File size: 6,969 Bytes
e11c92f |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 |
"""Test gradient."""
import matplotlib.pyplot as plt
import numpy as np
import torch
from numpy.testing import assert_array_almost_equal
from numpy.testing import assert_array_equal
from MARBLE import construct_dataset
from MARBLE import geometry
from MARBLE import utils
from MARBLE.layers import AnisoConv
# pylint: disable=too-many-statements
def f1(x, alpha):
"""Linear feature function"""
return np.cos(alpha) * x[:, [0]] + np.sin(alpha) * x[:, [1]]
def f2(x, alpha):
"""Quadratic feature function"""
return np.cos(alpha) * x[:, [0]] ** 2 - np.sin(alpha) * x[:, [1]] ** 2
def test_gauges(plot=False):
"""Test creation of local gauges."""
n = 100
k = 8
alpha = np.pi / 4
np.random.seed(1)
x = np.random.uniform(low=(-1, -1), high=(1, 1), size=(n, 2))
xv, yv = np.meshgrid(np.linspace(-1, 1, int(np.sqrt(n))), np.linspace(-1, 1, int(np.sqrt(n))))
x = np.vstack([xv.flatten(), yv.flatten()]).T
y = f1(x, alpha)
# y = torch.tensor(y)
data = construct_dataset(x, y, graph_type="cknn", k=k)
gauges = data.gauges
assert_array_equal(data.gauges, np.repeat(np.array([[[1.0, 0.0], [0.0, 1.0]]]), 100, axis=0))
K = geometry.gradient_op(data.pos, data.edge_index, gauges)
K = [utils.to_SparseTensor(_K.coalesce().indices(), value=_K.coalesce().values()) for _K in K]
assert_array_almost_equal(
K[0].to_dense()[:5, :5],
np.array(
[
[-1.0, 0.25, 0.5, 0.0, 0.0],
[-0.16666667, -0.3333333, 0.16666667, 0.33333334, 0.0],
[-0.33333334, -0.16666667, 0.3333333, 0.16666669, 0.0],
[0.0, -0.25, -0.12500001, 0.0, 0.12500001],
[0.0, 0.0, 0.0, -0.16666667, -0.3333333],
]
),
decimal=5,
)
grad = AnisoConv()
der = grad(torch.tensor(y), K)
assert_array_almost_equal(
der.numpy()[:10],
np.array(
[
[0.27498597, 0.27498597],
[0.20951309, 0.15713481],
[0.20951313, 0.15713481],
[0.23570227, 0.15713482],
[0.20951313, 0.15713482],
[0.20951311, 0.15713483],
[0.23570227, 0.15713483],
[0.20951313, 0.15713484],
[0.20951313, 0.15713484],
[0.19641855, 0.19641855],
]
),
decimal=5,
)
derder = grad(der, K)
assert_array_almost_equal(
derder.numpy()[:10],
np.array(
[
[-7.85674201e-02, -1.17851151e-01, -1.17851155e-01, -7.85674242e-02],
[-2.18240134e-03, -5.23782543e-02, -2.83715625e-02, 1.74594472e-02],
[-1.74594164e-02, -5.23782863e-02, -3.92837183e-02, 2.34149155e-08],
[6.43910189e-09, -7.85674248e-02, 6.43910197e-09, 2.10734241e-08],
[4.36484562e-03, -5.23782887e-02, 7.80497299e-10, 1.87319325e-08],
[-4.36486123e-03, -5.23782699e-02, 5.46348028e-09, 1.63904412e-08],
[1.75611907e-09, -7.85674201e-02, 6.43910208e-09, 1.40489496e-08],
[-8.72971660e-03, -5.23782770e-02, 1.30945743e-02, 1.17074580e-08],
[-1.09121464e-02, -5.23782762e-02, 1.52770041e-02, 1.74594379e-02],
[-7.02447468e-09, -3.92837112e-02, 3.92837112e-02, 8.19522059e-09],
]
),
decimal=5,
)
if plot:
_, (ax1, ax2, ax3) = plt.subplots(
1, 3, sharey=True, figsize=(14, 3), subplot_kw={"aspect": 1}
)
ax1.scatter(x[:, 0], x[:, 1], c=y)
ax1.set_title(r"$(f_x,f_y)$")
ax1.axis("off")
xlim = ax1.get_xlim()
ylim = ax1.get_ylim()
ax2.scatter(x[:, 0], x[:, 1], c=y)
ax2.set_title(r"$f_{xx}$,$f_{yy}$")
ax2.axis("off")
ax2.set_xlim(xlim)
ax2.set_ylim(ylim)
ax3.scatter(x[:, 0], x[:, 1], c=y)
ax3.set_title(r"$f_{xy}$,$f_{yx}$")
ax3.axis("off")
ax3.set_xlim(xlim)
ax3.set_ylim(ylim)
for ind in range(x.shape[0]):
ax1.arrow(x[ind, 0], x[ind, 1], der[ind, 0], der[ind, 1], width=0.01)
ax2.arrow(x[ind, 0], x[ind, 1], derder[ind, 0], 0, width=0.01, color="r")
ax2.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 3], width=0.01, color="b")
ax3.arrow(x[ind, 0], x[ind, 1], derder[ind, 1], 0, width=0.01, color="r")
ax3.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 2], width=0.01, color="b")
PCM = ax1.get_children()[0] # get the mappable, the 1st and the 2nd are the x and y axes
plt.colorbar(PCM, ax=ax1)
y = f2(x, alpha)
y = torch.tensor(y)
der = grad(y, K)
assert_array_almost_equal(
der.numpy()[:5, :5],
np.array(
[
[-3.14269681e-01, 3.14269681e-01],
[-2.79350844e-01, 3.02630063e-01],
[-2.79350835e-01, 3.02630057e-01],
[-1.57134847e-01, 3.02630053e-01],
[1.45692810e-08, 3.02630051e-01],
]
),
decimal=5,
)
derder = grad(der, K)
assert_array_almost_equal(
derder.numpy()[:5, :5],
np.array(
[
[4.36485566e-02, 2.61891408e-02, -2.61891408e-02, -4.36485566e-02],
[6.78977669e-02, 3.87987339e-02, -7.75974289e-03, -4.65584549e-02],
[5.52881903e-02, 1.04756561e-01, -3.87987803e-03, -5.81980716e-02],
[1.22216001e-01, 5.23782832e-02, -4.29273473e-09, -5.81980696e-02],
[1.01846653e-01, -3.49188700e-02, -7.97841570e-09, -5.81980685e-02],
]
),
decimal=5,
)
if plot:
_, (ax1, ax2, ax3) = plt.subplots(
1, 3, sharey=True, figsize=(14, 3), subplot_kw={"aspect": 1}
)
ax1.scatter(x[:, 0], x[:, 1], c=y)
ax1.set_title(r"$(f_x,f_y)$")
ax1.axis("off")
xlim = ax1.get_xlim()
ylim = ax1.get_ylim()
ax2.scatter(x[:, 0], x[:, 1], c=y)
ax2.set_title(r"$f_{xx}$,$f_{yy}$")
ax2.axis("off")
ax2.set_xlim(xlim)
ax2.set_ylim(ylim)
ax3.scatter(x[:, 0], x[:, 1], c=y)
ax3.set_title(r"$f_{xy}$,$f_{yx}$")
ax3.axis("off")
ax3.set_xlim(xlim)
ax3.set_ylim(ylim)
for ind in range(x.shape[0]):
ax1.arrow(x[ind, 0], x[ind, 1], der[ind, 0], der[ind, 1], width=0.01)
ax2.arrow(x[ind, 0], x[ind, 1], derder[ind, 0], 0, width=0.01, color="r")
ax2.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 3], width=0.01, color="b")
ax3.arrow(x[ind, 0], x[ind, 1], derder[ind, 1], 0, width=0.01, color="r")
ax3.arrow(x[ind, 0], x[ind, 1], 0, derder[ind, 2], width=0.01, color="b")
PCM = ax1.get_children()[0] # get the mappable, the 1st and the 2nd are the x and y axes
plt.colorbar(PCM, ax=ax1)
plt.show()
|