torch_openreml.covariance.HadamardProduct¶

class torch_openreml.covariance.HadamardProduct(*args, **kwargs)[source]¶

Bases: Operator

Hadamard (element-wise) product of two covariance matrices.

\[\symbf{V} = \symbf{A} \odot \symbf{B}\]

Both operands must have the same shape. Either or both may be trainable Matrix instances or fixed torch.Tensor values.

Initialize a Hadamard product operator from exactly two operands.

Parameters:

*args – Exactly two operands as positional arguments or a single dict. The first is \(\symbf{A}\), the second \(\symbf{B}\).
**kwargs – Exactly two operands as keyword arguments.

Raises:

ValueError – If the number of operands is not exactly two.

Example:

import torch
from torch_openreml.covariance import EquicorrelationMatrix, HadamardProduct

n = 4
op = HadamardProduct(a=EquicorrelationMatrix(n), b=torch.tensor([5.0]))
free_params = torch.tensor([1.0])
op(free_params)

tensor([[5.0000, 3.2071, 3.2071, 3.2071],
        [3.2071, 5.0000, 3.2071, 3.2071],
        [3.2071, 3.2071, 5.0000, 3.2071],
        [3.2071, 3.2071, 3.2071, 5.0000]])

Methods

`__call__`([free_params])	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_operands`([free_params])	Evaluate each operand at the current free parameters.
`build_params`([free_params, include_fixed, ...])	Construct the full parameter tensor by delegating to each operand.
`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 trainable 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.
`operands_grad`([free_params])	Compute the Jacobian of each operand with respect to its parameters.
`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.
`operands`	Mapping from operand names to operand matrices or tensors.
`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__(free_params=None)[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

manual_grad(free_params=None)[source]¶

Compute the Jacobian of __call__() with respect to trainable parameters using a closed-form analytic expression.

Applies the product rule: if \(\symbf{V} = \symbf{A} \odot \symbf{B}\) then the gradient with respect to \(\theta_{\symbf{A}}\) is \(\frac{\partial \symbf{A}}{\partial \theta_{\symbf{A}}} \odot \symbf{B}\), and similarly for \(\theta_{\symbf{B}}\). Per-operand Jacobians from operands_grad() are multiplied element-wise by the other operand’s value.

Parameters:

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

Returns:

(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.

Return type:

tuple

Raises:

TypeError – If free_params is not a Torch tensor.
ValueError – If free_params is not a 1D tensor or has the wrong length, or if free_params is a dict with missing or unexpected keys.

Example:

import torch
from torch_openreml.covariance import EquicorrelationMatrix, HadamardProduct

op = HadamardProduct(
    a=EquicorrelationMatrix(4),
    b=torch.tensor([5.0])
)
free_params = torch.tensor([1.0])
grad, grad_names = op.manual_grad(free_params)
grad

tensor([[[0.0000, 1.3107, 1.3107, 1.3107],
         [1.3107, 0.0000, 1.3107, 1.3107],
         [1.3107, 1.3107, 0.0000, 1.3107],
         [1.3107, 1.3107, 1.3107, 0.0000]]])

grad_names

['a/rho']