code: def test_fit_predict_non_regular_gram_matrix() -> None:
      # This test case validates that the GP class works even when the Gram matrix is non-regular,
      # which typically orrcurs when multiple trials share the same parameters.
  
      trials = [
          create_trial(
              value=1.0,
              distributions={
                  "bacon": FloatDistribution(-1.0, 1.0),
                  "egg": FloatDistribution(-1.0, 1.0),
              },
              params={
                  "bacon": 1.0,
                  "egg": 0.0,
              },
          ),
          create_trial(
              value=1.0,
              distributions={
                  "bacon": FloatDistribution(-1.0, 1.0),
                  "egg": FloatDistribution(-1.0, 1.0),
              },
              params={
                  "bacon": 1.0,
                  "egg": 0.0,
              },
          ),
      ]
  
      gp = _BoTorchGaussianProcess()
      gp.fit(trials)
      gp.predict_mean_std(trials)
  
imports: from optuna.distributions import FloatDistribution
  from optuna.terminator.improvement.gp.botorch import _BoTorchGaussianProcess
  from optuna.trial import create_trial
label_desc: Use image node_id 4 for calling a global function with example usage: test_fit_predict_non_regular_gram_matrix() without return types