torch_openreml.covariance.IdentityMatrix¶

class torch_openreml.covariance.IdentityMatrix(n, dtype=None, device=None)[source]¶

Bases: Matrix

Fixed \(n \times n\) identity covariance matrix.

\[\symbf{V} = \symbf{I}_n\]

This matrix has no trainable parameters, so grad() always returns (None, []). It is typically used to represent independent, homoscedastic residuals.

Initialize a fixed identity matrix of size n x n.

Parameters:

n (int) – Matrix dimension.
dtype (torch.dtype, optional) – Desired dtype of the matrix. Defaults to the PyTorch default dtype.
device (torch.device, optional) – Desired device of the matrix. Defaults to the PyTorch default device.

Example:

import torch
from torch_openreml.covariance import IdentityMatrix

mat = IdentityMatrix(3)
mat()

tensor([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.]])

Methods

`__call__`(args, *kwargs)	Construct the matrix from a flat parameter tensor.
`auto_grad`([free_params])	Compute the Jacobian of `build()` with respect to free parameters using automatic differentiation.
`build_params`([free_params, include_fixed, ...])	Construct the full parameter tensor from free parameters.
`get_intermediates`(params)	Retrieve cached intermediate computation results if still valid.
`grad`([free_params])	Compute the Jacobian of `__call__()` with respect to trainable parameters.
`manual_grad`([free_params])	Compute the Jacobian of `__call__()` with respect to free parameters using a closed-form analytic expression.
`map_theta_to_dv`(theta)	An interface compatible with `torch_openreml.REML` that maps parameters to the matrix Jacobian.
`map_theta_to_v`(theta)	An interface compatible with `torch_openreml.REML` that maps parameters to a matrix.
`reset_intermediates`()	Clear the intermediate computation cache.
`set_intermediates`(params, intermediates)	Cache intermediate computation results keyed by parameter hash.
`trans_grad`([free_params])	Compute the element-wise derivative of the free parameter transforms.

Attributes

`fixed_param_defaults`	Fixed parameter defaults.
`fixed_param_index`	Index of fixed parameters.
`fixed_param_names`	Fixed parameter names.
`fixed_param_trans`	Transforms for fixed parameters.
`free_param_defaults`	Free parameter defaults.
`free_param_index`	Index of free parameters.
`free_param_names`	Free parameter names.
`free_param_trans`	Transforms for free parameters.
`num_fixed_params`	Total number of fixed parameters.
`num_free_params`	Total number of free parameters.
`num_params`	Total number of parameters.
`param_defaults`	Parameter defaults.
`param_names`	Parameter names.
`param_specs`	Parameter specifications.
`param_trans`	Parameter transforms.
`repr_dict`	Key-value pairs used to build the string representation.
`shape`	Output matrix shape.

__call__(*args, **kwargs)[source]¶

Construct the matrix from a flat parameter tensor.

Must be implemented by subclasses. Implementations should convert free_params via build_params() to validate, include fixed parameters, and apply transforms before any computation.

Parameters:: free_params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary. If omitted, default values are used. Default: None.
Returns:: Constructed matrix of shape shape.
Return type:: torch.Tensor