code: def gen_batch_initial_conditions(
      acq_function: AcquisitionFunction,
      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,
      generator: Optional[Callable[[int, int, int], Tensor]] = None,
      fixed_X_fantasies: Optional[Tensor] = None,
  ) -> Tensor:
      r"""Generate a batch of initial conditions for random-restart optimziation.
  
      TODO: Support t-batches of initial conditions.
  
      Args:
          acq_function: The acquisition function to be optimized.
          bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`.
          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. Note: if `sample_around_best` is True (the default is False),
              then `2 * raw_samples` samples are used.
          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. For valid options see
              `initialize_q_batch` and `initialize_q_batch_nonneg`. If `options`
              contains a `nonnegative=True` entry, then `acq_function` is
              assumed to be non-negative (useful when using custom acquisition
              functions). In addition, an "init_batch_limit" option can be passed
              to specify the batch limit for the initialization. This is useful
              for avoiding memory limits when computing the batch posterior over
              raw samples.
          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`.
          generator: Callable for generating samples that are then further
              processed. It receives `n`, `q` and `seed` as arguments and
              returns a tensor of shape `n x q x d`.
          fixed_X_fantasies: A fixed set of fantasy points to concatenate to
              the `q` candidates being initialized along the `-2` dimension. The
              shape should be `num_pseudo_points x d`. E.g., this should be
              `num_fantasies x d` for KG and `num_fantasies*num_pareto x d`
              for HVKG.
  
      Returns:
          A `num_restarts x q x d` tensor of initial conditions.
  
      Example:
          >>> qEI = qExpectedImprovement(model, best_f=0.2)
          >>> bounds = torch.tensor([[0.], [1.]])
          >>> Xinit = gen_batch_initial_conditions(
          >>>     qEI, bounds, q=3, num_restarts=25, raw_samples=500
          >>> )
      """
      if bounds.isinf().any():
          raise NotImplementedError(
              "Currently only finite values in `bounds` are supported "
              "for generating initial conditions for optimization."
          )
      options = options or {}
      sample_around_best = options.get("sample_around_best", False)
      if sample_around_best and equality_constraints:
          raise UnsupportedError(
              "Option 'sample_around_best' is not supported when equality"
              "constraints are present."
          )
      if sample_around_best and generator:
          raise UnsupportedError(
              "Option 'sample_around_best' is not supported when custom "
              "generator is be used."
          )
      seed: Optional[int] = options.get("seed")
      batch_limit: Optional[int] = options.get(
          "init_batch_limit", options.get("batch_limit")
      )
      factor, max_factor = 1, 5
      init_kwargs = {}
      device = bounds.device
      bounds_cpu = bounds.cpu()
      if "eta" in options:
          init_kwargs["eta"] = options.get("eta")
      if options.get("nonnegative") or is_nonnegative(acq_function):
          init_func = initialize_q_batch_nonneg
          if "alpha" in options:
              init_kwargs["alpha"] = options.get("alpha")
      else:
          init_func = initialize_q_batch
  
      q = 1 if q is None else q
      # the dimension the samples are drawn from
      effective_dim = bounds.shape[-1] * q
      if effective_dim > SobolEngine.MAXDIM and settings.debug.on():
          warnings.warn(
              f"Sample dimension q*d={effective_dim} exceeding Sobol max dimension "
              f"({SobolEngine.MAXDIM}). Using iid samples instead.",
              SamplingWarning,
          )
  
      while factor < max_factor:
          with warnings.catch_warnings(record=True) as ws:
              n = raw_samples * factor
              if generator is not None:
                  X_rnd = generator(n, q, seed)
              # check if no constraints are provided
              elif not (inequality_constraints or equality_constraints):
                  if effective_dim <= SobolEngine.MAXDIM:
                      X_rnd = draw_sobol_samples(
                          bounds=bounds_cpu, n=n, q=q, seed=seed
                      )
                  else:
                      with manual_seed(seed):
                          # load on cpu
                          X_rnd_nlzd = torch.rand(
                              n,
                              q,
                              bounds_cpu.shape[-1],
                              dtype=bounds.dtype,
                          )
                      X_rnd = (
                          bounds_cpu[0]
                          + (bounds_cpu[1] - bounds_cpu[0]) * X_rnd_nlzd
                      )
              else:
                  X_rnd = sample_q_batches_from_polytope(
                      n=n,
                      q=q,
                      bounds=bounds,
                      n_burnin=options.get("n_burnin", 10000),
                      thinning=options.get("thinning", 32),
                      seed=seed,
                      equality_constraints=equality_constraints,
                      inequality_constraints=inequality_constraints,
                  )
              # sample points around best
              if sample_around_best:
                  X_best_rnd = sample_points_around_best(
                      acq_function=acq_function,
                      n_discrete_points=n * q,
                      sigma=options.get(
                          "sample_around_best_sigma", 1e-3
                      ),
                      bounds=bounds,
                      subset_sigma=options.get(
                          "sample_around_best_subset_sigma", 1e-1
                      ),
                      prob_perturb=options.get(
                          "sample_around_best_prob_perturb"
                      ),
                  )
                  if X_best_rnd is not None:
                      X_rnd = torch.cat(
                          [
                              X_rnd,
                              X_best_rnd.view(
                                  n, q, bounds.shape[-1]
                              ).cpu(),
                          ],
                          dim=0,
                      )
              X_rnd = fix_features(X_rnd, fixed_features=fixed_features)
              if fixed_X_fantasies is not None:
                  if (d_f := fixed_X_fantasies.shape[-1]) != (
                      d_r := X_rnd.shape[-1]
                  ):
                      raise BotorchTensorDimensionError(
                          "`fixed_X_fantasies` and `bounds` must both have the same "
                          f"trailing dimension `d`, but have {d_f} and {d_r}, "
                          "respectively."
                      )
                  X_rnd = torch.cat(
                      [
                          X_rnd,
                          fixed_X_fantasies.cpu()
                          .unsqueeze(0)
                          .expand(
                              X_rnd.shape[0], *fixed_X_fantasies.shape
                          ),
                      ],
                      dim=-2,
                  )
              with torch.no_grad():
                  if batch_limit is None:
                      batch_limit = X_rnd.shape[0]
                  Y_rnd_list = []
                  start_idx = 0
                  while start_idx < X_rnd.shape[0]:
                      end_idx = min(
                          start_idx + batch_limit, X_rnd.shape[0]
                      )
                      Y_rnd_curr = acq_function(
                          X_rnd[start_idx:end_idx].to(device=device)
                      ).cpu()
                      Y_rnd_list.append(Y_rnd_curr)
                      start_idx += batch_limit
                  Y_rnd = torch.cat(Y_rnd_list)
              batch_initial_conditions = init_func(
                  X=X_rnd, Y=Y_rnd, n=num_restarts, **init_kwargs
              ).to(device=device)
              if not any(
                  issubclass(w.category, BadInitialCandidatesWarning)
                  for w in ws
              ):
                  return batch_initial_conditions
              if factor < max_factor:
                  factor += 1
                  if seed is not None:
                      seed += 1  # make sure to sample different X_rnd
      warnings.warn(
          "Unable to find non-zero acquisition function values - initial conditions "
          "are being selected randomly.",
          BadInitialCandidatesWarning,
      )
      return batch_initial_conditions
  
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 5 for calling a global function with example usage: gen_batch_initial_conditions(acq_function, bounds, q, num_restarts, raw_samples, fixed_features, options, inequality_constraints, equality_constraints, generator, fixed_X_fantasies) and returns: batch_initial_conditions, batch_initial_conditions