text: # This script calls [PaCMAP](https://arxiv.org/abs/1910.00204) functions to operate on the TopOGraph class
  # TriMAP was originally implemented by Yingfan Wang at https://github.com/YingfanWang/PaCMAP.
  # This is rather a modular adaptation, and does not change much of the optimization algorithm.
  # The main change is the similarity metric used to learn the lower-dimensional layout.
  # License: Apache
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  import time
  from numpy import random
  try:
      from typing import Literal
  except ImportError:
      try:
          from typing_extensions import Literal
      except ImportError:
  
          class LiteralMeta(type):
              def __getitem__(cls, values):
                  if not isinstance(values, tuple):
                      values = (values,)
                  return type('Literal_', (Literal,), dict(__args__=values))
  
  
          class Literal(metaclass=LiteralMeta):
              pass
  
  # PaCMAP
  
  def PaCMAP(data=None,
                 init=None,
                 n_dims=2,
                 n_neighbors=10,
                 MN_ratio=0.5,
                 FP_ratio=2.0,
                 pair_neighbors=None,
                 pair_MN=None,
                 pair_FP=None,
                 distance="angular",
                 lr=1.0,
                 num_iters=450,
                 verbose=False,
                 intermediate=False):
      """
      Dimensionality Reduction Using Pairwise-controlled Manifold Approximation and Projectio
  
      Inputs
      ------
      data : np.array with the data to be reduced
  
      init : the initialization of the lower dimensional embedding. One of "pca" or "random", or a user-provided numpy ndarray with the shape (N, 2). Default to "random".
  
      n_dims :  the number of dimension of the output. Default to 2.
  
      n_neighbors : the number of neighbors considered in the k-Nearest Neighbor graph. Default to 10 for dataset whose
          sample size is smaller than 10000. For large dataset whose sample size (n) is larger than 10000, the default value
          is: 10 + 15 * (log10(n) - 4).
  
      MN_ratio :  the ratio of the number of mid-near pairs to the number of neighbors, n_MN = \lfloor n_neighbors * MN_ratio \rfloor .
       Default to 0.5.
  
      FP_ratio : the ratio of the number of further pairs to the number of neighbors, n_FP = \lfloor n_neighbors * FP_ratio \rfloor Default to 2.
  
      distance : Distance measure ('euclidean' (default), 'manhattan', 'angular',
      'hamming')
  
  
      lr : Optimization method ('sd': steepest descent,  'momentum': GD
      with momentum, 'dbd': GD with momentum delta-bar-delta (default))
  
      num_iters : number of iterations. Default to 450. 450 iterations is enough for most dataset to converge.
  
      pair_neighbors, pair_MN and pair_FP: pre-specified neighbor pairs, mid-near points, and further pairs. Allows user to use their own graphs. Default to None.
  
      verbose : controls verbosity (default False)
  
      intermediate : whether pacmap should also output the intermediate stages of the optimization process of the lower dimension embedding. If True, then the output will be a numpy array of the size (n, n_dims, 13), where each slice is a "screenshot" of the output embedding at a particular number of steps, from [0, 10, 30, 60, 100, 120, 140, 170, 200, 250, 300, 350, 450].
  
      random_state :
          RandomState object (default None)
  
      """
  
  
      try:
          import pacmap
          _have_pacmap = True
      except ImportError('TriMAP is needed for this embedding. Install it with `pip install trimap`'):
          return print('TriMAP is needed for this embedding. Install it with `pip install trimap`')
  
      pacmap_emb = pacmap.PaCMAP(n_dims=n_dims,
                                 n_neighbors=n_neighbors,
                                 MN_ratio=MN_ratio,
                                 FP_ratio=FP_ratio,
                                 pair_neighbors=pair_neighbors,
                                 pair_MN=pair_MN,
                                 pair_FP=pair_FP,
                                 distance=distance,
                                 lr=lr,
                                 num_iters=num_iters,
                                 verbose=verbose,
                                 intermediate=intermediate).fit_transform(X=data, init=init)
  
      return pacmap_emb
  