Source code for torch_openreml.covariance.compound_symmetric_matrix

"""
Compound symmetric covariance matrix.

This module provides a compound symmetric covariance matrix with a shared
variance and a shared correlation parameter, for use in linear mixed-effects
models.

Classes:
    CompoundSymmetricMatrix:
        A compound symmetric covariance matrix
        :math:`V = \\sigma^2 [(1 - \\rho) I_n + \\rho J_n]`.
"""

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



class CompoundSymmetricMatrix(Matrix):
    r"""
    Compound symmetric covariance matrix with shared variance and correlation.

    .. math::
        \symbf{V} = \sigma^2 \left[(1 - \rho)\symbf{I}_n + \rho \symbf{J}_n \right]

    where :math:`\symbf{I}_n` is the identity matrix and :math:`\symbf{J}_n`
    is the matrix of ones. All diagonal entries equal :math:`\sigma^2` and
    all off-diagonal entries equal :math:`\sigma^2 \rho`.

    For :math:`\symbf{V}` to be positive definite, the correlation parameter
    must satisfy :math:`\rho > -1/(n-1)`. The default transform enforces this
    by mapping an unconstrained scalar through a sigmoid scaled to
    :math:`(-1/(n-1),\, 1)`.
    """

    def __init__(self, n, param_specs=None):
        """
        Initialize a compound symmetric 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 CompoundSymmetricMatrix

            mat = CompoundSymmetricMatrix(3)
            mat

        .. jupyter-execute::

            free_params = torch.tensor([0.5, 0.0])
            mat(free_params)

        .. jupyter-execute::

            mat.grad(free_params)
        """
        if n <= 1:
            raise ValueError("'n' must be greater than 1!")
        self.rho_min = -1/(n - 1)
        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((1 - self.rho_min), self.rho_min)])
            }
        }

        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

            i_n = torch.eye(self.shape[0], device=device, dtype=dtype)
            j_n = torch.ones((self.shape[0], self.shape[0]), device=device, dtype=dtype)
            rho_mat = ((1 - rho) * i_n + rho * j_n)

            cache = {"sigma2": sigma2, "i_n": i_n, "j_n": j_n, "rho_mat": rho_mat}
            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_mat"]

        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_mat"])
            i = i + 1

        if 1 in free_param_index:
            grad.append(cache["sigma2"] * (cache["j_n"] - cache["i_n"]) * free_param_trans_grad[i])

        grad = torch.stack(grad)

        return grad, self.free_param_names