| import torch |
| import math |
|
|
| torch.manual_seed(0) |
|
|
|
|
| class GaussianRF(object): |
| def __init__(self, dim, size, length=1.0, alpha=2.0, tau=3.0, sigma=None, boundary="periodic", constant_eig=False, device=None): |
|
|
| self.dim = dim |
| self.device = device |
|
|
| if sigma is None: |
| sigma = tau**(0.5*(2*alpha - self.dim)) |
|
|
| k_max = size//2 |
|
|
| const = (4*(math.pi**2))/(length**2) |
|
|
| if dim == 1: |
| k = torch.cat((torch.arange(start=0, end=k_max, step=1, device=device), \ |
| torch.arange(start=-k_max, end=0, step=1, device=device)), 0) |
|
|
| self.sqrt_eig = size*math.sqrt(2.0)*sigma*((const*(k**2) + tau**2)**(-alpha/2.0)) |
|
|
| if constant_eig: |
| self.sqrt_eig[0] = size*sigma*(tau**(-alpha)) |
| else: |
| self.sqrt_eig[0] = 0.0 |
|
|
| elif dim == 2: |
| wavenumers = torch.cat((torch.arange(start=0, end=k_max, step=1, device=device), \ |
| torch.arange(start=-k_max, end=0, step=1, device=device)), 0).repeat(size,1) |
|
|
| k_x = wavenumers.transpose(0,1) |
| k_y = wavenumers |
|
|
| self.sqrt_eig = (size**2)*math.sqrt(2.0)*sigma*((const*(k_x**2 + k_y**2) + tau**2)**(-alpha/2.0)) |
|
|
| if constant_eig: |
| self.sqrt_eig[0,0] = (size**2)*sigma*(tau**(-alpha)) |
| else: |
| self.sqrt_eig[0,0] = 0.0 |
|
|
| elif dim == 3: |
| wavenumers = torch.cat((torch.arange(start=0, end=k_max, step=1, device=device), \ |
| torch.arange(start=-k_max, end=0, step=1, device=device)), 0).repeat(size,size,1) |
|
|
| k_x = wavenumers.transpose(1,2) |
| k_y = wavenumers |
| k_z = wavenumers.transpose(0,2) |
|
|
| self.sqrt_eig = (size**3)*math.sqrt(2.0)*sigma*((const*(k_x**2 + k_y**2 + k_z**2) + tau**2)**(-alpha/2.0)) |
|
|
| if constant_eig: |
| self.sqrt_eig[0,0,0] = (size**3)*sigma*(tau**(-alpha)) |
| else: |
| self.sqrt_eig[0,0,0] = 0.0 |
|
|
| self.size = [] |
| for j in range(self.dim): |
| self.size.append(size) |
|
|
| self.size = tuple(self.size) |
|
|
| def sample(self, N): |
|
|
| coeff = torch.randn(N, *self.size, dtype=torch.cfloat, device=self.device) |
| coeff = self.sqrt_eig*coeff |
|
|
| u = torch.fft.irfftn(coeff, self.size, norm="backward") |
| return u |
