def test_pidon_operator_on_spherical_pde(): set_random_seed(0) diff_eq = DiffusionEquation(3) mesh = Mesh( [(1., 11.), (0., 2 * np.pi), (.25 * np.pi, .75 * np.pi)], [2., np.pi / 5., np.pi / 4], CoordinateSystem.SPHERICAL) bcs = [ (DirichletBoundaryCondition( lambda x, t: np.ones((len(x), 1)), is_static=True), DirichletBoundaryCondition( lambda x, t: np.full((len(x), 1), 1. / 11.), is_static=True)), (NeumannBoundaryCondition( lambda x, t: np.zeros((len(x), 1)), is_static=True), NeumannBoundaryCondition( lambda x, t: np.zeros((len(x), 1)), is_static=True)), (NeumannBoundaryCondition( lambda x, t: np.zeros((len(x), 1)), is_static=True), NeumannBoundaryCondition( lambda x, t: np.zeros((len(x), 1)), is_static=True)) ] cp = ConstrainedProblem(diff_eq, mesh, bcs) ic = ContinuousInitialCondition(cp, lambda x: 1. / x[:, :1]) t_interval = (0., .5) ivp = InitialValueProblem(cp, t_interval, ic) sampler = UniformRandomCollocationPointSampler() pidon = PIDONOperator(sampler, .001, True) training_loss_history, test_loss_history = pidon.train( cp, t_interval, training_data_args=DataArgs( y_0_functions=[ic.y_0], n_domain_points=20, n_boundary_points=10, n_batches=1 ), model_args=ModelArgs( latent_output_size=20, branch_hidden_layer_sizes=[30, 30], trunk_hidden_layer_sizes=[30, 30], ), optimization_args=OptimizationArgs( optimizer=optimizers.Adam(learning_rate=2e-5), epochs=3, verbose=False ) ) assert len(training_loss_history) == 3 for i in range(2): assert np.all( training_loss_history[i + 1].weighted_total_loss.numpy() < training_loss_history[i].weighted_total_loss.numpy()) solution = pidon.solve(ivp) assert solution.d_t == .001 assert solution.discrete_y().shape == (500, 6, 11, 3, 1)
def test_discrete_initial_condition_2d_pde(): diff_eq = WaveEquation(2) mesh = Mesh([(0., 2.), (0., 2.)], [1., 1.]) bcs = [(DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (0., 2.)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (1., 2.)), is_static=True)), (DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (3., 2.)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (4., 2.)), is_static=True))] cp = ConstrainedProblem(diff_eq, mesh, bcs) initial_condition = DiscreteInitialCondition(cp, np.zeros((3, 3, 2)), True) y = initial_condition.y_0(np.array([1.5, .5]).reshape((1, 2))) assert np.allclose(y, [1.75, 1.5]) y_0_vertices = initial_condition.discrete_y_0(True) assert y_0_vertices.shape == (3, 3, 2) assert np.all(y_0_vertices[0, 1:-1, 0] == 0.) assert np.all(y_0_vertices[0, 1:-1, 1] == 2.) assert np.all(y_0_vertices[-1, 1:-1, 0] == 1.) assert np.all(y_0_vertices[-1, 1:-1, 1] == 2.) assert np.all(y_0_vertices[:, 0, 0] == 3.) assert np.all(y_0_vertices[:, 0, 1] == 2.) assert np.all(y_0_vertices[:, -1, 0] == 4.) assert np.all(y_0_vertices[:, -1, 1] == 2.) assert np.all(y_0_vertices[1:-1, 1:-1, :] == 0.) y_0_cell_centers = initial_condition.discrete_y_0(False) assert y_0_cell_centers.shape == (2, 2, 2)
def test_fdm_operator_on_2d_pde(): diff_eq = NavierStokesEquation(5000.) mesh = Mesh([(0., 10.), (0., 10.)], [1., 1.]) bcs = [(DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (1., .1, None, None)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (0., 0., None, None)), is_static=True)), (DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (0., 0., None, None)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (0., 0., None, None)), is_static=True))] cp = ConstrainedProblem(diff_eq, mesh, bcs) ic = ContinuousInitialCondition(cp, lambda x: np.zeros((len(x), 4))) ivp = InitialValueProblem(cp, (0., 10.), ic) op = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .25) solution = op.solve(ivp) assert solution.vertex_oriented assert solution.d_t == .25 assert solution.discrete_y().shape == (40, 11, 11, 4) assert solution.discrete_y(False).shape == (40, 10, 10, 4)
def test_gaussian_initial_condition_2d_pde(): diff_eq = WaveEquation(2) mesh = Mesh([(0., 2.), (0., 2.)], [1., 1.]) bcs = [(DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (0., 2.)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (1., 2.)), is_static=True)), (DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (3., 2.)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (4., 2.)), is_static=True))] cp = ConstrainedProblem(diff_eq, mesh, bcs) initial_condition = GaussianInitialCondition(cp, [ (np.array([1., 1.]), np.array([[1., 0.], [0., 1.]])), (np.array([1., 1.]), np.array([[.75, .25], [.25, .75]])), ], [1., 2.]) x_coordinates = np.array([[1., 1.], [.5, 1.5]]) expected_y_0 = [[.15915494, .45015816], [.12394999, .27303472]] actual_y_0 = initial_condition.y_0(x_coordinates) assert np.allclose(actual_y_0, expected_y_0) expected_vertex_discrete_y_0 = [[[3., 2.], [0., 2.], [4., 2.]], [[3., 2.], [.15915494, .45015816], [4., 2.]], [[3., 2.], [1., 2.], [4., 2.]]] actual_vertex_discrete_y_0 = initial_condition.discrete_y_0(True) assert np.allclose(actual_vertex_discrete_y_0, expected_vertex_discrete_y_0) expected_cell_discrete_y_0 = [[[.12394999, .35058353], [.12394999, .27303472]], [[.12394999, .27303472], [.12394999, .35058353]]] actual_cell_discrete_y_0 = initial_condition.discrete_y_0(False) assert np.allclose(actual_cell_discrete_y_0, expected_cell_discrete_y_0)
def test_continuous_initial_condition_1d_pde(): diff_eq = DiffusionEquation(1) mesh = Mesh([(0., 20.)], [.1]) bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 1)), is_static=True), DirichletBoundaryCondition(lambda x, t: np.full((len(x), 1), 1.5), is_static=True))] cp = ConstrainedProblem(diff_eq, mesh, bcs) initial_condition = ContinuousInitialCondition( cp, lambda x: np.exp(-np.square(np.array(x) - 10.) / (2 * 5**2))) assert np.isclose(initial_condition.y_0(np.full((1, 1), 10.)), 1.) assert np.isclose( initial_condition.y_0(np.full((1, 1), np.sqrt(50) + 10.)), np.e**-1) assert np.allclose(initial_condition.y_0(np.full((5, 1), 10.)), np.ones((5, 1))) y_0_vertices = initial_condition.discrete_y_0(True) assert y_0_vertices.shape == (201, 1) assert y_0_vertices[0, 0] == 0. assert y_0_vertices[-1, 0] == 1.5 assert y_0_vertices[100, 0] == 1. assert np.all(0. < y_0_vertices[1:100, 0]) \ and np.all(y_0_vertices[1:100, 0] < 1.) assert np.all(0. < y_0_vertices[101:-1, 0]) \ and np.all(y_0_vertices[101:-1, 0] < 1.) y_0_cell_centers = initial_condition.discrete_y_0(False) assert y_0_cell_centers.shape == (200, 1) assert np.all(0. < y_0_cell_centers) and np.all(y_0_cell_centers < 1.)
def test_pidon_operator_on_pde_system(): set_random_seed(0) diff_eq = NavierStokesEquation() mesh = Mesh([(-2.5, 2.5), (0., 4.)], [1., 1.]) ic_function = vectorize_ic_function(lambda x: [ 2. * x[0] - 4., 2. * x[0] ** 2 + 3. * x[1] - x[0] * x[1] ** 2, 4. * x[0] - x[1] ** 2, 2. * x[0] * x[1] - 3. ]) bcs = [ (DirichletBoundaryCondition( lambda x, t: ic_function(x), is_static=True), DirichletBoundaryCondition( lambda x, t: ic_function(x), is_static=True)) ] * 2 cp = ConstrainedProblem(diff_eq, mesh, bcs) ic = ContinuousInitialCondition(cp, ic_function) t_interval = (0., .5) ivp = InitialValueProblem(cp, t_interval, ic) sampler = UniformRandomCollocationPointSampler() pidon = PIDONOperator(sampler, .001, True) training_loss_history, test_loss_history = pidon.train( cp, t_interval, training_data_args=DataArgs( y_0_functions=[ic.y_0], n_domain_points=20, n_boundary_points=10, n_batches=1 ), model_args=ModelArgs( latent_output_size=20, branch_hidden_layer_sizes=[20, 20], trunk_hidden_layer_sizes=[20, 20], ), optimization_args=OptimizationArgs( optimizer=optimizers.Adam(learning_rate=1e-5), epochs=3, verbose=False ) ) assert len(training_loss_history) == 3 for i in range(2): assert np.all( training_loss_history[i + 1].weighted_total_loss.numpy() < training_loss_history[i].weighted_total_loss.numpy()) solution = pidon.solve(ivp) assert solution.d_t == .001 assert solution.discrete_y().shape == (500, 6, 5, 4)
def test_dirichlet_boundary_condition(): bc = DirichletBoundaryCondition(lambda x, t: t * x) assert not bc.is_static assert bc.has_y_condition assert not bc.has_d_y_condition assert np.allclose( bc._y_condition(np.ones((2, 1)), 5.), np.full((2, 1), 5.)) with pytest.raises(RuntimeError): bc.d_y_condition(np.ones((2, 1)), 5.)
def test_cp_pde_with_wrong_boundary_constraint_width(): diff_eq = WaveEquation(2) mesh = Mesh([(0., 5.), (-5., 5.)], [.1, .2]) bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 1)), is_static=True), ) * 2] * 2 with pytest.raises(ValueError): ConstrainedProblem(diff_eq, mesh, bcs) bcs = [(DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: [0.]), is_static=True), ) * 2] * 2 with pytest.raises(ValueError): ConstrainedProblem(diff_eq, mesh, bcs)
def test_cp_pde_with_wrong_boundary_constraint_length(): diff_eq = DiffusionEquation(2) mesh = Mesh([(0., 5.), (-5., 5.)], [.1, .2]) static_bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((13, 1)), is_static=True), ) * 2] * 2 with pytest.raises(ValueError): ConstrainedProblem(diff_eq, mesh, static_bcs) dynamic_bcs = [ (DirichletBoundaryCondition(lambda x, t: np.zeros((13, 1))), ) * 2 ] * 2 cp = ConstrainedProblem(diff_eq, mesh, dynamic_bcs) with pytest.raises(ValueError): cp.create_boundary_constraints(True, 0.)
def test_discrete_initial_condition_pde_with_wrong_shape(): diff_eq = WaveEquation(1) mesh = Mesh([(0., 10.)], [1.]) bcs = [(DirichletBoundaryCondition(lambda x: np.zeros((len(x), 2))), ) * 2] cp = ConstrainedProblem(diff_eq, mesh, bcs) with pytest.raises(ValueError): DiscreteInitialCondition(cp, np.zeros((10, 2)), vertex_oriented=True)
def test_continuous_initial_condition_pde_with_wrong_shape(): diff_eq = WaveEquation(1) mesh = Mesh([(0., 10.)], [1.]) bcs = [(DirichletBoundaryCondition(lambda x: np.zeros((len(x), 2))), ) * 2] cp = ConstrainedProblem(diff_eq, mesh, bcs) with pytest.raises(ValueError): ContinuousInitialCondition(cp, lambda x: np.zeros((3, 2)))
def test_gaussian_initial_condition_pde_with_wrong_means_and_cov_length(): diff_eq = WaveEquation(1) mesh = Mesh([(0., 10.)], [1.]) bcs = [(DirichletBoundaryCondition(lambda x: np.zeros((len(x), 2))), ) * 2] cp = ConstrainedProblem(diff_eq, mesh, bcs) with pytest.raises(ValueError): GaussianInitialCondition(cp, [(np.array([1.]), np.array([[1.]]))] * 1)
def test_auto_regression_operator_on_pde(): set_random_seed(0) diff_eq = WaveEquation(2) mesh = Mesh([(-5., 5.), (-5., 5.)], [1., 1.]) bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 2)), is_static=True), DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 2)), is_static=True))] * 2 cp = ConstrainedProblem(diff_eq, mesh, bcs) ic = GaussianInitialCondition( cp, [(np.array([0., 2.5]), np.array([[.1, 0.], [0., .1]]))] * 2, [3., .0]) ivp = InitialValueProblem(cp, (0., 10.), ic) oracle = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .1) ref_solution = oracle.solve(ivp) ml_op = AutoRegressionOperator(2.5, True) ml_op.train( ivp, oracle, SKLearnKerasRegressor( DeepONet([ np.prod(cp.y_shape(True)).item(), 100, 50, diff_eq.y_dimension * 10 ], [1 + diff_eq.x_dimension, 50, 50, diff_eq.y_dimension * 10], diff_eq.y_dimension), optimizer=optimizers.Adam( learning_rate=optimizers.schedules.ExponentialDecay( 1e-2, decay_steps=500, decay_rate=.95)), batch_size=968, epochs=500, ), 20, lambda t, y: y + np.random.normal(0., t / 75., size=y.shape)) ml_solution = ml_op.solve(ivp) assert ml_solution.vertex_oriented assert ml_solution.d_t == 2.5 assert ml_solution.discrete_y().shape == (4, 11, 11, 2) diff = ref_solution.diff([ml_solution]) assert np.all(diff.matching_time_points == np.linspace(2.5, 10., 4)) assert np.max(np.abs(diff.differences[0])) < .5
def test_ode_operator_on_pde(): diff_eq = DiffusionEquation(1, 1.5) mesh = Mesh([(0., 10.)], [.1]) bcs = [ (NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1))), DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 1)))), ] cp = ConstrainedProblem(diff_eq, mesh, bcs) ic = GaussianInitialCondition(cp, [(np.array([5.]), np.array([[2.5]]))], [20.]) ivp = InitialValueProblem(cp, (0., 10.), ic) op = ODEOperator('RK23', 2.5e-3) with pytest.raises(ValueError): op.solve(ivp)
def test_fdm_operator_on_pde_with_dynamic_boundary_conditions(): diff_eq = DiffusionEquation(1, 1.5) mesh = Mesh([(0., 10.)], [1.]) bcs = [ (NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1))), DirichletBoundaryCondition(lambda x, t: np.full((len(x), 1), t / 5.)) ), ] cp = ConstrainedProblem(diff_eq, mesh, bcs) ic = GaussianInitialCondition(cp, [(np.array([5.]), np.array([[2.5]]))], [20.]) ivp = InitialValueProblem(cp, (0., 10.), ic) op = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .5) solution = op.solve(ivp) y = solution.discrete_y() assert solution.vertex_oriented assert solution.d_t == .5 assert y.shape == (20, 11, 1) assert solution.discrete_y(False).shape == (20, 10, 1) assert np.isclose(y[0, -1, 0], .1) assert np.isclose(y[-1, -1, 0], 2.)
def test_cp_2d_pde(): diff_eq = WaveEquation(2) mesh = Mesh([(2., 6.), (-3., 3.)], [.1, .2]) bcs = ((DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (999., None)), is_static=True), NeumannBoundaryCondition( vectorize_bc_function(lambda x, t: (100., -100.)), is_static=True)), (NeumannBoundaryCondition( vectorize_bc_function(lambda x, t: (-x[0], None)), is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (x[0], x[1])), is_static=True))) cp = ConstrainedProblem(diff_eq, mesh, bcs) assert cp.are_all_boundary_conditions_static assert cp.are_there_boundary_conditions_on_y y_vertices = np.full(cp.y_shape(True), 13.) apply_constraints_along_last_axis(cp.static_y_vertex_constraints, y_vertices) assert np.all(y_vertices[0, :-1, 0] == 999.) assert np.all(y_vertices[0, :-1, 1] == 13.) assert np.all(y_vertices[-1, :-1, :] == 13.) assert np.all(y_vertices[1:, 0, :] == 13.) assert np.allclose(y_vertices[:, -1, 0], np.linspace(2., 6., y_vertices.shape[0])) assert np.all(y_vertices[:, -1, 1] == 3.) y_vertices = np.zeros(cp.y_shape(True)) diff = ThreePointCentralDifferenceMethod() d_y_boundary_constraints = cp.static_boundary_vertex_constraints[1] d_y_0_over_d_x_0 = diff.gradient(y_vertices[..., :1], mesh, 0, d_y_boundary_constraints[:, :1]) assert np.all(d_y_0_over_d_x_0[-1, :, :] == 100.) assert np.all(d_y_0_over_d_x_0[:-1, :, :] == 0.) d_y_0_over_d_x_1 = diff.gradient(y_vertices[..., :1], mesh, 1, d_y_boundary_constraints[:, :1]) assert np.allclose(d_y_0_over_d_x_1[:, 0, 0], np.linspace(-2., -6., y_vertices.shape[0])) assert np.all(d_y_0_over_d_x_1[:, 1:, :] == 0.) d_y_1_over_d_x_0 = diff.gradient(y_vertices[..., 1:], mesh, 0, d_y_boundary_constraints[:, 1:]) assert np.all(d_y_1_over_d_x_0[-1, :, :] == -100.) assert np.all(d_y_1_over_d_x_0[:-1, :, :] == 0.) d_y_1_over_d_x_1 = diff.gradient(y_vertices[..., 1:], mesh, 1, d_y_boundary_constraints[:, 1:]) assert np.all(d_y_1_over_d_x_1 == 0.) y_boundary_cell_constraints = cp.static_boundary_cell_constraints[0] assert np.all(y_boundary_cell_constraints[0, 0][0].mask == [True] * cp.y_cells_shape[1]) assert np.all(y_boundary_cell_constraints[0, 0][0].values == 999.) assert np.all(y_boundary_cell_constraints[0, 1][0].mask == [False] * cp.y_cells_shape[1]) assert y_boundary_cell_constraints[0, 1][0].values.size == 0 assert np.all(y_boundary_cell_constraints[1, 0][1].mask == [True] * cp.y_cells_shape[0]) assert np.allclose(y_boundary_cell_constraints[1, 0][1].values, np.linspace(2.05, 5.95, cp.y_cells_shape[0])) assert np.all(y_boundary_cell_constraints[1, 1][1].mask == [True] * cp.y_cells_shape[0]) assert np.all(y_boundary_cell_constraints[1, 1][1].values == 3.) assert y_boundary_cell_constraints[1, 0][0] is None
def test_cp_3d_pde(): mesh = Mesh([(2., 6.), (-3., 3.), (10., 12.)], [.1, .2, .5]) assert mesh.shape(True) == (41, 31, 5) assert mesh.shape(False) == (40, 30, 4) diff_eq = WaveEquation(3) cp = ConstrainedProblem( diff_eq, mesh, ((DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (999., None)), is_static=True), NeumannBoundaryCondition( vectorize_bc_function(lambda x, t: (None, None)), is_static=True)), (DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (0., 0.)), is_static=True), NeumannBoundaryCondition(lambda x, t: np.full((len(x), 2), t))), (NeumannBoundaryCondition(lambda x, t: -x[:, :2] * x[:, 1:3], is_static=True), DirichletBoundaryCondition( vectorize_bc_function(lambda x, t: (-999., None)))))) assert cp.y_shape(True) == (41, 31, 5, 2) assert cp.y_shape(False) == (40, 30, 4, 2) assert not cp.are_all_boundary_conditions_static assert cp.are_there_boundary_conditions_on_y assert cp.static_y_vertex_constraints.shape == (2, ) y = np.full(cp._y_vertices_shape, -1) cp.static_y_vertex_constraints[0].apply(y[..., :1]) cp.static_y_vertex_constraints[1].apply(y[..., 1:]) assert np.all(y[0, 1:, :, 0] == 999.) assert np.all(y[:, 0, :, 0] == 0.) assert np.all(y[1:, 1:, :, 0] == -1.) assert np.all(y[:, 0, :, 1] == 0.) assert np.all(y[:, 1:, :, 1] == -1.) vertex_boundary_constraints = cp.static_boundary_vertex_constraints cell_boundary_constraints = cp.static_boundary_cell_constraints for y_boundary_constraints in \ [vertex_boundary_constraints[0], cell_boundary_constraints[0]]: assert y_boundary_constraints.shape == (3, 2) assert y_boundary_constraints[0, 0][0] is not None assert y_boundary_constraints[0, 1][0] is not None assert y_boundary_constraints[0, 0][1] is None assert y_boundary_constraints[0, 1][1] is None assert y_boundary_constraints[1, 0][0] is not None assert y_boundary_constraints[1, 1][0] is not None assert y_boundary_constraints[1, 0][1] is None assert y_boundary_constraints[1, 1][1] is None assert y_boundary_constraints[2, 0][0] is None assert y_boundary_constraints[2, 1][0] is None assert y_boundary_constraints[2, 0][1] is None assert y_boundary_constraints[2, 1][1] is None for d_y_boundary_constraints in \ [vertex_boundary_constraints[1], cell_boundary_constraints[1]]: assert d_y_boundary_constraints.shape == (3, 2) assert d_y_boundary_constraints[0, 0][0] is None assert d_y_boundary_constraints[0, 1][0] is None assert d_y_boundary_constraints[0, 0][1] is not None assert d_y_boundary_constraints[0, 1][1] is not None assert d_y_boundary_constraints[1, 0][0] is None assert d_y_boundary_constraints[1, 1][0] is None assert d_y_boundary_constraints[1, 0][1] is None assert d_y_boundary_constraints[1, 1][1] is None assert d_y_boundary_constraints[2, 0][0] is not None assert d_y_boundary_constraints[2, 1][0] is not None assert d_y_boundary_constraints[2, 0][1] is None assert d_y_boundary_constraints[2, 1][1] is None new_vertex_boundary_constraints = cp.create_boundary_constraints(True, 1.) new_y_boundary_constraints = new_vertex_boundary_constraints[0] new_d_y_boundary_constraints = new_vertex_boundary_constraints[1] assert new_y_boundary_constraints[2, 0][1] is not None assert new_y_boundary_constraints[2, 1][1] is not None assert new_d_y_boundary_constraints[1, 0][1] is not None assert new_d_y_boundary_constraints[1, 1][1] is not None d_y_boundary = np.full((41, 1, 5, 2), np.nan) new_d_y_boundary_constraints[1, 0][1].apply(d_y_boundary[..., :1]) new_d_y_boundary_constraints[1, 1][1].apply(d_y_boundary[..., 1:]) assert np.all(d_y_boundary == 1.) new_y_vertex_constraints = \ cp.create_y_vertex_constraints(new_y_boundary_constraints) assert new_y_vertex_constraints.shape == (2, ) y = np.full(cp._y_vertices_shape, -1) new_y_vertex_constraints[0].apply(y[..., :1]) new_y_vertex_constraints[1].apply(y[..., 1:]) assert np.all(y[0, 1:, :-1, 0] == 999.) assert np.all(y[:, 0, :-1, 0] == 0.) assert np.all(y[:, :, -1, 0] == -999.) assert np.all(y[1:, 1:, :-1, 0] == -1.) assert np.all(y[:, 0, :, 1] == 0.) assert np.all(y[:, 1:, :, 1] == -1.)