor, Tensor, float]]
      ] = None,
  ) -> Optional[Tensor]:
      r"""Generate a batch of smart initializations for qKnowledgeGradient.
  
      This function generates initial conditions for optimizing one-shot KG using
      the maximizer of the posterior objective. Intutively, the maximizer of the
      fantasized posterior will often be close to a maximizer of the current
      posterior. This function uses that fact to generate the initial conditions
      for the fantasy points. Specifically, a fraction of `1 - frac_random` (see
      options) is generated by sampling from the set of maximizers of the
      posterior objective (obtained via random restart optimization) according to
      a softmax transformation of their respective values. This means that this
      initialization strategy internally solves an acquisition function
      maximization problem. The remaining `frac_random` fantasy points as well as
      all `q` candidate points are chosen according to the standard initialization
      strategy in `gen_batch_initial_conditions`.
  
      Args:
          acq_function: The qHypervolumeKnowledgeGradient instance to be optimized.
          bounds: A `2 x d` tensor of lower and upper bounds for each column of
              task features.
          q: The number of candidates to consider.
          num_restarts: The number of starting points for multistart acquisition
              function optimization.
          raw_samples: The number of raw samples to consider in the initialization
              heuristic.
          fixed_features: A map `{feature_index: value}` for features that
              should be fixed to a particular value during generation.
          options: Options for initial condition generation. These contain all
              settings for the standard heuristic initialization from
              `gen_batch_initial_conditions`. In addition, they contain
              `frac_random` (the fraction of fully random fantasy points),
              `num_inner_restarts` and `raw_inner_samples` (the number of random
              restarts and raw samples for solving the posterior objective
              maximization problem, respectively) and `eta` (temperature parameter
              for sampling heuristic from posterior objective maximizers).
          inequality constraints: A list of tuples (indices, coefficients, rhs),
              with each tuple encoding an inequality constraint of the form
              `\sum_i (X[indices[i]] * coefficients[i]) >= rhs`.
          equality constraints: A list of tuples (indices, coefficients, rhs),
              with each tuple encoding an inequality constraint of the form
              `\sum_i (X[indices[i]] * coefficients[i]) = rhs`.
  
      Returns:
          A `num_restarts x q' x d` tensor that can be used as initial conditions
          for `optimize_acqf()`. Here `q' = q + num_fantasies` is the total number
          of points (candidate points plus fantasy points).
  
      Example:
          >>> qHVKG = qHypervolumeKnowledgeGradient(model, ref_point=num_fantasies=64)
          >>> bounds = torch.tensor([[0., 0.], [1., 1.]])
          >>> Xinit = gen_one_shot_hvkg_initial_conditions(
          >>>     qHVKG, bounds, q=3, num_restarts=10, raw_samples=512,
          >>>     options={"frac_random": 0.25},
          >>> )
      """
      options = options or {}
      frac_random: float = options.get("frac_random", 0.1)
      if not 0 < frac_random < 1:
          raise ValueError(
              f"frac_random must take on values in (0,1). Value: {frac_random}"
          )
      q_aug = acq_function.get_augmented_q_batch_size(q=q)
  
      # TODO: Avoid unnecessary computation by not generating all candidates
      ics = gen_batch_initial_conditions(
          acq_function=acq_function,
          bounds=bounds,
          q=q_aug,
          num_restarts=num_restarts,
          raw_samples=raw_samples,
          fixed_features=fixed_features,
          options=options,
          inequality_constraints=inequality_constraints,
          equality_constraints=equality_constraints,
      )
  
      # compute maximizer of the value function
      value_function = _get_value_function(
          model=acq_function.model,
          objective=acq_function.objective,
          posterior_transform=acq_function.posterior_transform,
          sampler=acq_function.inner_sampler,
          project=getattr(acq_function, "project", None),
      )
      from botorch.optim.optimize import optimize_acqf
  
      fantasy_cands, fantasy_vals = optimize_acqf(
          acq_function=value_function,
          bounds=bounds,
          q=1,
          num_restarts=options.get("num_inner_restarts", 20),
          raw_samples=options.get("raw_inner_samples", 1024),
          fixed_features=fixed_features,
          return_best_only=False,
          inequality_constraints=inequality_constraints,
          equality_constraints=equality_constraints,
      )
  
      # sampling from the optimizers
      n_value = int(
          (1 - frac_random) * (q_aug - q)
      )  # number of non-random ICs
      eta = options.get("eta", 2.0)
      weights = torch.exp(eta * standardize(fantasy_vals))
      idx = torch.multinomial(
          weights, num_restarts * n_value, replacement=True
      )
  
      # set the respective initial conditions to the sampled optimizers
      ics[..., -n_value:, :] = fantasy_cands[idx, 0].view(
          num_restarts, n_value, -1
      )
      return ics
  
imports: from __future__ import annotations
  import warnings
  from math import ceil
  from typing import Callable, Dict, List, Optional, Tuple, Union
  import torch
  from botorch import settings
  from botorch.acquisition import analytic, monte_carlo, multi_objective
  from botorch.acquisition.acquisition import AcquisitionFunction
  from botorch.acquisition.fixed_feature import FixedFeatureAcquisitionFunction
  from botorch.acquisition.knowledge_gradient import _get_value_function, qKnowledgeGradient
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import _get_hv_value_function, qHypervolumeKnowledgeGradient, qMultiFidelityHypervolumeKnowledgeGradient
  from botorch.exceptions.errors import BotorchTensorDimensionError, UnsupportedError
  from botorch.exceptions.warnings import BadInitialCandidatesWarning, BotorchWarning, SamplingWarning
  from botorch.models.model import Model
  from botorch.optim.utils import fix_features, get_X_baseline
  from botorch.utils.multi_objective.pareto import is_non_dominated
  from botorch.utils.sampling import batched_multinomial, draw_sobol_samples, get_polytope_samples, manual_seed
  from botorch.utils.transforms import normalize, standardize, unnormalize
  from torch import Tensor
  from torch.distributions import Normal
  from torch.quasirandom import SobolEngine
label_desc: Use image node_id 6 for calling a global function with example usage: gen_one_shot_kg_initial_conditions(acq_function, bounds, q, num_restarts, raw_samples, fixed_features, options, inequality_constraints, equality_constraints) and returns: ics