code: def make_sparse_spd_matrix(
      dim=1,
      *,
      alpha=0.95,
      norm_diag=False,
      smallest_coef=0.1,
      largest_coef=0.9,
      random_state=None,
  ):
      """Generate a sparse symmetric definite positive matrix.
  
      Read more in the :ref:`User Guide <sample_generators>`.
  
      Parameters
      ----------
      dim : int, default=1
          The size of the random matrix to generate.
  
      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.
  
      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>`.
  
      Returns
      -------
      prec : sparse matrix of shape (dim, dim)
          The generated matrix.
  
      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)
  
      chol = -np.eye(dim)
      aux = random_state.uniform(size=(dim, dim))
      aux[aux < alpha] = 0
      aux[aux > alpha] = smallest_coef + (
          largest_coef - smallest_coef
      ) * random_state.uniform(size=np.sum(aux > alpha))
      aux = np.tril(aux, k=-1)
  
      # Permute the lines: we don't want to have asymmetries in the final
      # SPD matrix
      permutation = random_state.permutation(dim)
      aux = aux[permutation].T[permutation]
      chol += aux
      prec = np.dot(chol.T, chol)
  
      if norm_diag:
          # Form the diagonal vector into a row matrix
          d = np.diag(prec).reshape(1, prec.shape[0])
          d = 1.0 / np.sqrt(d)
  
          prec *= d
          prec *= d.T
  
      return prec
  
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(dim) and returns: prec