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new and improved test for simple analytic examples on Karcher mean of…
… grassman manifold
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| import copy | ||
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| import numpy as np | ||
| import numpy.random | ||
| from beartype import beartype | ||
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| from UQpy.utilities.distances.grassmannian_distances import GeodesicDistance | ||
| from UQpy.utilities.GrassmannPoint import GrassmannPoint | ||
| from UQpy.dimension_reduction.grassmann_manifold.projections.SVDProjection import SVDProjection | ||
| from UQpy.dimension_reduction.grassmann_manifold.GrassmannOperations import GrassmannOperations | ||
| import sys | ||
| from numpy.random import RandomState | ||
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| sol0 = np.array([[0.61415, 1.03029, 1.02001, 0.57327, 0.79874, 0.73274], | ||
| [0.56924, 0.91700, 0.88841, 0.53737, 0.68676, 0.67751], | ||
| [0.51514, 0.87898, 0.87779, 0.47850, 0.69085, 0.61525], | ||
| [0.63038, 1.10822, 1.12313, 0.58038, 0.89142, 0.75429], | ||
| [0.69666, 1.03114, 0.95037, 0.67211, 0.71184, 0.82522], | ||
| [0.66595, 1.03789, 0.98690, 0.63420, 0.75416, 0.79110]]) | ||
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| sol1 = np.array([[1.05134, 1.37652, 0.95634, 0.85630, 0.47570, 1.22488], | ||
| [0.16370, 0.63105, 0.14533, 0.81030, 0.44559, 0.43358], | ||
| [1.23478, 2.10342, 1.04698, 1.68755, 0.92792, 1.73277], | ||
| [0.90538, 1.64067, 0.62027, 1.17577, 0.63644, 1.34925], | ||
| [0.58210, 0.75795, 0.65519, 0.65712, 0.37251, 0.65740], | ||
| [0.99174, 1.59375, 0.63724, 0.89107, 0.47631, 1.36581]]) | ||
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| sol2 = np.array([[1.04142, 0.91670, 1.47962, 1.23350, 0.94111, 0.61858], | ||
| [1.00464, 0.65684, 1.35136, 1.11288, 0.96093, 0.42340], | ||
| [1.05567, 1.33192, 1.56286, 1.43412, 0.77044, 0.97182], | ||
| [0.89812, 0.86136, 1.20204, 1.17892, 0.83788, 0.61160], | ||
| [0.46935, 0.39371, 0.63534, 0.57856, 0.47615, 0.26407], | ||
| [1.14102, 0.80869, 1.39123, 1.33076, 0.47719, 0.68170]]) | ||
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| sol3 = np.array([[0.60547, 0.11492, 0.78956, 0.13796, 0.76685, 0.41661], | ||
| [0.32771, 0.11606, 0.67630, 0.15208, 0.44845, 0.34840], | ||
| [0.58959, 0.10156, 0.72623, 0.11859, 0.73671, 0.38714], | ||
| [0.36283, 0.07979, 0.52824, 0.09760, 0.46313, 0.27906], | ||
| [0.87487, 0.22452, 1.30208, 0.30189, 1.22015, 0.62918], | ||
| [0.56006, 0.16879, 1.09635, 0.20431, 0.69439, 0.60317]]) | ||
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| # def test_karcher(): | ||
| # # Creating a list of matrices. | ||
| # matrices = [sol0, sol1, sol2, sol3] | ||
| # manifold_projection = SVDProjection(matrices, p="max") | ||
| # | ||
| # # optimization_method = GradientDescent(acceleration=True, error_tolerance=1e-4, max_iterations=1000) | ||
| # psi_mean = GrassmannOperations.karcher_mean(grassmann_points=manifold_projection.u, | ||
| # optimization_method="GradientDescent", | ||
| # distance=GeodesicDistance()) | ||
| # | ||
| # phi_mean = GrassmannOperations.karcher_mean(grassmann_points=manifold_projection.v, | ||
| # optimization_method="GradientDescent", | ||
| # distance=GeodesicDistance()) | ||
| # | ||
| # assert round(psi_mean.data[0, 0], 9) == -0.387197957 | ||
| # # assert round(psi_mean.data[0, 0], 9) == -0.418075902 | ||
| # # assert round(phi_mean.data[0, 0], 9) == -0.353239531 | ||
| # | ||
| # | ||
| # def test_karcher_stochastic(): | ||
| # matrices = [sol0, sol1, sol2, sol3] | ||
| # manifold_projection = SVDProjection(matrices, p="max") | ||
| # | ||
| # # optimization_method = GradientDescent(acceleration=True, error_tolerance=1e-4, max_iterations=1000) | ||
| # psi_mean = GrassmannOperations.karcher_mean(grassmann_points=manifold_projection.u, | ||
| # optimization_method="StochasticGradientDescent", | ||
| # distance=GeodesicDistance()) | ||
| # | ||
| # phi_mean = GrassmannOperations.karcher_mean(grassmann_points=manifold_projection.v, | ||
| # optimization_method="StochasticGradientDescent", | ||
| # distance=GeodesicDistance()) | ||
| from UQpy.utilities.distances.grassmannian_distances.GeodesicDistance import GeodesicDistance | ||
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| def test_karcher_mean_2point(): | ||
| """Test karcher mean on 2 points in the manifold Gr(1, 2)""" | ||
| theta1 = np.deg2rad(60) | ||
| x1 = np.array([[np.cos(theta1)], | ||
| [np.sin(theta1)]]) | ||
| theta2 = np.deg2rad(120) | ||
| x2 = np.array([[np.cos(theta2)], | ||
| [np.sin(theta2)]]) | ||
| points = [GrassmannPoint(x1), GrassmannPoint(x2)] | ||
| mean = GrassmannOperations.karcher_mean(grassmann_points=points, | ||
| optimization_method='GradientDescent', | ||
| distance=GeodesicDistance(), | ||
| tolerance=1e-9) | ||
| theta_solution = np.deg2rad(90) | ||
| solution = np.array([[np.cos(theta_solution)], | ||
| [np.sin(theta_solution)]]) | ||
| assert np.allclose(mean.data, solution) | ||
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| def test_karcher_mean_3point(): | ||
| """Test karcher mean on 3 points in the manifold Gr(1, 2)""" | ||
| points = [np.array([[np.cos(np.deg2rad(theta))], | ||
| [np.sin(np.deg2rad(theta))]]) for theta in (0, 15, 75, 90)] | ||
| mean = GrassmannOperations.karcher_mean(grassmann_points=points, | ||
| optimization_method='GradientDescent', | ||
| distance=GeodesicDistance(), | ||
| tolerance=1e-9) | ||
| solution = np.array([[np.cos(np.deg2rad(45))], | ||
| [np.sin(np.deg2rad(45))]]) | ||
| assert np.allclose(mean.data, solution) |