def test_NormalQMCEngineSeededInvTransform(self): # test even dimension engine = NormalQMCEngine(d=2, seed=12345, inv_transform=True) samples = engine.draw(n=2) self.assertEqual(samples.dtype, torch.float) self.assertEqual(samples.shape, torch.Size([2, 2])) # test odd dimension engine = NormalQMCEngine(d=3, seed=12345, inv_transform=True) samples = engine.draw(n=2) self.assertEqual(samples.shape, torch.Size([2, 3]))
def test_NormalQMCEngineSeededOut(self): # test even dimension engine = NormalQMCEngine(d=2, seed=12345) out = torch.zeros(2, 2) self.assertIsNone(engine.draw(n=2, out=out)) self.assertTrue(torch.all(out != 0)) # test odd dimension engine = NormalQMCEngine(d=3, seed=12345) out = torch.empty(2, 3) self.assertIsNone(engine.draw(n=2, out=out)) self.assertTrue(torch.all(out != 0))
def draw_sobol_normal_samples( d: int, n: int, device: Optional[torch.device] = None, dtype: Optional[torch.dtype] = None, seed: Optional[int] = None, ) -> Tensor: r"""Draw qMC samples from a multi-variate standard normal N(0, I_d) A primary use-case for this functionality is to compute an QMC average of f(X) over X where each element of X is drawn N(0, 1). Args: d: The dimension of the normal distribution. n: The number of samples to return. device: The torch device. dtype: The torch dtype. seed: The seed used for initializing Owen scrambling. If None (default), use a random seed. Returns: A tensor of qMC standard normal samples with dimension `n x d` with device and dtype specified by the input. Example: >>> samples = draw_sobol_normal_samples(2, 10) """ normal_qmc_engine = NormalQMCEngine(d=d, seed=seed, inv_transform=True) samples = normal_qmc_engine.draw(n, dtype=torch.float if dtype is None else dtype) return samples.to(device=device)
def test_NormalQMCEngineSeededInvTransform(self): # test even dimension engine = NormalQMCEngine(d=2, seed=12345, inv_transform=True) samples = engine.draw(n=2) self.assertEqual(samples.dtype, torch.float) samples_expected = torch.tensor([[-0.41622922, 0.46622792], [-0.96063897, -0.75568963]]) self.assertTrue(torch.allclose(samples, samples_expected)) # test odd dimension engine = NormalQMCEngine(d=3, seed=12345, inv_transform=True) samples = engine.draw(n=2) samples_expected = torch.tensor([ [-1.40525266, 1.37652443, -0.8519666], [-0.166497, -2.3153681, -0.15975676], ]) self.assertTrue(torch.allclose(samples, samples_expected))
def test_NormalQMCEngineSeeded(self): # test even dimension engine = NormalQMCEngine(d=2, seed=12345) samples = engine.draw(n=2) self.assertEqual(samples.dtype, torch.float) samples_expected = torch.tensor([[-0.63099602, -1.32950772], [0.29625805, 1.86425618]]) self.assertTrue(torch.allclose(samples, samples_expected)) # test odd dimension engine = NormalQMCEngine(d=3, seed=12345) samples = engine.draw(n=2) samples_expected = torch.tensor([ [1.83169884, -1.40473647, 0.24334828], [0.36596099, 1.2987395, -1.47556275], ]) self.assertTrue(torch.allclose(samples, samples_expected))
def test_NormalQMCEngineInvTransform(self): # d = 1 engine = NormalQMCEngine(d=1, inv_transform=True) samples = engine.draw() self.assertEqual(samples.dtype, torch.float) self.assertEqual(samples.shape, torch.Size([1, 1])) samples = engine.draw(n=5) self.assertEqual(samples.shape, torch.Size([5, 1])) # d = 2 engine = NormalQMCEngine(d=2, inv_transform=True) samples = engine.draw() self.assertEqual(samples.shape, torch.Size([1, 2])) samples = engine.draw(n=5) self.assertEqual(samples.shape, torch.Size([5, 2])) # test double dtype samples = engine.draw(dtype=torch.double) self.assertEqual(samples.dtype, torch.double)
def test_NormalQMCEngineSeededOut(self): # test even dimension engine = NormalQMCEngine(d=2, seed=12345) out = torch.empty(2, 2) self.assertIsNone(engine.draw(n=2, out=out)) samples_expected = torch.tensor([[-0.63099602, -1.32950772], [0.29625805, 1.86425618]]) self.assertTrue(torch.allclose(out, samples_expected)) # test odd dimension engine = NormalQMCEngine(d=3, seed=12345) out = torch.empty(2, 3) self.assertIsNone(engine.draw(n=2, out=out)) samples_expected = torch.tensor([ [1.83169884, -1.40473647, 0.24334828], [0.36596099, 1.2987395, -1.47556275], ]) self.assertTrue(torch.allclose(out, samples_expected))
def __init__(self, ndim, use_sobol=False, use_inv=True, cache=False): self.ndim = ndim self.cache = cache if use_sobol: self.sampler = NormalQMCEngine(d=ndim, inv_transform=use_inv) self.cached_points = torch.tensor([]) else: self.sampler = None
def test_NormalQMCEngineInvTransform(self): for d in (1, 2): engine = NormalQMCEngine(d=d, inv_transform=True) samples = engine.draw() self.assertEqual(samples.dtype, torch.float) self.assertEqual(samples.shape, torch.Size([1, d])) samples = engine.draw(n=5) self.assertEqual(samples.shape, torch.Size([5, d])) # test double dtype samples = engine.draw(dtype=torch.double) self.assertEqual(samples.dtype, torch.double) self.assertEqual(samples.shape, torch.Size([1, d]))
def test_NormalQMCEngineShapiroInvTransform(self): engine = NormalQMCEngine(d=2, seed=12345, inv_transform=True) samples = engine.draw(n=256) self.assertEqual(samples.dtype, torch.float) self.assertTrue(torch.all(torch.abs(samples.mean(dim=0)) < 1e-2)) self.assertTrue(torch.all(torch.abs(samples.std(dim=0) - 1) < 1e-2)) # perform Shapiro-Wilk test for normality for i in (0, 1): _, pval = shapiro(samples[:, i]) self.assertGreater(pval, 0.9) # make sure samples are uncorrelated cov = np.cov(samples.numpy().transpose()) self.assertLess(np.abs(cov[0, 1]), 1e-2)