text: # Copyright 2016 the GPflow authors.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  # http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  import numpy as np
  import pytest
  
  import gpflow
  from gpflow.inducing_variables import InducingPoints
  from gpflow.kernels import Matern32
  
  rng = np.random.RandomState(0)
  
  
  class ModelSetup:
      def __init__(self,
                   model_class,
                   kernel=Matern32(),
                   likelihood=gpflow.likelihoods.Gaussian(),
                   whiten=None,
                   q_diag=None,
                   requires_inducing_variables=True,
                   requires_data=False,
                   requires_likelihood=True):
          self.model_class = model_class
          self.kernel = kernel
          self.likelihood = likelihood
          self.whiten = whiten
          self.q_diag = q_diag
          self.requires_inducing_variables = requires_inducing_variables
          self.requires_data = requires_data
          self.requires_likelihood = requires_likelihood
  
      def get_model(self, Z, num_latent, data=None):
          params = dict(kernel=self.kernel, num_latent=num_latent)
  
          if self.whiten is not None and self.q_diag is not None:
              params.update(inducing_variable=Z, whiten=self.whiten, q_diag=self.q_diag)
  
          if self.requires_inducing_variables:
              params.update(dict(inducing_variable=Z))
  
          if self.requires_data:
              params.update(dict(data=data))
  
          if self.requires_likelihood:
              params.update(dict(likelihood=self.likelihood))
  
          return self.model_class(**params)
  
      def __repr__(self):
          return f"ModelSetup({self.model_class.__name__}, {self.whiten}, {self.q_diag})"
  
  
  model_setups = [
      ModelSetup(model_class=gpflow.models.SVGP, whiten=False, q_diag=True),
      ModelSetup(model_class=gpflow.models.SVGP, whiten=True, q_diag=False),
      ModelSetup(model_class=gpflow.models.SVGP, whiten=True, q_diag=True),
      ModelSetup(model_class=gpflow.models.SVGP, whiten=False, q_diag=False),
      ModelSetup(model_class=gpflow.models.SGPR, requires_data=True, requires_likelihood=False),
      ModelSetup(model_class=gpflow.models.VGP, requires_inducing_variables=False, requires_data=True),
      #     ModelSetup(model_class=gpflow.models.GPRF),
      ModelSetup(model_class=gpflow.models.GPMC, requires_data=True, requires_inducing_variables=False),
      ModelSetup(model_class=gpflow.models.SGPMC, requires_data=True, requires_inducing_variables=True)
  ]
  
  
  @pytest.mark.parametrize('Ntrain, Ntest, D', [[100, 10, 2]])
  def test_gaussian_mean_and_variance(Ntrain, Ntest, D):
      data = rng.randn(Ntrain, D), rng.randn(Ntrain, 1)
      Xtest, _ = rng.randn(Ntest, D), rng.randn(Ntest, 1)
      kernel = Matern32() + gpflow.kernels.White()
      model_gp = gpflow.models.GPR(data, kernel=kernel)
  
      mu_f, var_f = model_gp.predict_f(Xtest)
      mu_y, var_y = model_gp.predict_y(Xtest)
  
      assert np.allclose(mu_f, mu_y)
      assert np.allclose(var_f, var_y - 1.)
  
  
  @pytest.mark.parametrize('Ntrain, Ntest, D', [[100, 10, 2]])
  def test_gaussian_log_density(Ntrain, Ntest, D):
      data = rng.randn(Ntrain, D), rng.randn(Ntrain, 1)
      Xtest, Ytest = rng.randn(Ntest, D), rng.randn(Ntest, 1)
      kernel = Matern32() + gpflow.kernels.White()
      model_gp = gpflow.models.GPR(data, kernel=kernel)
  
      mu_y, var_y = model_gp.predict_y(Xtest)
      data = Xtest, Ytest
      log_density = model_gp.predict_log_density(data)
      log_density_hand = (-0.5 * np.log(2 * np.pi) - 0.5 * np.log(var_y) - 0.5 * np.square(mu_y - Ytest) / var_y)
  
      assert np.allclose(log_density_hand, log_density)
  
  
  @pytest.mark.parametrize('input_dim, output_dim, N, Ntest, M', [[3, 2, 20, 30, 5]])
  def test_gaussian_full_cov(input_dim, output_dim, N, Ntest, M):
      covar_shape = (output_dim, Ntest, Ntest)
      X, Y, Z = rng.randn(N, input_dim), rng.randn(N, output_dim), rng.randn(M, input_dim)
      Xtest = rng.randn(Ntest, input_dim)
      kernel = Matern32()
      model_gp = gpflow.models.GPR([X, Y], kernel=kernel)
  
      mu1, var = model_gp.predict_f(Xtest, full_cov=False)
      mu2, covar = model_gp.predict_f(Xtest, full_cov=True)
  
      assert np.allclose(mu1, mu2, atol=1.e-10)
      assert covar.shape == covar_shape
      assert var.shape == (Ntest, output_dim)
      for i in range(output_dim):
          assert np.allclose(var[:, i], np.diag(covar[i, :, :]))
  
  
  @pytest.mark.skip(reason='GPR model is not ready')
  @pytest.mark.parametrize('input_dim, output_dim, N, Ntest, M, num_samples', [[3, 2, 20, 30, 5, 5]])
  def test_gaussian_full_cov_samples(input_dim, output_dim, N, Ntest, M, num_samples):
      samples_shape = (num_samples, Ntest, output_dim)
      X, Y, _ = rng.randn(N, input_dim), rng.randn(N, output_dim), rng.randn(M, input_dim)
      Xtest = rng.randn(Ntest, input_dim)
      kernel = Matern32()
      model_gp = gpflow.models.GPR([X, Y], kernel=kernel)
  
      samples = model_gp.predict_f_samples(Xtest, num_samples)
      assert samples.shape == samples_shape
  
  
  @pytest.mark.parametrize('model_setup', model_setups)
  @pytest.mark.parametrize('input_dim', [3])
  @pytest.mark.parametrize('output_dim', [2])
  @pytest.mark.parametrize('N', [20])
  @pytest.mark.parametrize('Ntest', [30])
  @pytest.mark.parametrize('M', [5])
  def test_other_models_full_cov(model_setup, input_dim, output_dim, N, Ntest, M):
      covar_shape = (output_dim, Ntest, Ntest)
      X, Y = rng.randn(N, input_dim), rng.randn(N, output_dim)
      Z = InducingPoints(rng.randn(M, input_dim))
      Xtest = rng.randn(Ntest, input_dim)
      model_gp = model_setup.get_model(Z, num_latent=output_dim, data=(X, Y))
  
      mu1, var = model_gp.predict_f(Xtest, full_cov=False)
      mu2, covar = model_gp.predict_f(Xtest, full_cov=True)
  
      assert np.allclose(mu1, mu2, atol=1.e-10)
      assert covar.shape == covar_shape
      assert var.shape == (Ntest, output_dim)
      for i in range(output_dim):
          assert np.allclose(var[:, i], np.diag(covar[i, :, :]))
  
  
  @pytest.mark.parametrize('model_setup', model_setups)
  @pytest.mark.parametrize('input_dim', [3])
  @pytest.mark.parametrize('output_dim', [2])
  @pytest.mark.parametrize('N', [20])
  @pytest.mark.parametrize('Ntest', [30])
  @pytest.mark.parametrize('M', [5])
  @pytest.mark.parametrize('num_samples', [5])
  def test_other_models_full_cov_samples(model_setup, input_dim, output_dim, N, Ntest, M, num_samples):
      samples_shape = (num_samples, Ntest, output_dim)
      X, Y, Z = rng.randn(N, input_dim), rng.randn(N, output_dim), rng.randn(M, input_dim)
      Xtest = rng.randn(Ntest, input_dim)
      model_gp = model_setup.get_model(Z, num_latent=output_dim, data=(X, Y))
  
      samples = model_gp.predict_f_samples(Xtest, num_samples)
      assert samples.shape == samples_shape
  