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    def forward(self, input_data):
        noise, conditional, mask, diffusion_steps, frk_basis = input_data

        # Handle mask and concatenate it to the conditional input
        conditional = conditional * mask
        conditional = torch.cat([conditional, mask.float(), frk_basis], dim=1)

        # Forward pass through the network
        x = noise  # Ensure x is 3D (B, C, L)
        x = self.init_conv(x)
        x = self.residual_layer((x, conditional, diffusion_steps))
        y = self.final_conv(x)

        return y

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def sampling(
    net: torch.nn.Module,
    size: Tuple[int, int, int],
    diffusion_hyperparams: Dict[str, torch.Tensor],
    cond: torch.Tensor,
    mask: torch.Tensor,
    only_generate_missing: int = 0,
    device: Union[torch.device, str] = "cpu",
) -> torch.Tensor:
    """
    Perform the complete sampling step according to p(x_0|x_T) = \prod_{t=1}^T p_{\theta}(x_{t-1}|x_t).

    Args:
        net (torch.nn.Module): The wavenet model.
        size (Tuple[int, int, int]): Size of tensor to be generated, usually (number of audios to generate, channels=1, length of audio).
        diffusion_hyperparams (Dict[str, torch.Tensor]): Dictionary of diffusion hyperparameters returned by calc_diffusion_hyperparams. Note, the tensors need to be cuda tensors.
        cond (torch.Tensor): Conditioning tensor.
        mask (torch.Tensor): Mask tensor.
        only_generate_missing (int, optional): Flag indicating whether to only generate missing values (default is 0).
        device (Union[torch.device, str], optional): Device to place tensors (default is 'cpu').

    Returns:
        torch.Tensor: The generated audio(s) in torch.Tensor, shape=size.
    """

    _dh = diffusion_hyperparams
    T, Alpha, Alpha_bar, Sigma = _dh["T"], _dh["Alpha"], _dh["Alpha_bar"], _dh["Sigma"]
    assert len(Alpha) == T
    assert len(Alpha_bar) == T
    assert len(Sigma) == T
    assert len(size) == 3

    x = std_normal(size, device)

    with torch.no_grad():
        for t in range(T - 1, -1, -1):
            if only_generate_missing == 1:
                x = x * (1 - mask).float() + cond * mask.float()
            diffusion_steps = (t * torch.ones((size[0], 1))).to(
                device
            )  # use the corresponding reverse step
            epsilon_theta = net(
                (x, cond, mask, diffusion_steps)
            )  # predict \epsilon according to \epsilon_\theta
            # update x_{t-1} to \mu_\theta(x_t)
            x = (
                x - (1 - Alpha[t]) / torch.sqrt(1 - Alpha_bar[t]) * epsilon_theta
            ) / torch.sqrt(Alpha[t])
            if t > 0:
                x = x + Sigma[t] * std_normal(
                    size, device
                )  # add the variance term to x_{t-1}

    return x

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def sampling(
    net: torch.nn.Module,
    size: Tuple[int, int, int],
    diffusion_hyperparams: Dict[str, torch.Tensor],
    cond: torch.Tensor,
    mask: torch.Tensor,
    frk_basis: torch.Tensor,
    only_generate_missing: int = 0,
    device: Union[torch.device, str] = "cpu",
) -> torch.Tensor:
    """
    Perform the complete sampling step according to p(x_0|x_T) = \prod_{t=1}^T p_{\theta}(x_{t-1}|x_t).

    Args:
        net (torch.nn.Module): The wavenet model.
        size (Tuple[int, int, int]): Size of tensor to be generated, usually (number of audios to generate, channels=1, length of audio).
        diffusion_hyperparams (Dict[str, torch.Tensor]): Dictionary of diffusion hyperparameters returned by calc_diffusion_hyperparams. Note, the tensors need to be cuda tensors.
        cond (torch.Tensor): Conditioning tensor.
        mask (torch.Tensor): Mask tensor.
        only_generate_missing (int, optional): Flag indicating whether to only generate missing values (default is 0).
        device (Union[torch.device, str], optional): Device to place tensors (default is 'cpu').

    Returns:
        torch.Tensor: The generated audio(s) in torch.Tensor, shape=size.
    """

    _dh = diffusion_hyperparams
    T, Alpha, Alpha_bar, Sigma = _dh["T"], _dh["Alpha"], _dh["Alpha_bar"], _dh["Sigma"]
    assert len(Alpha) == T
    assert len(Alpha_bar) == T
    assert len(Sigma) == T
    assert len(size) == 3

    x = std_normal(size, device)

    with torch.no_grad():
        for t in range(T - 1, -1, -1):
            if only_generate_missing == 1:
                x = x * (1 - mask).float() + cond * mask.float()
            diffusion_steps = (t * torch.ones((size[0], 1))).to(
                device
            )  # use the corresponding reverse step
            epsilon_theta = net(
                (x, cond, mask, diffusion_steps, frk_basis)
            )  # predict \epsilon according to \epsilon_\theta
            # update x_{t-1} to \mu_\theta(x_t)
            x = (
                x - (1 - Alpha[t]) / torch.sqrt(1 - Alpha_bar[t]) * epsilon_theta
            ) / torch.sqrt(Alpha[t])
            if t > 0:
                x = x + Sigma[t] * std_normal(
                    size, device
                )  # add the variance term to x_{t-1}

    return x

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    def generate(self) -> list:
        """Generate samples using the given neural network model."""
        all_mses = []
        all_mapes = []
        for index, (batch,) in enumerate(self.dataloader):
            batch = batch.to(self.device)
            mask = self._update_mask(batch)

            if torch.isnan(mask).any():  # debug
                print(f"[Batch {index}] NaN in mask!")

            batch = torch.nan_to_num(batch, nan=0.0)  # Replace NaN with 0.0

            if torch.isnan(batch).any():  # debug
                print(f"[NaN DETECTED] Batch {index} has NaNs!")

            batch = batch.permute(0, 2, 1)

            generated_series = (
                sampling(
                    net=self.net,
                    size=batch.shape,
                    diffusion_hyperparams=self.diffusion_hyperparams,
                    cond=batch,
                    mask=mask,
                    frk_basis=self.frk_basis,
                    only_generate_missing=self.only_generate_missing,
                    device=self.device,
                )
                .detach()
                .cpu()
                .numpy()
            )

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import logging
import os
from typing import Dict, Iterable, Optional, Union

import numpy as np
import torch
import torch.nn as nn
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error
from torch.utils.data import DataLoader

from sssd.core.model_specs import MASK_FN
from sssd.utils.logger import setup_logger
from sssd.utils.utils import find_max_epoch, sampling

from sssd.core.mrts.mrts import MRTS

LOGGER = setup_logger()


class DiffusionGenerator:
    """
    Generate data based on ground truth.

    Args:
        net (torch.nn.Module): The neural network model.
        device (Optional[Union[torch.device, str]]): The device to run the model on (e.g., 'cuda' or 'cpu').
        diffusion_hyperparams (dict): Dictionary of diffusion hyperparameters.
        local_path (str): Local path format for the model.
        testing_data (torch.Tensor): Tensor containing testing data.
        output_directory (str): Path to save generated samples.
        batch_size (int): Number of samples to generate.
        ckpt_path (str): Checkpoint directory.
        ckpt_iter (str): Pretrained checkpoint to load; 'max' selects the maximum iteration.
        masking (str): Type of masking: 'mnr' (missing not at random), 'bm' (black-out), 'rm' (random missing).
        missing_k (int): Number of missing time points for each channel across the length.
        only_generate_missing (int): Whether to generate only missing portions of the signal:
                                      - 0 (all sample diffusion),
                                      - 1 (generate missing portions only).
        saved_data_names (Iterable[str], optional): Names of data arrays to save (default is ("imputation", "original", "mask")).
        logger (Optional[logging.Logger], optional): Logger object for logging messages (default is None).
    """

    def __init__(
        self,
        net: torch.nn.Module,
        device: Optional[Union[torch.device, str]],
        diffusion_hyperparams: dict,
        local_path: str,
        dataloader: DataLoader,
        output_directory: str,
        batch_size: int,
        ckpt_path: str,
        ckpt_iter: str,
        masking: str,
        missing_k: int,
        only_generate_missing: int,
        saved_data_names: Iterable[str] = ("imputation", "original", "mask"),
        logger: Optional[logging.Logger] = None,
        locs: Optional[torch.Tensor] = None
    ):
        self.net = net
        self.device = device
        self.diffusion_hyperparams = diffusion_hyperparams
        self.local_path = local_path
        self.dataloader = dataloader
        self.batch_size = batch_size
        self.masking = masking
        self.missing_k = missing_k
        self.only_generate_missing = only_generate_missing
        self.logger = logger or LOGGER

        self.output_directory = self._prepare_output_directory(
            output_directory, local_path, ckpt_iter
        )
        self.saved_data_names = saved_data_names
        self._load_checkpoint(ckpt_path, ckpt_iter)


        self.locs = locs
        frk = MRTS(locs=self.locs, device=self.device)
        self.frk_basis = frk()
        batch_size_shape, time_shape, loc_shape = next(iter(dataloader))[0].shape
        
        #print(f"self.frk_basis is None, initializing...")
        frk_linear = nn.Linear(self.frk_basis.shape[1], time_shape).to(self.device)
        loc_embed = nn.Embedding(loc_shape, time_shape).to(self.device)

        self.frk_basis = frk_linear(self.frk_basis)  # [26, 29] → [26, 2000]
        loc_ids = torch.arange(loc_shape, device=self.device)
        self.frk_basis += loc_embed(loc_ids)  # 加入地點特徵
        self.frk_basis = self.frk_basis.unsqueeze(0).expand(batch_size_shape, -1, -1)  # [1, 26, 2000]
        self.frk_basis = self.frk_basis.detach()
        #print(f"frk unsqueeze shape: {self.frk_basis.shape}")
        #print(f"frk original shape: {self.frk_basis.shape}")

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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

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())
    net = setup_model(inference_config["use_model"], model_config, 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}"

    locations_loder = get_locations_loader(inference_config["data"]["location_path"], device)

    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,
            locs=locations_loder,
        ).generate()

        LOGGER.info(f"Average MSE: {sum(mses) / len(mses)}")
        LOGGER.info(f"Average MAPE: {sum(mapes) / len(mapes)}")
        LOGGER.info(display_current_time())

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# Inference configuration
batch_size: 1  # Batch size for inference
output_directory: "./results/real_time/train_200_with_custom/tf/200/original/tf"  # Output directory for inference results
ckpt_path: "./results/real_time/checkpoints/test"  # Path to checkpoint for inference
trials: 1 # Replications

# Additional training settings
only_generate_missing: true  # Generate missing values only
use_model: 2  # Model to use for training
masking: "forecast"  # Masking strategy for missing values
missing_k: 200  # Number of missing values

# Data paths
data:
  test_path: "./datasets/real_time/pollutants_test.npy"  # Path to test data
  location_path: "./datasets/real_time/locations.npy"  # Path to location data

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"""
Title: Multi-Resolution Thin-plate Spline basis function for Spatial Data, and calculate the basis function by using rectangular or spherical coordinates.
Author: Hsu, Yao-Chih
Version: 1140611
Reference: Resolution Adaptive Fixed Rank Kringing by ShengLi Tzeng & Hsin-Cheng Huang
"""

# import modules
import numpy as np
import pandas as pd
import torch
import torch.nn as nn
from scipy.integrate import quad
from scipy.sparse.linalg import eigsh
from typing import Optional, Union
import logging
#import colorlog
#import datetime

## logger config
logger = logging.getLogger()
#handler = colorlog.StreamHandler()
#handler.setFormatter(colorlog.ColoredFormatter(
#    fmt='%(log_color)s%(asctime)s %(levelname)s: %(message)s',
#    datefmt='%Y-%m-%d %H:%M:%S',
#    log_colors={
#        'INFO': 'green',
#        'WARNING': 'yellow',
#        'ERROR': 'red',
#        'DEBUG': 'cyan',
#        'CRITICAL': 'bold_red',
#    }
#))
#logger.addHandler(handler)
#logger.setLevel(logging.INFO)

# classes
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).
        """
        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.
        """

        # 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]
    
# functions


# main program
if __name__ == "__main__":
    # time
    start_time = datetime.datetime.now()

    # Load locations
    locations = np.load(f'locations.npy')

    print(f'locations:\n{locations}')
    print(f'locations shape: {locations.shape}')

    # Convert to tensor
    locs = torch.tensor(locations, dtype=torch.float32)

    # Create FRK basis
    device = 'cuda' if torch.cuda.is_available() else 'cpu'
    frk_basis = MRTS(locs, device=device, calculate_with_spherical=False)

    # Forward pass
    #F = pd.DataFrame(frk_basis().detach().cpu().numpy())
    F = pd.DataFrame(frk_basis())
    #.detach().cpu().numpy()

    print(f'F:\n{F}')
    # print(f'F sum:\n{np.sum(F**2, axis=0)}')
    # print(f'F shape: {F.shape}')

    # time
    end_time = datetime.datetime.now()
    use_time = end_time - start_time
    print(f'Use time: {use_time}')





    # bx = pd.DataFrame(np.load('bx.npy'))
    # print(f'bx:\n{bx}')
    # print(f'bx shape: {bx.shape}')
    # print(f'bx sum:\n{np.sum(bx**2, axis=0)}')


    # # Compare with bx
    # temp = F.iloc[:, :bx.shape[1]] - bx
    # print(f'F - bx:\n{temp}')
    # print(f'F - bx sum**2:\n{np.sum(temp**2, axis=0)}')

    # from scipy.optimize import linear_sum_assignment

    # # 假設 F 和 bx 是 numpy array
    # # 計算 cost matrix（F[i] 和 bx[j] 的差異平方）
    # cost_matrix = np.array([[np.sum((F[i] - bx[j])**2) for j in range(bx.shape[0])] for i in range(F.shape[0])])

    # # 使用匈牙利演算法找出最小成本配對
    # row_ind, col_ind = linear_sum_assignment(cost_matrix)

    # # 印出結果
    # for i, j in zip(row_ind, col_ind):
    #     print(f'F[{i}] 對應到 bx[{j}], 差異平方: {cost_matrix[i, j]:.4f}')

    # # 如果你想印出總差異平方和
    # total_cost = cost_matrix[row_ind, col_ind].sum()
    # print(f'總差異平方和: {total_cost:.4f}')

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def run_job(
    model_config: dict,
    training_config: dict,
    device: Optional[Union[torch.device, str]],
) -> None:
    output_directory = setup_output_directory(model_config, training_config)
    dataloader = get_dataloader(
        training_config["data"]["train_path"],
        batch_size=training_config.get("batch_size"),
        device=device,
    )

    locations_loder = get_locations_loader(training_config["data"]["location_path"], device)

    diffusion_hyperparams = calc_diffusion_hyperparams(
        **model_config["diffusion"], device=device
    )
    net = setup_model(training_config["use_model"], model_config, device)


    ## 包裝成 DataParallel（多 GPU）
    #if torch.cuda.device_count() > 1:
    #    LOGGER.info(f"Wrapping model with DataParallel across {torch.cuda.device_count()} GPUs")
    #    net = torch.nn.DataParallel(net)
    #net = net.to(device)


    LOGGER.info(display_current_time())
    trainer = DiffusionTrainer(
        dataloader=dataloader,
        diffusion_hyperparams=diffusion_hyperparams,
        net=net,
        device=device,
        output_directory=output_directory,
        ckpt_iter=training_config.get("ckpt_iter"),
        n_iters=training_config.get("n_iters"),
        iters_per_ckpt=training_config.get("iters_per_ckpt"),
        iters_per_logging=training_config.get("iters_per_logging"),
        learning_rate=training_config.get("learning_rate"),
        only_generate_missing=training_config.get("only_generate_missing"),
        masking=training_config.get("masking"),
        missing_k=training_config.get("missing_k"),
        batch_size=training_config.get("batch_size"),
        logger=LOGGER,
        locs=locations_loder,
    )
    trainer.train()

    LOGGER.info(display_current_time())