code: def _test(self, xp):
      v_min, v_max = (-1, 1)
      n_atoms = 3
      z = xp.linspace(v_min, v_max, num=n_atoms, dtype=np.float32)
      y = xp.asarray(
          [
              [-1, 0, 1],
              [1, -1, 0],
              [1, 1, 1],
              [-1, -1, -1],
              [0, 0, 0],
              [-0.5, 0, 1],
              [-0.5, 0, 0.5],
          ],
          dtype=np.float32,
      )
      y_probs = xp.asarray(
          [
              [0.5, 0.2, 0.3],
              [0.5, 0.2, 0.3],
              [0.5, 0.2, 0.3],
              [0.5, 0.2, 0.3],
              [0.5, 0.2, 0.3],
              [0.5, 0.2, 0.3],
              [0.5, 0.2, 0.3],
          ],
          dtype=np.float32,
      )
  
      proj_gt = xp.asarray(
          [
              [0.5, 0.2, 0.3],
              [0.2, 0.3, 0.5],
              [0.0, 0.0, 1.0],
              [1.0, 0.0, 0.0],
              [0.0, 1.0, 0.0],
              [0.25, 0.45, 0.3],
              [0.25, 0.6, 0.15],
          ],
          dtype=np.float32,
      )
  
      proj = categorical_dqn._apply_categorical_projection(
          y, y_probs, z
      )
      xp.testing.assert_allclose(proj, proj_gt, atol=1e-5)
  
imports: import unittest
  import chainer
  import chainer.links
  from chainer import testing
  import numpy
  import basetest_dqn_like
  from basetest_training import _TestBatchTrainingMixin
  import chainerrl
  from chainerrl.agents import categorical_dqn
  from chainerrl.agents.categorical_dqn import compute_value_loss
  from chainerrl.agents.categorical_dqn import compute_weighted_value_loss
  from chainerrl.agents import CategoricalDQN
label_desc: Use image node_id 1 for calling the TestApplyCategoricalProjectionToManualCases obj's underlying member method code with example usage: obj._test(xp) without return types