code: def testSampleAndPdfForMeanDirNorthPole(self):
      mean_dir = np.array([1.0, 0.0, 0.0, 0.0, 0.0], dtype=self.dtype)
      concentration = [[0], [5e-2], [0.1], [1], [4]]
      pspherical = power_spherical.PowerSpherical(
          mean_direction=mean_dir,
          concentration=concentration,
          validate_args=True,
          allow_nan_stats=False,
      )
      self.VerifySampleAndPdfConsistency(pspherical)
      self.VerifyPdfWithNumpy(pspherical, atol=2e-4)
      self.VerifySampleMean(mean_dir, concentration, [5, 1])
  
      # Verify the covariance.
      samples = pspherical.sample(int(7e4), seed=test_util.test_seed())
      sample_cov = sample_stats.covariance(samples, sample_axis=0)
      true_cov, sample_cov = self.evaluate(
          [pspherical.covariance(), sample_cov]
      )
      self.assertAllClose(true_cov, sample_cov, rtol=0.15, atol=1.5e-3)
  
imports: import numpy
  from scipy import special
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import kullback_leibler
  from tensorflow_probability.python.distributions import power_spherical
  from tensorflow_probability.python.distributions import spherical_uniform
  from tensorflow_probability.python.distributions import von_mises_fisher
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import tensorshape_util
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.stats import sample_stats
label_desc: Use image node_id 12 for calling the _PowerSphericalTest obj's underlying member method code with example usage: obj.testSampleAndPdfForMeanDirNorthPole() without return types