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# SPDX-FileCopyrightText: Copyright (c) 2023 - 2024 NVIDIA CORPORATION & AFFILIATES.
# SPDX-FileCopyrightText: All rights reserved.
# SPDX-License-Identifier: Apache-2.0
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import torch
import torch.nn.functional as F
import math
from math import pi, gamma, sqrt
import numpy as np
torch.manual_seed(0)
class GRF_Mattern(object):
"""Generate Random Fields"""
def __init__(
self,
dim,
size,
length=1.0,
nu=None,
l=0.1,
sigma=1.0,
boundary="periodic",
constant_eig=None,
device=None,
):
self.dim = dim
self.device = device
self.bc = boundary
a = sqrt(2 / length)
if self.bc == "dirichlet":
constant_eig = None
if nu is not None:
kappa = sqrt(2 * nu) / l
alpha = nu + 0.5 * dim
self.eta2 = (
size**dim
* sigma
* (4.0 * pi) ** (0.5 * dim)
* gamma(alpha)
/ (kappa**dim * gamma(nu))
)
else:
self.eta2 = size**dim * sigma * (sqrt(2.0 * pi) * l) ** dim
k_max = size // 2
if self.bc == "periodic":
const = (4.0 * (pi**2)) / (length**2)
else:
const = (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,
)
k2 = k**2
if nu is not None:
eigs = 1.0 + (const / (kappa * length) ** 2 * k2)
self.sqrt_eig = self.eta2 / (length**dim) * eigs ** (-alpha / 2.0)
else:
self.sqrt_eig = (
self.eta2
/ (length**dim)
* torch.exp(-((l) ** 2) * const * k2 / 4.0)
)
if constant_eig is not None:
self.sqrt_eig[0] = constant_eig # (size**dim)*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
k2 = k_x**2 + k_y**2
if nu is not None:
eigs = 1.0 + (const / (kappa * length) ** 2 * k2)
self.sqrt_eig = self.eta2 / (length**dim) * eigs ** (-alpha / 2.0)
else:
self.sqrt_eig = (
self.eta2
/ (length**dim)
* torch.exp(-((l) ** 2) * const * k2 / 4.0)
)
if constant_eig is not None:
self.sqrt_eig[0, 0] = constant_eig # (size**dim)*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)
k2 = k_x**2 + k_y**2 + k_z**2
if nu is not None:
eigs = 1.0 + (const / (kappa * length) ** 2 * k2)
self.sqrt_eig = self.eta2 / (length**dim) * eigs ** (-alpha / 2.0)
else:
self.sqrt_eig = (
self.eta2
/ (length**dim)
* torch.exp(-((l) ** 2) * const * k2 / 4.0)
)
if constant_eig is not None:
self.sqrt_eig[
0, 0, 0
] = constant_eig # (size**dim)*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)
if self.bc == "dirichlet":
coeff.real[:] = 0
if self.bc == "neumann":
coeff.imag[:] = 0
coeff = self.sqrt_eig * coeff
u = torch.fft.irfftn(coeff, self.size, norm="backward")
return u
if __name__ == "__main__":
from hydra import compose, initialize
import h5py
import os
import matplotlib.pyplot as plt
initialize(version_base=None, config_path=".", job_name="generate_random_field")
cfg = compose(config_name="example_field")
N = cfg.num_samples
n = cfg.num_points
dim = cfg.dim
L = cfg.length
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
grf = GRF_Mattern(
dim=cfg.dim,
size=cfg.num_points,
length=cfg.length,
nu=cfg.nu,
l=cfg.length_scale,
sigma=cfg.sigma,
boundary=cfg.boundary_condition,
constant_eig=cfg.mean,
device=device,
)
U = grf.sample(N)
# convert to pad periodically
pad_width = [(0, 0)] + [(0, 1) for _ in range(dim)]
u = np.pad(U.cpu().numpy(), pad_width, mode="wrap")
x = np.linspace(0, L, n + 1)
digits = int(math.log10(N)) + 1
basefile = cfg.file
if basefile:
filedir, file = os.path.split(basefile)
if filedir:
os.makedirs(filedir, exist_ok=True)
for i, u0 in enumerate(u):
filename = f"{basefile}-{i:0{digits}d}.h5"
with h5py.File(filename, "w") as hf:
hf.create_dataset("u", data=u0)
for j in range(dim):
coord_name = f"x{j+1}"
hf.create_dataset(coord_name, data=x)
if cfg.plot:
# coords = [x for _ in dim]
# X = np.meshgrid(*coords, indexing='ij')
if dim == 2:
X, Y = np.meshgrid(x, x, indexing="ij")
plt.close("all")
fig = plt.figure()
pmesh = plt.pcolormesh(X, Y, u[0], cmap="jet", shading="gouraud")
plt.colorbar(pmesh)
plt.axis("square")
plt.title("Random Initial Data")
plt.show()
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