def test_interpolation(self):
x = torch.linspace(0.01, 1, 100).unsqueeze(1)
grid = torch.linspace(-0.05, 1.05, 50).unsqueeze(1)
indices, values = Interpolation().interpolate(grid, x)
indices = indices.squeeze_(0)
values = values.squeeze_(0)
test_func_grid = grid.squeeze(1).pow(2)
test_func_x = x.pow(2).squeeze(-1)
interp_func_x = gpytorch.utils.interpolation.left_interp(indices, values, test_func_grid.unsqueeze(1)).squeeze()
self.assertTrue(test._utils.approx_equal(interp_func_x, test_func_x))
def test_interpolation(self):
x = torch.linspace(0.01, 1, 100).unsqueeze(1)
grid = torch.linspace(-0.05, 1.05, 50).unsqueeze(0)
indices, values = Interpolation().interpolate(Variable(grid), Variable(x))
indices = indices.squeeze_(0)
values = values.squeeze_(0)
test_func_grid = grid.squeeze(0).pow(2)
test_func_x = x.pow(2).squeeze(-1)
interp_func_x = utils.left_interp(indices.data, values.data, test_func_grid.unsqueeze(1)).squeeze()
self.assertTrue(utils.approx_equal(interp_func_x, test_func_x))
def test_interpolation():
x = torch.linspace(0.01, 1, 100).unsqueeze(1)
grid = torch.linspace(-0.05, 1.05, 50).unsqueeze(0)
indices, values = Interpolation().interpolate(grid, x)
indices.squeeze_(0)
values.squeeze_(0)
test_func_grid = grid.squeeze(0).pow(2)
test_func_x = x.pow(2).squeeze(-1)
interp_func_x = utils.left_interp(indices, values,
test_func_grid.unsqueeze(1)).squeeze()
assert utils.approx_equal(interp_func_x, test_func_x)
def test_interpolation():
x = torch.linspace(0.01, 1, 100)
grid = torch.linspace(-0.05, 1.05, 50)
J, C = Interpolation().interpolate(grid, x)
W = utils.toeplitz.index_coef_to_sparse(J, C, len(grid))
test_func_grid = grid.pow(2)
test_func_x = x.pow(2)
interp_func_x = torch.dsmm(W, test_func_grid.unsqueeze(1)).squeeze()
assert all(
torch.abs(interp_func_x - test_func_x) / (test_func_x + 1e-10) < 1e-5)
def forward(self, x1, x2, **kwargs):
n, d = x1.size()
m, _ = x2.size()
if d > 1:
raise RuntimeError(' '.join([
'The grid interpolation kernel can only be applied to inputs of a single dimension at this time \
until Kronecker structure is implemented.'
]))
if self.grid is None:
raise RuntimeError(' '.join([
'This GridInterpolationKernel has no grid. Call initialize_interpolation_grid \
on a GPModel first.'
]))
both_min = torch.min(x1.min(0)[0].data, x2.min(0)[0].data)[0]
both_max = torch.max(x1.max(0)[0].data, x2.max(0)[0].data)[0]
if both_min < self.grid_bounds[0] or both_max > self.grid_bounds[1]:
# Out of bounds data is still ok if we are specifically computing kernel values for grid entries.
if torch.abs(both_min - self.grid[0].data)[0] > 1e-7 or torch.abs(
both_max - self.grid[-1].data)[0] > 1e-7:
raise RuntimeError(
'Received data that was out of bounds for the specified grid. \
Grid bounds were ({}, {}), but min = {}, max = {}'
.format(self.grid_bounds[0], self.grid_bounds[1], both_min,
both_max))
J1, C1 = Interpolation().interpolate(self.grid.data, x1.data.squeeze())
J2, C2 = Interpolation().interpolate(self.grid.data, x2.data.squeeze())
k_UU = self.base_kernel_module(self.grid[0], self.grid,
**kwargs).squeeze()
K_XX = ToeplitzLazyVariable(k_UU, J1, C1, J2, C2)
return K_XX
def test_multidim_interpolation(self):
x = torch.Tensor([
[0.25, 0.45, 0.65, 0.85],
[0.35, 0.375, 0.4, 0.425],
[0.45, 0.5, 0.55, 0.6],
]).t().contiguous()
grid = torch.linspace(0., 1., 11).unsqueeze(0).repeat(3, 1)
indices, values = Interpolation().interpolate(Variable(grid),
Variable(x))
actual_indices = torch.cat([
torch.LongTensor([
[
146, 147, 148, 149, 157, 158, 159, 160, 168, 169, 170, 171,
179
],
[
389, 390, 391, 392, 400, 401, 402, 403, 411, 412, 413, 414,
422
],
[
642, 643, 644, 645, 653, 654, 655, 656, 664, 665, 666, 667,
675
],
[
885, 886, 887, 888, 896, 897, 898, 899, 907, 908, 909, 910,
918
],
]),
torch.LongTensor([
[
180, 181, 182, 267, 268, 269, 270, 278, 279, 280, 281, 289,
290
],
[
423, 424, 425, 510, 511, 512, 513, 521, 522, 523, 524, 532,
533
],
[
676, 677, 678, 763, 764, 765, 766, 774, 775, 776, 777, 785,
786
],
[
919, 920, 921, 1006, 1007, 1008, 1009, 1017, 1018, 1019,
1020, 1028, 1029
],
]),
torch.LongTensor([
[
291, 292, 300, 301, 302, 303, 388, 389, 390, 391, 399, 400,
401
],
[
534, 535, 543, 544, 545, 546, 631, 632, 633, 634, 642, 643,
644
],
[
787, 788, 796, 797, 798, 799, 884, 885, 886, 887, 895, 896,
897
],
[
1030, 1031, 1039, 1040, 1041, 1042, 1127, 1128, 1129, 1130,
1138, 1139, 1140
],
]),
torch.LongTensor([
[
402, 410, 411, 412, 413, 421, 422, 423, 424, 509, 510, 511,
512
],
[
645, 653, 654, 655, 656, 664, 665, 666, 667, 752, 753, 754,
755
],
[
898, 906, 907, 908, 909, 917, 918, 919, 920, 1005, 1006,
1007, 1008
],
[
1141, 1149, 1150, 1151, 1152, 1160, 1161, 1162, 1163, 1248,
1249, 1250, 1251
],
]),
torch.LongTensor([
[520, 521, 522, 523, 531, 532, 533, 534, 542, 543, 544, 545],
[763, 764, 765, 766, 774, 775, 776, 777, 785, 786, 787, 788],
[
1016, 1017, 1018, 1019, 1027, 1028, 1029, 1030, 1038, 1039,
1040, 1041
],
[
1259, 1260, 1261, 1262, 1270, 1271, 1272, 1273, 1281, 1282,
1283, 1284
],
])
], 1)
self.assertTrue(utils.approx_equal(indices.data, actual_indices))
actual_values = torch.cat([
torch.Tensor([
[
-0.0002, 0.0022, 0.0022, -0.0002, 0.0022, -0.0198, -0.0198,
0.0022, 0.0022, -0.0198
],
[
0.0000, 0.0015, 0.0000, 0.0000, -0.0000, -0.0142, -0.0000,
-0.0000, -0.0000, -0.0542
],
[
0.0000, -0.0000, -0.0000, 0.0000, 0.0039, -0.0352, -0.0352,
0.0039, 0.0000, -0.0000
],
[
0.0000, 0.0044, 0.0000, 0.0000, -0.0000, -0.0542, -0.0000,
-0.0000, -0.0000, -0.0142
],
]),
torch.Tensor([
[
-0.0198, 0.0022, -0.0002, 0.0022, 0.0022, -0.0002, 0.0022,
-0.0198, -0.0198, 0.0022
],
[
-0.0000, -0.0000, 0.0000, 0.0044, 0.0000, 0.0000, -0.0000,
-0.0132, -0.0000, -0.0000
],
[
-0.0000, 0.0000, 0.0000, -0.0000, -0.0000, 0.0000, -0.0000,
0.0000, 0.0000, -0.0000
],
[
-0.0000, -0.0000, 0.0000, 0.0015, 0.0000, 0.0000, -0.0000,
-0.0396, -0.0000, -0.0000
],
]),
torch.Tensor([
[
-0.0198, 0.1780, 0.1780, -0.0198, -0.0198, 0.1780, 0.1780,
-0.0198, 0.0022, -0.0198
],
[
0.0000, 0.1274, 0.0000, 0.0000, 0.0000, 0.4878, 0.0000,
0.0000, -0.0000, -0.0396
],
[
-0.0352, 0.3164, 0.3164, -0.0352, -0.0000, 0.0000, 0.0000,
-0.0000, -0.0000, 0.0000
],
[
0.0000, 0.4878, 0.0000, 0.0000, 0.0000, 0.1274, 0.0000,
0.0000, -0.0000, -0.0132
],
]),
torch.Tensor([
[
-0.0198, 0.0022, 0.0022, -0.0198, -0.0198, 0.0022, -0.0198,
0.1780, 0.1780, -0.0198
],
[
-0.0000, -0.0000, -0.0000, -0.0132, -0.0000, -0.0000,
0.0000, 0.1274, 0.0000, 0.0000
],
[
0.0000, -0.0000, -0.0000, 0.0000, 0.0000, -0.0000, -0.0352,
0.3164, 0.3164, -0.0352
],
[
-0.0000, -0.0000, -0.0000, -0.0396, -0.0000, -0.0000,
0.0000, 0.4878, 0.0000, 0.0000
],
]),
torch.Tensor([
[
-0.0198, 0.1780, 0.1780, -0.0198, 0.0022, -0.0198, -0.0198,
0.0022, -0.0002, 0.0022
],
[
0.0000, 0.4878, 0.0000, 0.0000, -0.0000, -0.0396, -0.0000,
-0.0000, 0.0000, 0.0015
],
[
-0.0000, 0.0000, 0.0000, -0.0000, -0.0000, 0.0000, 0.0000,
-0.0000, 0.0000, -0.0000
],
[
0.0000, 0.1274, 0.0000, 0.0000, -0.0000, -0.0132, -0.0000,
-0.0000, 0.0000, 0.0044
],
]),
torch.Tensor([
[
0.0022, -0.0002, 0.0022, -0.0198, -0.0198, 0.0022, 0.0022,
-0.0198, -0.0198, 0.0022
],
[
0.0000, 0.0000, -0.0000, -0.0142, -0.0000, -0.0000,
-0.0000, -0.0542, -0.0000, -0.0000
],
[
-0.0000, 0.0000, 0.0039, -0.0352, -0.0352, 0.0039, 0.0000,
-0.0000, -0.0000, 0.0000
],
[
0.0000, 0.0000, -0.0000, -0.0542, -0.0000, -0.0000,
-0.0000, -0.0142, -0.0000, -0.0000
],
]),
torch.Tensor([
[-0.0002, 0.0022, 0.0022, -0.0002],
[0.0000, 0.0044, 0.0000, 0.0000],
[0.0000, -0.0000, -0.0000, 0.0000],
[0.0000, 0.0015, 0.0000, 0.0000],
]),
], 1)
self.assertTrue(utils.approx_equal(values.data, actual_values))
def _compute_grid(self, x1, x2):
if not self.has_grid:
raise RuntimeError(
'GridInterpolationKernel requires setting the interpolation grid'
)
n, d = x1.size()
m, _ = x2.size()
if d > 1:
Js1 = x1.data.new(d, len(x1.data), 4).zero_().long()
Cs1 = x1.data.new(d, len(x1.data), 4).zero_()
Js2 = x1.data.new(d, len(x1.data), 4).zero_().long()
Cs2 = x1.data.new(d, len(x1.data), 4).zero_()
for i in range(d):
both_min = torch.min(x1.min(0)[0].data, x2.min(0)[0].data)[i]
both_max = torch.max(x1.max(0)[0].data, x2.max(0)[0].data)[i]
if both_min < self.grid_bounds[i][
0] or both_max > self.grid_bounds[i][1]:
# Out of bounds data is still ok if we are specifically computing kernel values for grid entries.
if math.fabs(both_min - self.grid[i, 0]) > 1e-7:
raise RuntimeError(
'Received data that was out of bounds for the specified grid. \
Grid bounds were ({}, {}), but min = {}, \
max = {}'.format(
self.grid_bounds[i][0], self.grid_bounds[i][1],
both_min, both_max))
elif math.fabs(both_max - self.grid[i, -1]) > 1e-7:
raise RuntimeError(
'Received data that was out of bounds for the specified grid. \
Grid bounds were ({}, {}), but min = {}, \
max = {}'.format(
self.grid_bounds[i][0], self.grid_bounds[i][1],
both_min, both_max))
Js1[i], Cs1[i] = Interpolation().interpolate(
self.grid[i], x1.data[:, i])
Js2[i], Cs2[i] = Interpolation().interpolate(
self.grid[i], x2.data[:, i])
return Js1, Cs1, Js2, Cs2
both_min = torch.min(x1.min(0)[0].data, x2.min(0)[0].data)[0]
both_max = torch.max(x1.max(0)[0].data, x2.max(0)[0].data)[0]
if both_min < self.grid_bounds[0][0] or both_max > self.grid_bounds[0][
1]:
# Out of bounds data is still ok if we are specifically computing kernel values for grid entries.
if math.fabs(both_min - self.grid[0, 0]) > 1e-7:
raise RuntimeError(
'Received data that was out of bounds for the specified grid. \
Grid bounds were ({}, {}), but min = {}, max = {}'
.format(self.grid_bounds[0][0], self.grid_bounds[0][1],
both_min, both_max))
elif math.fabs(both_max - self.grid[0, -1]) > 1e-7:
raise RuntimeError(
'Received data that was out of bounds for the specified grid. \
Grid bounds were ({}, {}), but min = {}, max = {}'
.format(self.grid_bounds[0][0], self.grid_bounds[0][1],
both_min, both_max))
J1, C1 = Interpolation().interpolate(self.grid[0], x1.data.squeeze())
J2, C2 = Interpolation().interpolate(self.grid[0], x2.data.squeeze())
return J1, C1, J2, C2