torch_openreml.covariance.IdentityMatrix

class torch_openreml.covariance.IdentityMatrix(n)

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.

__call__() follows the dtype and the device of its input; when it receives none, the PyTorch default dtype and device are used.

Initialize a fixed identity matrix of size n x n.

Parameters:

n (int, list, tuple or pandas.Series) – Matrix dimension, or a vector of levels whose distinct elements define it.

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__([free_params])	Return the identity matrix, on the dtype and device of the input.
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.
disable_cache()	Disable caching of intermediate computation results.
enable_cache()	Enable caching of intermediate computation results.
get_default_dtype_device()	Get the dtype and the device of the parameter defaults.
get_intermediates(params)	Retrieve cached intermediate computation results if still valid.
grad([free_params])	Compute the Jacobian of __call__() with respect to trainable parameters.
inverse([free_params])	Return the inverse of the identity matrix, which is the identity.
manual_grad([free_params])	Compute the Jacobian of __call__() with respect to free parameters using a closed-form analytic expression.
reset_intermediates()	Clear the intermediate computation cache.
resolve_dim(n)	Resolve a matrix dimension from an integer or a vector of levels.
set_intermediates(params, intermediates)	Cache intermediate computation results keyed by the parameter values.
set_param_specs(key, *[, fixed, default, trans])	Update the fields of one or more parameter specifications in place.
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, returned as stored rather than copied.
param_trans	Parameter transforms.
repr_dict	Key-value pairs used to build the string representation.
shape	Output matrix shape.
grad_mode	Gradient computation mode.
jacobian_method	Jacobian method used by auto_grad(), one of "jacrev", "jacfwd", or "jacobian".
jacobian_chunk_size	Number of outputs held per batch when auto_grad() differentiates with "jacrev", or None to compute the Jacobian in a single batch.
cache	Whether intermediate computation results are cached, toggled by enable_cache() and disable_cache().

__call__(free_params=None)

Return the identity matrix, on the dtype and device of the input.

The identity matrix has no parameters, so free_params carries no values: only its dtype and device are used. When it is omitted, the PyTorch default dtype and device are used.

Parameters:

free_params (torch.Tensor or dict, optional) – Empty 1D parameter tensor whose dtype and device are followed, or an empty parameter dict. If omitted, the PyTorch default dtype and device are used. Default: None.

Returns:

The n x n identity matrix.

Return type:

torch.Tensor

Raises:

• TypeError – If free_params is not a Torch tensor or a dict.

• ValueError – If free_params is not empty, since the matrix has no parameters to receive.

Example:

import torch
from torch_openreml.covariance import IdentityMatrix

mat = IdentityMatrix(3)
mat()

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

mat(torch.tensor([], dtype=torch.float64))

tensor([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.]], dtype=torch.float64)

inverse(free_params=None)

Return the inverse of the identity matrix, which is the identity.

\(\symbf{I}_n^{-1} = \symbf{I}_n\), so the matrix is returned unchanged.

Parameters:

free_params (torch.Tensor or dict, optional) – Empty 1D parameter tensor whose dtype and device are followed, or an empty parameter dict. If omitted, the PyTorch default dtype and device are used. Default: None.

Returns:

The n x n identity matrix.

Return type:

torch.Tensor

Raises:

• TypeError – If free_params is not a Torch tensor or a dict.

• ValueError – If free_params is not empty, since the matrix has no parameters to receive.

Example:

import torch
from torch_openreml.covariance import IdentityMatrix

mat = IdentityMatrix(3)
mat.inverse()

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

mat.inverse(torch.tensor([], dtype=torch.float64))

tensor([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.]], dtype=torch.float64)