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| import argparse
from typing import Optional, Union
import torch
import torch.nn as nn
import yaml
from sssd.core.model_specs import MODEL_PATH_FORMAT, setup_model
from sssd.data.utils import get_dataloader
from sssd.inference.generator import DiffusionGenerator
from sssd.utils.logger import setup_logger
from sssd.utils.utils import calc_diffusion_hyperparams, display_current_time
import numpy as np
import torch
import torch.nn as nn
from scipy.integrate import quad
from scipy.sparse.linalg import eigsh
from typing import Optional, Union
LOGGER = setup_logger()
def fetch_args() -> argparse.Namespace:
parser = argparse.ArgumentParser()
parser.add_argument(
"-m",
"--model_config",
type=str,
default="configs/model.yaml",
help="Model configuration",
)
parser.add_argument(
"-i",
"--inference_config",
type=str,
default="configs/inference_config.yaml",
help="Inference configuration",
)
parser.add_argument(
"-ckpt_iter",
"--ckpt_iter",
default="max",
help='Which checkpoint to use; assign a number or "max" to find the latest checkpoint',
)
return parser.parse_args()
# New function to load locations
def get_locations_loader(location_path, device: torch.device) -> torch.Tensor:
locations = np.load(location_path)
locations_tensor = torch.from_numpy(locations).float().to(device)
return locations_tensor
def run_job(
model_config: dict,
inference_config: dict,
device: Optional[Union[torch.device, str]],
ckpt_iter: Union[str, int],
) -> None:
trials = inference_config.get("trials")
batch_size = inference_config["batch_size"]
dataloader = get_dataloader(
inference_config["data"]["test_path"],
batch_size,
device=device,
)
local_path = MODEL_PATH_FORMAT.format(
T=model_config["diffusion"]["T"],
beta_0=model_config["diffusion"]["beta_0"],
beta_T=model_config["diffusion"]["beta_T"],
)
diffusion_hyperparams = calc_diffusion_hyperparams(
**model_config["diffusion"], device=device
)
LOGGER.info(display_current_time())
locs = get_locations_loader(inference_config["data"]["location_path"], device)
mrts = MRTS(locs=locs, k=locs.shape[0], device=device)
net = setup_model(inference_config["use_model"], model_config, mrts, device)
# Check if multiple GPUs are available
if torch.cuda.device_count() > 0:
net = nn.DataParallel(net)
data_names = ["imputation", "original", "mask"]
directory = inference_config["output_directory"]
if trials > 1:
directory += "_{trial}"
for trial in range(1, trials + 1):
LOGGER.info(f"The {trial}th inference trial")
saved_data_names = data_names if trial == 0 else data_names[0]
mses, mapes = DiffusionGenerator(
net=net,
device=device,
diffusion_hyperparams=diffusion_hyperparams,
dataloader=dataloader,
local_path=local_path,
output_directory=directory.format(trial=trial) if trials > 1 else directory,
ckpt_path=inference_config["ckpt_path"],
ckpt_iter=ckpt_iter,
batch_size=batch_size,
masking=inference_config["masking"],
missing_k=inference_config["missing_k"],
only_generate_missing=inference_config["only_generate_missing"],
saved_data_names=saved_data_names,
).generate()
LOGGER.info(f"Average MSE: {sum(mses) / len(mses)}")
LOGGER.info(f"Average MAPE: {sum(mapes) / len(mapes)}")
LOGGER.info(display_current_time())
class MRTS(nn.Module):
def __init__(self, locs: torch.Tensor,
k: int=None,
device: Optional[Union[torch.device, str]]=None,
calculate_with_spherical: bool=False,
standardize: bool=True,
unbiased_std: bool=False
):
"""
Multi-Resolution Thin-plate Spline basis function.
Args:
locs: [N, d] tensor of spatial locations.
k: (Optional) parameter for controlling resolution.
device: (Optional) PyTorch device to use.
calculate_with_spherical: (Optional) If True, use spherical coordinates for TPS calculation (default is False) (only supported when d == 2).
standardize: (Optional) If True, perform standardization on locs (Recommended).
unbiased_std: (Optional) If True, use unbiased standard deviation (dividing by N-1) (Recommended);
if False, use biased standard deviation (dividing by N).
"""
self.logger = LOGGER
logger = self.logger
super().__init__()
try:
if device is None:
self.device = torch.device('cpu')
logger.warning(f'Parameter "device" was not set. Default value "cpu" is used.')
else:
self.device = torch.device(device)
logger.info(f'Successfully using device "{self.device}".')
except (TypeError, ValueError) as e:
self.device = torch.device('cpu')
logger.warning(f'Parameter "device" is not a valid device ({device}). Default value "cpu" is used. Error: {e}')
self.register_buffer("locs", locs.to(self.device))
self.N, self.d = locs.shape
# number of basis
max_k = self.N + self.d
try:
if k is None:
self.k = max_k
logger.warning(f'Parameter "k" was not set. Default value {self.k} is used.')
elif 0 < k <= (max_k):
self.k = k
else:
self.k = max_k
logger.warning(f'Parameter "k" is out of valid range, it should be between 1 to {self.k}. Default value {self.k} is used.')
except TypeError:
self.k = max_k
logger.warning(f'Parameter "k" is not an integer, the type you input is "{type(k).__name__}." Default value {self.k} is used.')
self.calculate_with_spherical = calculate_with_spherical
if type(self.calculate_with_spherical) is not bool:
self.calculate_with_spherical = False
logger.warning(f'Parameter "calculate_with_spherical" should be a boolean, the type you input is "{type(calculate_with_spherical).__name__}". Default value False is used.')
elif self.calculate_with_spherical and self.d != 2:
self.calculate_with_spherical = False
logger.warning(f'Spherical TPS not implemented for d = {self.d}, only d = 2 is supported. Using rectangular coordinate system instead.')
if self.calculate_with_spherical:
logger.info(f'Calculate TPS with spherical coordinates.')
else:
logger.info(f'Calculate TPS with rectangular coordinates.')
self.standardize = standardize
if type(self.standardize) is not bool:
self.standardize = True
logger.warning(f'Parameter "standardize" should be a boolean, the type you input is "{type(standardize).__name__}". Default value True is used.')
self.unbiased_std = unbiased_std
if type(self.unbiased_std) is not bool:
self.unbiased_std = False
logger.warning(f'Parameter "unbiased_std" should be a boolean, the type you input is "{type(unbiased_std).__name__}". Default value False is used.')
def _tps_phi(self, locs: torch.Tensor, calculate_with_spherical: bool=False) -> torch.Tensor:
"""
Compute the Thin Plate Spline (TPS) radial basis matrix for input locations.
Args:
locs: [N, d] tensor of spatial locations.
calculate_with_spherical: (Optional) If True, use spherical coordinates for TPS calculation (default is False) (only supported when d == 2).
Returns:
A [N, N] tensor representing the TPS radial basis matrix.
"""
# rectangular coordinate system
if not calculate_with_spherical:
return self.__calculate_phi_by_rectangular_coordinate(locs)
# spherical coordinate system
else:
# convert to spherical coordinates
ret = torch.zeros((self.N, self.N), device=locs.device)
locs = locs * torch.pi / 180.0
x = locs[:, 0]
y = locs[:, 1]
for i in range(self.N):
for j in range(self.N):
ret[i, j] = self.__calculate_phi_by_spherical_coordinate(x[i], y[i], x[j], y[j])
return ret
def __calculate_phi_by_rectangular_coordinate(self, locs: torch.Tensor) -> torch.Tensor:
"""
Calculate the TPS radial basis matrix using rectangular (Euclidean) coordinates.
Args:
locs: [N, d] tensor of spatial locations.
Returns:
A [N, N] tensor representing the TPS radial basis matrix.
"""
dists = torch.cdist(locs, locs) # Euclidean distances
if self.d == 1:
return (dists ** 3) / 12
elif self.d == 2:
mask = dists != 0
ret = torch.zeros_like(dists)
ret[mask] = (dists[mask] ** 2) * torch.log(dists[mask]) / (8 * torch.pi)
return ret
elif self.d == 3:
return -dists / 8
else:
raise NotImplementedError(f"TPS not implemented for d = {self.d}")
def __calculate_phi_by_spherical_coordinate(self, x1: float, y1: float, x2: float, y2: float) -> float:
"""
Calculate the TPS radial basis function using spherical coordinates.
Args:
x1, y1: Spherical coordinates of the first point (in radians).
x2, y2: Spherical coordinates of the second point (in radians).
Returns:
A float representing the TPS radial basis function value.
"""
cos_theta = torch.sin(x1) * torch.sin(x2) + torch.cos(x1) * torch.cos(x2) * torch.cos(y1 - y2)
cos_theta = torch.clamp(cos_theta, -1.0, 1.0)
#theta = torch.acos(cos_theta)
ret = 1 - (torch.pi ** 2) / 6
if not torch.isclose(cos_theta, torch.tensor(-1.0, device=cos_theta.device)):
cos_theta = cos_theta.item()
upper = (cos_theta + 1) / 2
lower = 0
result, _ = quad(self.__integrand_for_spherical_in_tps, lower, upper, epsabs=1e-6, epsrel=1e-6, limit=50)
result = torch.tensor(result, dtype=torch.float32, device=self.device)
ret -= result
return ret
# # method by GPT can just use tenser to calculate and efficient
# # spherical coordinate system
# locs_rad = locs * torch.pi / 180.0 # convert to radians
# lat1 = locs_rad[:, 0].unsqueeze(1) # [N, 1]
# lon1 = locs_rad[:, 1].unsqueeze(1) # [N, 1]
# lat2 = locs_rad[:, 0].unsqueeze(0) # [1, N]
# lon2 = locs_rad[:, 1].unsqueeze(0) # [1, N]
# # Cosine of angular distance
# cos_theta = (
# torch.sin(lat1) @ torch.sin(lat2) + torch.cos(lat1) @ torch.cos(lat2) * torch.cos(lon1 - lon2)
# )
# cos_theta = torch.clamp(cos_theta, -1.0, 1.0)
# # Compute integral using trapezoidal rule
# N = 100 # Number of steps in the integral approximation
# x = torch.linspace(1e-6, 1.0, N, device=locs.device) # avoid x=0
# ln_term = torch.log(1 - x) / x # [N]
# def trapezoid_integrate(upper): # upper: [N, N]
# upper = torch.clamp(upper, 1e-6, 1.0)
# area = torch.zeros_like(upper)
# for i in range(N - 1):
# x0, x1 = x[i], x[i + 1]
# y0, y1 = ln_term[i], ln_term[i + 1]
# h = x1 - x0
# area += h * (y0 + y1) / 2 * ((upper >= x1).float()) # only add where upper > x1
# return area
# upper_bound = (cos_theta + 1) / 2 # [N, N]
# integral_vals = trapezoid_integrate(upper_bound) # [N, N]
# ret = 1 - (torch.pi ** 2) / 6 - integral_vals
# return ret
def __integrand_for_spherical_in_tps(self, x):
"""
Integrand function for the spherical TPS radial basis function.
Args:
x: The variable of integration.
Returns:
The value of the integrand at x.
"""
return np.log(1 - x) / x
def _standardize(self, x: torch.Tensor, unbiased_std: Optional[bool] = None) -> torch.Tensor:
"""
A function to standardize the input tensor x.
Args:
x: Input tensor to be standardized.
unbiased_std: (Optional) If True, use unbiased standard deviation (dividing by N-1);
if False, use biased standard deviation (dividing by N).
Default is None, which uses the class attribute self.unbiased_std.
Returns:
A standardized tensor with mean 0 and standard deviation 1.
"""
if unbiased_std is None:
unbiased_std = self.unbiased_std
mean = x.mean(dim=0, keepdim=True) # keepdim=True to keep the same shape
std = x.std(dim=0, unbiased=unbiased_std, keepdim=True) # unbiased=False for population std
std[std == 0] = 1.0
x = (x - mean) / std
return x
def forward(self) -> torch.Tensor:
"""
Forward pass to compute the basis functions. Constructs the basis functions based on the input locations and parameters.
Returns:
A tensor of shape [N, k] representing the basis functions.
"""
logger = self.logger
# Construct X = [1, x1, x2, ..., xd]
ones = torch.ones(self.N, 1, device=self.device)
X = torch.cat([ones, self.locs], dim=1) # [N, d+1]
if self.k == 1:
return ones
elif self.k <= self.d:
if self.standardize:
X[:, 1:self.k] = self._standardize(X[:, 1:self.k])
return X[:, :self.k]
# TPS basis
Phi = self._tps_phi(locs=self.locs, calculate_with_spherical=self.calculate_with_spherical) # [N, N]
# Q = I - X(XᵗX)⁻¹Xᵗ
try:
XtX_inv = torch.inverse(X.T @ X) # [(d+1), (d+1)]
except RuntimeError as e:
logger.warning(f'torch.inverse failed due to {e}, this implies "X.T @ X" didn\'t have inverse. Using torch.linalg.pinv instead.')
XtX_inv = torch.linalg.pinv(X.T @ X)
Q = torch.eye(self.N, device=self.device) - X @ XtX_inv @ X.T
# Eigen-decomposition
G = Q @ Phi @ Q
#eigenvalues, eigenvectors = torch.linalg.eigh(G) # ascending order
G = G.detach().cpu().numpy()
eigenvalues, eigenvectors = eigsh(G, k=self.k - self.d - 1, which='LM') # 'LM': Largest Magnitude, max k < N
eigenvalues = torch.from_numpy(eigenvalues).to(self.device)
eigenvectors = torch.from_numpy(eigenvectors).to(self.device)
# Filter out near-zero eigenvalues and sort descending
#valid = eigenvalues > 1e-10
#eigenvalues[~valid] *= -1.0 # make them positive
#eigenvectors[:, ~valid] *= -1.0 # make them positive
idx_desc = torch.argsort(eigenvalues, descending=True)
eigenvalues = eigenvalues[idx_desc]
eigenvectors = eigenvectors[:, idx_desc]
Basis_high = eigenvectors * torch.sqrt(torch.tensor(self.N, dtype=torch.float32))
# # Construct basis functions
# Basis_high = (Phi.T - Phi @ X @ XtX_inv @ X.T).T @ eigenvectors @ torch.diag(1.0 / eigenvalues).to(self.device)
# # the for loop
# Basis_high_1 = torch.zeros(self.N, self.N, device=self.locs.device)
# for i in range(self.N):
# phi_i = Phi[i, :]
# x_i = X[i, :]
# Phi_XXtXinv_x = (phi_i.T - Phi @ X @ XtX_inv @ x_i.T).T
# for j in range(self.N):
# lambda_j = 1 / eigenvalues[j]
# v_j = eigenvectors[:, j]
# Basis_high_1[i, j] = lambda_j * Phi_XXtXinv_x @ v_j
# print(f'Basis_high:\n{Basis_high}, \n\nBasis_high_1:\n{Basis_high_1}')
# print(torch.mean((Basis_high - Basis_high_1)**2))
# Concatenate [1, x1, ..., xd] and B_high
Basis_low = X # [N, d+1]
# Standardize
if self.standardize:
Basis_low[:, 1:(self.d + 1)] = self._standardize(Basis_low[:, 1:(self.d + 1)])
F = torch.cat([Basis_low, Basis_high], dim=1)
# Output k basis
F = F[:, :self.k]
# print('1')
# eigenvalues = eigenvalues[:self.k - self.d - 1] # Select top k - (d + 1) eigenvalues
# eigenvectors = eigenvectors[:, :self.k - self.d - 1] # Select top k - (d + 1) eigenvectors
# # compute BBBH and UZ
# BBB = XtX_inv @ X.T
# BBBH = BBB @ Phi
# BBB_gamma = BBB @ eigenvectors
# B_BBB_gamma = X @ BBB_gamma
# gammas = (eigenvectors - B_BBB_gamma) / eigenvalues.reshape(1, -1) * torch.sqrt(torch.tensor(self.N, dtype=torch.float32))
# print('2')
# col_sd = self.locs.std(dim=0, unbiased=True)
# adjustment = torch.sqrt(torch.tensor(self.N / (self.N - 1), dtype=col_sd.dtype, device=col_sd.device))
# diag_values = (adjustment / col_sd).cpu().numpy()
# xobs_diag = np.diag(diag_values)
# print('3')
# # 初始化组合矩阵
# UZ = np.zeros((self.N + self.d + 1, self.k))
# print('4')
# # 区块填充
# UZ[:self.N, :self.k - self.d - 1] = gammas # 左上区块
# UZ[self.N, self.k - self.d - 1] = 1.0 # 中心单位元素
# UZ[self.N + 1:, self.k - self.d:] = xobs_diag # 右下对角区块
return F # [N, d+1 + k]
if __name__ == "__main__":
args = fetch_args()
with open(args.model_config, "rt") as f:
model_config = yaml.safe_load(f.read())
with open(args.inference_config, "rt") as f:
inference_config = yaml.safe_load(f.read())
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
if torch.cuda.device_count() > 0:
LOGGER.info(f"Using {torch.cuda.device_count()} GPUs!")
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
run_job(model_config, inference_config, device, args.ckpt_iter)
|
