code: def linear_kernel(X, Y=None):
      """
      Compute the linear kernel between X and Y.
  
      Read more in the :ref:`User Guide <linear_kernel>`.
  
      Parameters
      ----------
      X : array of shape (n_samples_1, n_features)
  
      Y : array of shape (n_samples_2, n_features)
  
      Returns
      -------
      Gram matrix : array of shape (n_samples_1, n_samples_2)
      """
      X, Y = check_pairwise_arrays(X, Y)
      return safe_sparse_dot(X, Y.T, dense_output=True)
  
imports: import itertools
  import numpy
  from scipy.spatial import distance
  from scipy.sparse import csr_matrix
  from scipy.sparse import issparse
  from ..utils import check_array
  from ..utils import gen_even_slices
  from ..utils import gen_batches
  from ..utils.fixes import partial
  from ..utils.extmath import row_norms, safe_sparse_dot
  from ..preprocessing import normalize
  from ..externals.joblib import Parallel
  from ..externals.joblib import delayed
  from ..externals.joblib import cpu_count
  from .pairwise_fast import _chi2_kernel_fast, _sparse_manhattan
label_desc: Use image node_id 13 for calling a global function with example usage: linear_kernel(X, Y) and returns: safe_sparse_dot