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"""Test gradient.""" |
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import matplotlib.pyplot as plt |
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import numpy as np |
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import torch |
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from numpy.testing import assert_array_almost_equal |
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from numpy.testing import assert_array_equal |
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from MARBLE import construct_dataset |
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from MARBLE import geometry |
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from MARBLE import utils |
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from MARBLE.layers import AnisoConv |
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def f1(x, alpha): |
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"""Linear feature function""" |
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return np.cos(alpha) * x[:, [0]] + np.sin(alpha) * x[:, [1]] |
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def f2(x, alpha): |
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"""Quadratic feature function""" |
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return np.cos(alpha) * x[:, [0]] ** 2 - np.sin(alpha) * x[:, [1]] ** 2 |
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def test_gauges(plot=False): |
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"""Test creation of local gauges.""" |
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n = 100 |
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k = 8 |
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alpha = np.pi / 4 |
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np.random.seed(1) |
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x = np.random.uniform(low=(-1, -1), high=(1, 1), size=(n, 2)) |
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xv, yv = np.meshgrid(np.linspace(-1, 1, int(np.sqrt(n))), np.linspace(-1, 1, int(np.sqrt(n)))) |
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x = np.vstack([xv.flatten(), yv.flatten()]).T |
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y = f1(x, alpha) |
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data = construct_dataset(x, y, graph_type="cknn", k=k) |
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gauges = data.gauges |
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assert_array_equal(data.gauges, np.repeat(np.array([[[1.0, 0.0], [0.0, 1.0]]]), 100, axis=0)) |
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K = geometry.gradient_op(data.pos, data.edge_index, gauges) |
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K = [utils.to_SparseTensor(_K.coalesce().indices(), value=_K.coalesce().values()) for _K in K] |
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assert_array_almost_equal( |
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K[0].to_dense()[:5, :5], |
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np.array( |
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[ |
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[-1.0, 0.25, 0.5, 0.0, 0.0], |
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[-0.16666667, -0.3333333, 0.16666667, 0.33333334, 0.0], |
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[-0.33333334, -0.16666667, 0.3333333, 0.16666669, 0.0], |
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[0.0, -0.25, -0.12500001, 0.0, 0.12500001], |
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[0.0, 0.0, 0.0, -0.16666667, -0.3333333], |
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] |
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), |
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decimal=5, |
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) |
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grad = AnisoConv() |
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der = grad(torch.tensor(y), K) |
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assert_array_almost_equal( |
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der.numpy()[:10], |
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np.array( |
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[ |
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[0.27498597, 0.27498597], |
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[0.20951309, 0.15713481], |
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[0.20951313, 0.15713481], |
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[0.23570227, 0.15713482], |
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[0.20951313, 0.15713482], |
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[0.20951311, 0.15713483], |
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[0.23570227, 0.15713483], |
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[0.20951313, 0.15713484], |
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[0.20951313, 0.15713484], |
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[0.19641855, 0.19641855], |
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] |
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), |
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decimal=5, |
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) |
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derder = grad(der, K) |
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assert_array_almost_equal( |
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derder.numpy()[:10], |
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np.array( |
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[ |
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[-7.85674201e-02, -1.17851151e-01, -1.17851155e-01, -7.85674242e-02], |
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[-2.18240134e-03, -5.23782543e-02, -2.83715625e-02, 1.74594472e-02], |
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[-1.74594164e-02, -5.23782863e-02, -3.92837183e-02, 2.34149155e-08], |
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[6.43910189e-09, -7.85674248e-02, 6.43910197e-09, 2.10734241e-08], |
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[4.36484562e-03, -5.23782887e-02, 7.80497299e-10, 1.87319325e-08], |
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[-4.36486123e-03, -5.23782699e-02, 5.46348028e-09, 1.63904412e-08], |
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[1.75611907e-09, -7.85674201e-02, 6.43910208e-09, 1.40489496e-08], |
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[-8.72971660e-03, -5.23782770e-02, 1.30945743e-02, 1.17074580e-08], |
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[-1.09121464e-02, -5.23782762e-02, 1.52770041e-02, 1.74594379e-02], |
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[-7.02447468e-09, -3.92837112e-02, 3.92837112e-02, 8.19522059e-09], |
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] |
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), |
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decimal=5, |
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) |
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if plot: |
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_, (ax1, ax2, ax3) = plt.subplots( |
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1, 3, sharey=True, figsize=(14, 3), subplot_kw={"aspect": 1} |
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) |
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ax1.scatter(x[:, 0], x[:, 1], c=y) |
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ax1.set_title(r"$(f_x,f_y)$") |
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ax1.axis("off") |
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xlim = ax1.get_xlim() |
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ylim = ax1.get_ylim() |
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ax2.scatter(x[:, 0], x[:, 1], c=y) |
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ax2.set_title(r"$f_{xx}$,$f_{yy}$") |
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ax2.axis("off") |
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ax2.set_xlim(xlim) |
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ax2.set_ylim(ylim) |
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ax3.scatter(x[:, 0], x[:, 1], c=y) |
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ax3.set_title(r"$f_{xy}$,$f_{yx}$") |
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ax3.axis("off") |
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ax3.set_xlim(xlim) |
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ax3.set_ylim(ylim) |
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for ind in range(x.shape[0]): |
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ax1.arrow(x[ind, 0], x[ind, 1], der[ind, 0], der[ind, 1], width=0.01) |
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ax2.arrow(x[ind, 0], x[ind, 1], derder[ind, 0], 0, width=0.01, color="r") |
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ax2.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 3], width=0.01, color="b") |
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ax3.arrow(x[ind, 0], x[ind, 1], derder[ind, 1], 0, width=0.01, color="r") |
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ax3.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 2], width=0.01, color="b") |
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PCM = ax1.get_children()[0] |
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plt.colorbar(PCM, ax=ax1) |
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y = f2(x, alpha) |
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y = torch.tensor(y) |
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der = grad(y, K) |
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assert_array_almost_equal( |
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der.numpy()[:5, :5], |
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np.array( |
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[ |
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[-3.14269681e-01, 3.14269681e-01], |
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[-2.79350844e-01, 3.02630063e-01], |
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[-2.79350835e-01, 3.02630057e-01], |
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[-1.57134847e-01, 3.02630053e-01], |
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[1.45692810e-08, 3.02630051e-01], |
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] |
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), |
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decimal=5, |
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) |
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derder = grad(der, K) |
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assert_array_almost_equal( |
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derder.numpy()[:5, :5], |
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np.array( |
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[ |
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[4.36485566e-02, 2.61891408e-02, -2.61891408e-02, -4.36485566e-02], |
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[6.78977669e-02, 3.87987339e-02, -7.75974289e-03, -4.65584549e-02], |
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[5.52881903e-02, 1.04756561e-01, -3.87987803e-03, -5.81980716e-02], |
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[1.22216001e-01, 5.23782832e-02, -4.29273473e-09, -5.81980696e-02], |
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[1.01846653e-01, -3.49188700e-02, -7.97841570e-09, -5.81980685e-02], |
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] |
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), |
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decimal=5, |
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) |
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if plot: |
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_, (ax1, ax2, ax3) = plt.subplots( |
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1, 3, sharey=True, figsize=(14, 3), subplot_kw={"aspect": 1} |
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) |
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ax1.scatter(x[:, 0], x[:, 1], c=y) |
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ax1.set_title(r"$(f_x,f_y)$") |
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ax1.axis("off") |
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xlim = ax1.get_xlim() |
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ylim = ax1.get_ylim() |
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ax2.scatter(x[:, 0], x[:, 1], c=y) |
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ax2.set_title(r"$f_{xx}$,$f_{yy}$") |
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ax2.axis("off") |
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ax2.set_xlim(xlim) |
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ax2.set_ylim(ylim) |
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ax3.scatter(x[:, 0], x[:, 1], c=y) |
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ax3.set_title(r"$f_{xy}$,$f_{yx}$") |
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ax3.axis("off") |
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ax3.set_xlim(xlim) |
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ax3.set_ylim(ylim) |
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for ind in range(x.shape[0]): |
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ax1.arrow(x[ind, 0], x[ind, 1], der[ind, 0], der[ind, 1], width=0.01) |
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ax2.arrow(x[ind, 0], x[ind, 1], derder[ind, 0], 0, width=0.01, color="r") |
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ax2.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 3], width=0.01, color="b") |
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ax3.arrow(x[ind, 0], x[ind, 1], derder[ind, 1], 0, width=0.01, color="r") |
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ax3.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 2], width=0.01, color="b") |
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PCM = ax1.get_children()[0] |
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plt.colorbar(PCM, ax=ax1) |
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plt.show() |
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