def forward(self, pos):
if self.initial_density_map is None:
self.compute_initial_density_map(pos)
# plot(0, self.initial_density_map.clone().div(self.bin_size_x*self.bin_size_y).cpu().numpy(), self.padding, 'summary/initial_potential_map')
logger.info("fixed density map: average %g, max %g, bin area %g" %
(self.initial_density_map.mean(),
self.initial_density_map.max(),
self.bin_size_x * self.bin_size_y))
# expk
M = self.num_bins_x
N = self.num_bins_y
self.exact_expkM = precompute_expk(M,
dtype=pos.dtype,
device=pos.device)
self.exact_expkN = precompute_expk(N,
dtype=pos.dtype,
device=pos.device)
# init dct2, idct2, idct_idxst, idxst_idct with expkM and expkN
self.dct2 = dct.DCT2(self.exact_expkM, self.exact_expkN)
if not self.fast_mode:
self.idct2 = dct.IDCT2(self.exact_expkM, self.exact_expkN)
self.idct_idxst = dct.IDCT_IDXST(self.exact_expkM,
self.exact_expkN)
self.idxst_idct = dct.IDXST_IDCT(self.exact_expkM,
self.exact_expkN)
# wu and wv
wu = torch.arange(M, dtype=pos.dtype, device=pos.device).mul(
2 * np.pi / M).view([M, 1])
# scale wv because the aspect ratio of a bin may not be 1
wv = torch.arange(N, dtype=pos.dtype,
device=pos.device).mul(2 * np.pi / N).view(
[1,
N]).mul_(self.bin_size_x / self.bin_size_y)
wu2_plus_wv2 = wu.pow(2) + wv.pow(2)
wu2_plus_wv2[0,
0] = 1.0 # avoid zero-division, it will be zeroed out
self.inv_wu2_plus_wv2 = 1.0 / wu2_plus_wv2
self.inv_wu2_plus_wv2[0, 0] = 0.0
self.wu_by_wu2_plus_wv2_half = wu.mul(self.inv_wu2_plus_wv2).mul_(
1. / 2)
self.wv_by_wu2_plus_wv2_half = wv.mul(self.inv_wu2_plus_wv2).mul_(
1. / 2)
return ElectricPotentialFunction.apply(
pos, self.node_size_x_clamped, self.node_size_y_clamped,
self.offset_x, self.offset_y, self.ratio, self.bin_center_x,
self.bin_center_y, self.initial_density_map, self.buf,
self.target_density, self.xl, self.yl, self.xh, self.yh,
self.bin_size_x, self.bin_size_y, self.num_movable_nodes,
self.num_filler_nodes, self.padding, self.padding_mask,
self.num_bins_x, self.num_bins_y, self.num_movable_impacted_bins_x,
self.num_movable_impacted_bins_y, self.num_filler_impacted_bins_x,
self.num_filler_impacted_bins_y, self.deterministic_flag,
self.sorted_node_map, self.exact_expkM, self.exact_expkN,
self.inv_wu2_plus_wv2, self.wu_by_wu2_plus_wv2_half,
self.wv_by_wu2_plus_wv2_half, self.dct2, self.idct2,
self.idct_idxst, self.idxst_idct, self.fast_mode, self.num_threads)
def forward(self, pos, mode="density"):
assert mode in {"density", "overflow"
}, "Only support density mode or overflow mode"
if (self.region_id is not None):
### reconstruct pos, only extract cells in this electric field
pos = pos[self.pos_mask]
if self.initial_density_map is None:
num_nodes = pos.size(0) // 2
if (self.fence_regions is not None):
if (self.placedb.num_terminals > 0):
### merge fence region density and macro density together as initial density map
### pay attention to the number of nodes, must use data from self
### here pos is reconstructed pos !
self.initial_density_map = self.compute_fence_region_map(
self.fence_regions,
pos[self.num_movable_nodes:self.num_movable_nodes +
self.num_terminals],
pos[num_nodes + self.num_movable_nodes:num_nodes +
self.num_movable_nodes + self.num_terminals],
self.node_size_x[self.num_movable_nodes:self.
num_movable_nodes +
self.num_terminals],
self.node_size_y[self.num_movable_nodes:self.
num_movable_nodes +
self.num_terminals])
else:
self.initial_density_map = self.compute_fence_region_map(
self.fence_regions)
else:
self.compute_initial_density_map(pos)
## sync the initial density map with
# self.compute_initial_density_map(pos)
# plot(0, self.initial_density_map.clone().div(self.bin_size_x*self.bin_size_y).cpu().numpy(), self.padding, 'summary/initial_potential_map')
logger.info("fixed density map: average %g, max %g, bin area %g" %
(self.initial_density_map.mean(),
self.initial_density_map.max(),
self.bin_size_x * self.bin_size_y))
# expk
M = self.num_bins_x
N = self.num_bins_y
self.exact_expkM = precompute_expk(M,
dtype=pos.dtype,
device=pos.device)
self.exact_expkN = precompute_expk(N,
dtype=pos.dtype,
device=pos.device)
# init dct2, idct2, idct_idxst, idxst_idct with expkM and expkN
self.dct2 = dct.DCT2(self.exact_expkM, self.exact_expkN)
if not self.fast_mode:
self.idct2 = dct.IDCT2(self.exact_expkM, self.exact_expkN)
self.idct_idxst = dct.IDCT_IDXST(self.exact_expkM,
self.exact_expkN)
self.idxst_idct = dct.IDXST_IDCT(self.exact_expkM,
self.exact_expkN)
# wu and wv
wu = torch.arange(M, dtype=pos.dtype, device=pos.device).mul(
2 * np.pi / M).view([M, 1])
# scale wv because the aspect ratio of a bin may not be 1
wv = torch.arange(N, dtype=pos.dtype,
device=pos.device).mul(2 * np.pi / N).view(
[1,
N]).mul_(self.bin_size_x / self.bin_size_y)
wu2_plus_wv2 = wu.pow(2) + wv.pow(2)
wu2_plus_wv2[0,
0] = 1.0 # avoid zero-division, it will be zeroed out
self.inv_wu2_plus_wv2 = 1.0 / wu2_plus_wv2
self.inv_wu2_plus_wv2[0, 0] = 0.0
self.wu_by_wu2_plus_wv2_half = wu.mul(self.inv_wu2_plus_wv2).mul_(
1. / 2)
self.wv_by_wu2_plus_wv2_half = wv.mul(self.inv_wu2_plus_wv2).mul_(
1. / 2)
if (mode == "density"):
return ElectricPotentialFunction.apply(
pos, self.node_size_x_clamped, self.node_size_y_clamped,
self.offset_x, self.offset_y, self.ratio, self.bin_center_x,
self.bin_center_y, self.initial_density_map,
self.target_density, self.xl, self.yl, self.xh, self.yh,
self.bin_size_x, self.bin_size_y, self.num_movable_nodes,
self.num_filler_nodes, self.padding, self.padding_mask,
self.num_bins_x, self.num_bins_y,
self.num_movable_impacted_bins_x,
self.num_movable_impacted_bins_y,
self.num_filler_impacted_bins_x,
self.num_filler_impacted_bins_y, self.deterministic_flag,
self.sorted_node_map, self.exact_expkM, self.exact_expkN,
self.inv_wu2_plus_wv2, self.wu_by_wu2_plus_wv2_half,
self.wv_by_wu2_plus_wv2_half, self.dct2, self.idct2,
self.idct_idxst, self.idxst_idct, self.fast_mode)
elif (mode == "overflow"):
### num_filler_nodes is set 0
density_map = ElectricDensityMapFunction.forward(
pos, self.node_size_x_clamped, self.node_size_y_clamped,
self.offset_x, self.offset_y, self.ratio, self.bin_center_x,
self.bin_center_y, self.initial_density_map,
self.target_density, self.xl, self.yl, self.xh, self.yh,
self.bin_size_x, self.bin_size_y, self.num_movable_nodes, 0,
self.padding, self.padding_mask, self.num_bins_x,
self.num_bins_y, self.num_movable_impacted_bins_x,
self.num_movable_impacted_bins_y,
self.num_filler_impacted_bins_x,
self.num_filler_impacted_bins_y, self.deterministic_flag,
self.sorted_node_map)
bin_area = self.bin_size_x * self.bin_size_y
density_cost = (density_map -
self.target_density * bin_area).clamp_(
min=0.0).sum()
return density_cost, density_map.max() / bin_area
def compare_different_methods(cuda_flag, M=1024, N=1024, dtype=torch.float64):
density_map = torch.empty(M, N, dtype=dtype).uniform_(0, 10.0)
if cuda_flag:
density_map = density_map.cuda()
expkM = discrete_spectral_transform.get_expk(M, dtype, density_map.device)
expkN = discrete_spectral_transform.get_expk(N, dtype, density_map.device)
exact_expkM = discrete_spectral_transform.get_exact_expk(M, dtype, density_map.device)
exact_expkN = discrete_spectral_transform.get_exact_expk(N, dtype, density_map.device)
print("M = {}, N = {}".format(M, N))
wu = torch.arange(M, dtype=density_map.dtype, device=density_map.device).mul(2 * np.pi / M).view([M, 1])
wv = torch.arange(N, dtype=density_map.dtype, device=density_map.device).mul(2 * np.pi / N).view([1, N])
wu2_plus_wv2 = wu.pow(2) + wv.pow(2)
wu2_plus_wv2[0, 0] = 1.0 # avoid zero-division, it will be zeroed out
inv_wu2_plus_wv2_2X = 2.0 / wu2_plus_wv2
inv_wu2_plus_wv2_2X[0, 0] = 0.0
wu_by_wu2_plus_wv2_2X = wu.mul(inv_wu2_plus_wv2_2X)
wv_by_wu2_plus_wv2_2X = wv.mul(inv_wu2_plus_wv2_2X)
# the first approach is used as the ground truth
auv_golden = dct.dct2(density_map, expk0=expkM, expk1=expkN)
auv = auv_golden.clone()
auv[0, :].mul_(0.5)
auv[:, 0].mul_(0.5)
auv_by_wu2_plus_wv2_wu = auv.mul(wu_by_wu2_plus_wv2_2X)
auv_by_wu2_plus_wv2_wv = auv.mul(wv_by_wu2_plus_wv2_2X)
field_map_x_golden = dct.idsct2(auv_by_wu2_plus_wv2_wu, expkM, expkN)
field_map_y_golden = dct.idcst2(auv_by_wu2_plus_wv2_wv, expkM, expkN)
# compute potential phi
# auv / (wu**2 + wv**2)
auv_by_wu2_plus_wv2 = auv.mul(inv_wu2_plus_wv2_2X).mul_(2)
#potential_map = discrete_spectral_transform.idcct2(auv_by_wu2_plus_wv2, expkM, expkN)
potential_map_golden = dct.idcct2(auv_by_wu2_plus_wv2, expkM, expkN)
# compute energy
energy_golden = potential_map_golden.mul(density_map).sum()
if density_map.is_cuda:
torch.cuda.synchronize()
# the second approach uses the idxst_idct and idct_idxst
dct2 = dct2_fft2.DCT2(exact_expkM, exact_expkN)
idct2 = dct2_fft2.IDCT2(exact_expkM, exact_expkN)
idct_idxst = dct2_fft2.IDCT_IDXST(exact_expkM, exact_expkN)
idxst_idct = dct2_fft2.IDXST_IDCT(exact_expkM, exact_expkN)
inv_wu2_plus_wv2 = 1.0 / wu2_plus_wv2
inv_wu2_plus_wv2[0, 0] = 0.0
wu_by_wu2_plus_wv2_half = wu.mul(inv_wu2_plus_wv2).mul_(0.5)
wv_by_wu2_plus_wv2_half = wv.mul(inv_wu2_plus_wv2).mul_(0.5)
buv = dct2.forward(density_map)
buv_by_wu2_plus_wv2_wu = buv.mul(wu_by_wu2_plus_wv2_half)
buv_by_wu2_plus_wv2_wv = buv.mul(wv_by_wu2_plus_wv2_half)
field_map_x = idxst_idct.forward(buv_by_wu2_plus_wv2_wu)
field_map_y = idct_idxst.forward(buv_by_wu2_plus_wv2_wv)
buv_by_wu2_plus_wv2 = buv.mul(inv_wu2_plus_wv2)
potential_map = idct2.forward(buv_by_wu2_plus_wv2)
energy = potential_map.mul(density_map).sum()
if density_map.is_cuda:
torch.cuda.synchronize()
# compare results
np.testing.assert_allclose(buv.data.cpu().numpy(), auv_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(field_map_x.data.cpu().numpy(), field_map_x_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(field_map_y.data.cpu().numpy(), field_map_y_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(potential_map.data.cpu().numpy(), potential_map_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(energy.data.cpu().numpy(), energy_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
# the third approach uses the dct.idxst_idct and dct.idxst_idct
dct2 = dct.DCT2(expkM, expkN)
idct2 = dct.IDCT2(expkM, expkN)
idct_idxst = dct.IDCT_IDXST(expkM, expkN)
idxst_idct = dct.IDXST_IDCT(expkM, expkN)
cuv = dct2.forward(density_map)
cuv_by_wu2_plus_wv2_wu = cuv.mul(wu_by_wu2_plus_wv2_half)
cuv_by_wu2_plus_wv2_wv = cuv.mul(wv_by_wu2_plus_wv2_half)
field_map_x = idxst_idct.forward(cuv_by_wu2_plus_wv2_wu)
field_map_y = idct_idxst.forward(cuv_by_wu2_plus_wv2_wv)
cuv_by_wu2_plus_wv2 = cuv.mul(inv_wu2_plus_wv2)
potential_map = idct2.forward(cuv_by_wu2_plus_wv2)
energy = potential_map.mul(density_map).sum()
if density_map.is_cuda:
torch.cuda.synchronize()
# compare results
np.testing.assert_allclose(cuv.data.cpu().numpy(), auv_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(field_map_x.data.cpu().numpy(), field_map_x_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(field_map_y.data.cpu().numpy(), field_map_y_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(potential_map.data.cpu().numpy(), potential_map_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
np.testing.assert_allclose(energy.data.cpu().numpy(), energy_golden.data.cpu().numpy(), rtol=1e-6, atol=1e-5)
def forward(self, pos):
if self.initial_density_map is None:
if self.num_terminals == 0:
num_fixed_impacted_bins_x = 0
num_fixed_impacted_bins_y = 0
else:
num_fixed_impacted_bins_x = int(
((self.node_size_x[
self.num_movable_nodes:self.num_movable_nodes +
self.num_terminals].max() + self.bin_size_x) /
self.bin_size_x).ceil().clamp(max=self.num_bins_x))
num_fixed_impacted_bins_y = int(
((self.node_size_y[
self.num_movable_nodes:self.num_movable_nodes +
self.num_terminals].max() + self.bin_size_y) /
self.bin_size_y).ceil().clamp(max=self.num_bins_y))
if pos.is_cuda:
self.initial_density_map = electric_potential_cuda.fixed_density_map(
pos.view(pos.numel()), self.node_size_x, self.node_size_y,
self.bin_center_x, self.bin_center_y, self.xl, self.yl,
self.xh, self.yh, self.bin_size_x, self.bin_size_y,
self.num_movable_nodes, self.num_terminals,
self.num_bins_x, self.num_bins_y,
num_fixed_impacted_bins_x, num_fixed_impacted_bins_y)
else:
self.initial_density_map = electric_potential_cpp.fixed_density_map(
pos.view(pos.numel()), self.node_size_x, self.node_size_y,
self.bin_center_x, self.bin_center_y, self.xl, self.yl,
self.xh, self.yh, self.bin_size_x, self.bin_size_y,
self.num_movable_nodes, self.num_terminals,
self.num_bins_x, self.num_bins_y,
num_fixed_impacted_bins_x, num_fixed_impacted_bins_y,
self.num_threads)
# plot(0, self.initial_density_map.clone().div(self.bin_size_x*self.bin_size_y).cpu().numpy(), self.padding, 'summary/initial_potential_map')
# scale density of fixed macros
self.initial_density_map.mul_(self.target_density)
# expk
M = self.num_bins_x
N = self.num_bins_y
self.exact_expkM = precompute_expk(M,
dtype=pos.dtype,
device=pos.device)
self.exact_expkN = precompute_expk(N,
dtype=pos.dtype,
device=pos.device)
# init dct2, idct2, idct_idxst, idxst_idct with expkM and expkN
self.dct2 = dct.DCT2(self.exact_expkM, self.exact_expkN)
if not self.fast_mode:
self.idct2 = dct.IDCT2(self.exact_expkM, self.exact_expkN)
self.idct_idxst = dct.IDCT_IDXST(self.exact_expkM,
self.exact_expkN)
self.idxst_idct = dct.IDXST_IDCT(self.exact_expkM,
self.exact_expkN)
# wu and wv
wu = torch.arange(M, dtype=pos.dtype, device=pos.device).mul(
2 * np.pi / M).view([M, 1])
# scale wv because the aspect ratio of a bin may not be 1
wv = torch.arange(N, dtype=pos.dtype,
device=pos.device).mul(2 * np.pi / N).view(
[1,
N]).mul_(self.bin_size_x / self.bin_size_y)
wu2_plus_wv2 = wu.pow(2) + wv.pow(2)
wu2_plus_wv2[0,
0] = 1.0 # avoid zero-division, it will be zeroed out
self.inv_wu2_plus_wv2 = 1.0 / wu2_plus_wv2
self.inv_wu2_plus_wv2[0, 0] = 0.0
self.wu_by_wu2_plus_wv2_half = wu.mul(self.inv_wu2_plus_wv2).mul_(
1. / 2)
self.wv_by_wu2_plus_wv2_half = wv.mul(self.inv_wu2_plus_wv2).mul_(
1. / 2)
return ElectricPotentialFunction.apply(
pos, self.node_size_x_clamped, self.node_size_y_clamped,
self.offset_x, self.offset_y, self.ratio, self.bin_center_x,
self.bin_center_y, self.initial_density_map, self.target_density,
self.xl, self.yl, self.xh, self.yh, self.bin_size_x,
self.bin_size_y, self.num_movable_nodes, self.num_filler_nodes,
self.padding, self.padding_mask, self.num_bins_x, self.num_bins_y,
self.num_movable_impacted_bins_x, self.num_movable_impacted_bins_y,
self.num_filler_impacted_bins_x, self.num_filler_impacted_bins_y,
self.sorted_node_map, self.exact_expkM, self.exact_expkN,
self.inv_wu2_plus_wv2, self.wu_by_wu2_plus_wv2_half,
self.wv_by_wu2_plus_wv2_half, self.dct2, self.idct2,
self.idct_idxst, self.idxst_idct, self.fast_mode, self.num_threads)
def eval_dct2d(x, expk0, expk1, expkM, expkN, runs):
x_numpy = x.data.cpu().numpy()
torch.cuda.synchronize()
tt = time.time()
y = fftpack.dct(fftpack.dct(x_numpy.T, norm=None).T/x.size(1), norm=None)/x.size(0)
torch.cuda.synchronize()
print("CPU scipy.fftpack.dct2d takes %.7f ms" % ((time.time()-tt)*1000))
# 9s for 200 iterations 1024x1024 on GTX 1080
torch.cuda.synchronize()
tt = time.time()
# with torch.autograd.profiler.profile(use_cuda=True) as prof:
for i in range(runs):
y_2N = discrete_spectral_transform.dct2_2N(x, expk0=expk0, expk1=expk1)
torch.cuda.synchronize()
# print(prof)
print("PyTorch: dct2d_2N takes %.7f ms" % ((time.time()-tt)/runs*1000))
# 11s for 200 iterations 1024x1024 on GTX 1080
perm0 = discrete_spectral_transform.get_perm(x.size(-2), dtype=torch.int64, device=x.device)
perm1 = discrete_spectral_transform.get_perm(x.size(-1), dtype=torch.int64, device=x.device)
torch.cuda.synchronize()
tt = time.time()
# with torch.autograd.profiler.profile(use_cuda=True) as prof:
for i in range(runs):
y_N = discrete_spectral_transform.dct2_N(x, perm0=perm0, expk0=expk0, perm1=perm1, expk1=expk1)
torch.cuda.synchronize()
# print(prof)
print("PyTorch: dct2d_N takes %.7f ms" % ((time.time()-tt)/runs*1000))
dct2func = dct.DCT2(expk0, expk1, algorithm='2N')
torch.cuda.synchronize()
tt = time.time()
# with torch.autograd.profiler.profile(use_cuda=True) as prof:
for i in range(runs):
y_2N = dct2func.forward(x)
torch.cuda.synchronize()
# print(prof)
print("DCT2d_2N Function takes %.7f ms" % ((time.time()-tt)/runs*1000))
dct2func = dct.DCT2(expk0, expk1, algorithm='N')
y_N = dct2func.forward(x)
torch.cuda.synchronize()
# with torch.autograd.profiler.profile(use_cuda=True) as prof:
tt = time.time()
for i in range(runs):
y_N = dct2func.forward(x)
torch.cuda.synchronize()
# print(prof)
print("DCT2d_N Function takes %.7f ms" % ((time.time()-tt)/runs*1000))
# The implementation below only supports float64 by now
dct2func = dct_lee.DCT2(expk0, expk1)
torch.cuda.synchronize()
tt = time.time()
# with torch.autograd.profiler.profile(use_cuda=True) as prof:
for i in range(runs):
y_N = dct2func.forward(x)
torch.cuda.synchronize()
# print(prof)
print("DCT2d_Lee Function takes %.7f ms" % ((time.time()-tt)/runs*1000))
dct2func = dct2_fft2.DCT2(expkM, expkN)
y = dct2func.forward(x)
torch.cuda.synchronize()
tt = time.time()
for i in range(runs):
y_test = dct2func.forward(x)
torch.cuda.synchronize()
print("DCT2_FFT2 Function takes %.7f ms" % ((time.time()-tt)/runs*1000))
print("")
def test_dct2Random(self):
torch.manual_seed(10)
M = 4
N = 8
x = torch.empty(M, N, dtype=dtype).uniform_(0, 10.0)
expkM = discrete_spectral_transform.get_exact_expk(M, dtype=x.dtype, device=x.device)
expkN = discrete_spectral_transform.get_exact_expk(N, dtype=x.dtype, device=x.device)
golden_value = discrete_spectral_transform.dct2_N(x).data.numpy()
print("2D DCT golden_value")
print(golden_value)
# test cpu using N-FFT
# pdb.set_trace()
custom = dct.DCT2(algorithm='N')
dct_value = custom.forward(x)
print("2D dct_value")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
# test cpu using 2N-FFT
# pdb.set_trace()
custom = dct.DCT2(algorithm='2N')
dct_value = custom.forward(x)
print("2D dct_value")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
# test cpu using dct_lee
# pdb.set_trace()
custom = dct_lee.DCT2()
dct_value = custom.forward(x)
print("2D dct_value")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
# test cpu using fft2
custom = dct2_fft2.DCT2(expkM, expkN)
dct_value = custom.forward(x)
print("2D dct_value")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
if torch.cuda.device_count():
# test gpu
custom = dct.DCT2(algorithm='N')
dct_value = custom.forward(x.cuda()).cpu()
print("2D dct_value cuda")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
# test gpu
custom = dct.DCT2(algorithm='2N')
dct_value = custom.forward(x.cuda()).cpu()
print("2D dct_value cuda")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
# test gpu
custom = dct_lee.DCT2()
dct_value = custom.forward(x.cuda()).cpu()
print("2D dct_value cuda")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)
# test gpu using fft2
custom = dct2_fft2.DCT2(expkM.cuda(), expkN.cuda())
dct_value = custom.forward(x.cuda()).cpu()
print("2D dct_value cuda")
print(dct_value.data.numpy())
np.testing.assert_allclose(dct_value.data.numpy(), golden_value, rtol=1e-6, atol=1e-5)