Source code for torch_openreml.covariance.ar1_matrix

"""
AR(1) covariance matrix.

This module provides a first-order autoregressive covariance matrix with
a variance and a correlation parameter, for use in linear mixed-effects
models.

Classes:
    AR1Matrix:
        An AR(1) covariance matrix :math:`V_{ij} = \\sigma^2 \\rho^{|i-j|}`.
"""

from torch_openreml.covariance.matrix import Matrix
from torch_openreml.covariance.transform import TransformExpPow2, TransformChain, TransformScaleShift, TransformSigmoid
import torch



class AR1Matrix(Matrix):
    r"""
    First-order autoregressive covariance matrix.

    .. math::
        \symbf{V}_{ij} = \sigma^2 \rho^{|i - j|}

    Covariance decays geometrically with the lag between observations.
    The variance :math:`\sigma^2 > 0` is enforced by
    :class:`~torch_openreml.covariance.transform.TransformExpPow2` and the
    correlation :math:`\rho \in (-1, 1)` is enforced by a sigmoid scaled
    to :math:`(-1, 1)` by default.
    """

  
    def __init__(self, n, param_specs=None):
        """
        Initialize an AR(1) covariance matrix of size ``n x n``.

        Args:
            n (int): Matrix dimension.
            param_specs (dict): Parameter specifications. Keys should be strings
                representing parameter names. Values should be dictionaries
                containing the specification for each parameter. Each specification
                dictionary should contain the keys ``"fixed"``, ``"default"``, and ``"trans"``,
                representing whether the parameter is fixed or free (bool), the
                default value (1D torch.Tensor), and the transform (:class:`~torch_openreml.covariance.transform.Transform`),
                respectively.

        Example:

        .. jupyter-execute::

            import torch
            from torch_openreml.covariance import AR1Matrix

            mat = AR1Matrix(4)
            mat

        .. jupyter-execute::

            free_params = torch.tensor([0.5, 1.0])
            mat(free_params)
        """
        param_specs = param_specs or {
            "sigma^2": {
                "fixed": False,
                "default": torch.tensor([0.0]),
                "trans": TransformExpPow2()},
            "rho" : {
                "fixed": False,
                "default": torch.tensor([0.0]),
                "trans": TransformChain([TransformSigmoid(), TransformScaleShift(2.0, -1.0)])
            }
        }
        super().__init__((n, n), param_specs)

    def _get_or_build_intermediates(self, free_params):
        built_params = self.build_params(free_params)
        cache = self.get_intermediates(built_params)

        if cache is None:
            device = built_params.device
            dtype = built_params.dtype
            sigma2, rho = built_params

            idx = torch.arange(self.shape[0], device=device, dtype=dtype)
            diff = torch.abs(idx.unsqueeze(0) - idx.unsqueeze(1))

            rho_power = rho ** diff

            cache = {"sigma2": sigma2, "rho": rho, "diff": diff, "rho_power": rho_power}
            self.set_intermediates(built_params, cache)

        return cache



    def __call__(self, free_params=None):
        if free_params is None:
            free_params = self.free_param_defaults
        cache = self._get_or_build_intermediates(free_params)
        v = cache["sigma2"] * cache["rho_power"]
            
        return v




    def manual_grad(self, free_params=None):
        """
        Compute the Jacobian of :meth:`__call__` with respect to trainable
        parameters using a closed-form analytic expression.

        Args:
            free_params (torch.Tensor or dict): Flat 1D parameter tensor or
                parameter dictionary.
                If omitted, default values are used. Default: ``None``.

        Returns:
            tuple: ``(grad, grad_names)``, where ``grad`` is a 3D tensor of
            shape ``(num_free_params, *shape)`` and
            ``grad_names`` is a list of the corresponding parameter names.
            Returns ``(None, [])`` if all parameters are fixed.
        """
        if free_params is None:
            free_params = self.free_param_defaults
        if len(free_params) == 0:
            return None, []

        cache = self._get_or_build_intermediates(free_params)

        grad = []

        free_param_trans_grad = self.trans_grad(free_params)
        free_param_index = self.free_param_index

        i = 0
        if 0 in free_param_index:
            grad.append(free_param_trans_grad[i] * cache["rho_power"])
            i = i + 1

        if 1 in free_param_index:
            scaled_rho = torch.sign(cache["rho"]) * torch.clamp(cache["rho"].abs(), min=1e-6)
            d_rho = free_param_trans_grad[i] * cache["sigma2"] * cache["diff"] * cache["rho_power"] / scaled_rho
            d_rho.fill_diagonal_(0.0)
            grad.append(d_rho)

        grad = torch.stack(grad)

        return grad, self.free_param_names