code: def dkl_gaussian(m1, P1, m2, P2):
      """
      Returns the KL divergence between gausians densities
  
      Parameters
      ----------
      m1: array of shape (n),
          the mean parameter of the first density
      P1: array of shape(n,n),
          the precision parameters of the first density
      m2: array of shape (n),
          the mean parameter of the second density
      P2: array of shape(n,n),
          the precision parameters of the second density
      """
      tiny = 1.0e-15
      dim = np.size(m1)
      if m1.shape != m2.shape:
          raise ValueError("incompatible dimensions for m1 and m2")
      if P1.shape != P2.shape:
          raise ValueError("incompatible dimensions for P1 and P2")
      if P1.shape[0] != dim:
          raise ValueError("incompatible dimensions for m1 and P1")
  
      d1 = max(detsh(P1), tiny)
      d2 = max(detsh(P2), tiny)
      dkl = np.log(d1 / d2) + np.trace(np.dot(P2, inv(P1))) - dim
      dkl += np.dot(np.dot((m1 - m2).T, P2), (m1 - m2))
      dkl /= 2
      return dkl
  
imports: import math
  import numpy
  import numpy.random
  from scipy.linalg import cholesky, eigvalsh, inv
  from scipy.special import gammaln
  from .gmm import GMM
  from .utils import kmeans
label_desc: Use image node_id 9 for calling a global function with example usage: dkl_gaussian(m1, P1, m2, P2) and returns: dkl