code: def make_sparse_spd_matrix(
      n_dim=None,
      *,
      alpha=0.95,
      norm_diag=False,
      smallest_coef=0.1,
      largest_coef=0.9,
      sparse_format=None,
      random_state=None,
      dim="deprecated",
  ):
      """Generate a sparse symmetric definite positive matrix.
  
      Read more in the :ref:`User Guide <sample_generators>`.
  
      Parameters
      ----------
      n_dim : int, default=1
          The size of the random matrix to generate.
  
          .. versionchanged:: 1.4
              Renamed from ``dim`` to ``n_dim``.
  
      alpha : float, default=0.95
          The probability that a coefficient is zero (see notes). Larger values
          enforce more sparsity. The value should be in the range 0 and 1.
  
      norm_diag : bool, default=False
          Whether to normalize the output matrix to make the leading diagonal
          elements all 1.
  
      smallest_coef : float, default=0.1
          The value of the smallest coefficient between 0 and 1.
  
      largest_coef : float, default=0.9
          The value of the largest coefficient between 0 and 1.
  
      sparse_format : str, default=None
          String representing the output sparse format, such as 'csc', 'csr', etc.
          If ``None``, return a dense numpy ndarray.
  
          .. versionadded:: 1.4
  
      random_state : int, RandomState instance or None, default=None
          Determines random number generation for dataset creation. Pass an int
          for reproducible output across multiple function calls.
          See :term:`Glossary <random_state>`.
  
      dim : int, default=1
          The size of the random matrix to generate.
  
          .. deprecated:: 1.4
              `dim` is deprecated and will be removed in 1.6.
  
      Returns
      -------
      prec : ndarray or sparse matrix of shape (dim, dim)
          The generated matrix. If ``sparse_format=None``, this would be an ndarray.
          Otherwise, this will be a sparse matrix of the specified format.
  
      See Also
      --------
      make_spd_matrix : Generate a random symmetric, positive-definite matrix.
  
      Notes
      -----
      The sparsity is actually imposed on the cholesky factor of the matrix.
      Thus alpha does not translate directly into the filling fraction of
      the matrix itself.
      """
      random_state = check_random_state(random_state)
  
      # TODO(1.6): remove in 1.6
      # Also make sure to change `n_dim` default back to 1 and deprecate None
      if n_dim is not None and dim != "deprecated":
          raise ValueError(
              "`dim` and `n_dim` cannot be both specified. Please use `n_dim` only "
              "as `dim` is deprecated in v1.4 and will be removed in v1.6."
          )
  
      if dim != "deprecated":
          warnings.warn(
              (
                  "dim was deprecated in version 1.4 and will be removed in 1.6."
                  "Please use ``n_dim`` instead."
              ),
              FutureWarning,
          )
          _n_dim = dim
      elif n_dim is None:
          _n_dim = 1
      else:
          _n_dim = n_dim
  
      chol = -sp.eye(_n_dim)
      aux = sp.random(
          m=_n_dim,
          n=_n_dim,
          density=1 - alpha,
          data_rvs=lambda x: random_state.uniform(
              low=smallest_coef, high=largest_coef, size=x
          ),
          random_state=random_state,
      )
      # We need to avoid "coo" format because it does not support slicing
      aux = sp.tril(aux, k=-1, format="csc")
  
      # Permute the lines: we don't want to have asymmetries in the final
      # SPD matrix
      permutation = random_state.permutation(_n_dim)
      aux = aux[permutation].T[permutation]
      chol += aux
      prec = chol.T @ chol
  
      if norm_diag:
          # Form the diagonal vector into a row matrix
          d = sp.diags(1.0 / np.sqrt(prec.diagonal()))
          prec = d @ prec @ d
  
      if sparse_format is None:
          return prec.toarray()
      else:
          return prec.asformat(sparse_format)
  
imports: import array
  import numbers
  import warnings
  from collections.abc import Iterable
  from numbers import Integral, Real
  import numpy
  import scipy.sparse
  from scipy import linalg
  from ..preprocessing import MultiLabelBinarizer
  from ..utils import check_array, check_random_state
  from ..utils import shuffle
  from ..utils._param_validation import Hidden, Interval, StrOptions, validate_params
  from ..utils.random import sample_without_replacement
label_desc: Use image node_id 16 for calling a global function with example usage: make_sparse_spd_matrix(n_dim) and returns: prec, prec