systems.base.utils.stochastic.NoiseCharacterizer

systems.base.utils.stochastic.NoiseCharacterizer(
    diffusion_expr,
    state_vars,
    control_vars,
    time_var=None,
)

Analyzes symbolic diffusion expressions to determine noise structure.

This is PURE ANALYSIS using only SymPy - no code generation, no numerical evaluation, no backend dependencies.

The analysis results enable: - Automatic selection of efficient specialized solvers - Validation of noise type claims - Optimization opportunities identification

Examples

>>> # Additive noise (constant)
>>> diffusion = sp.Matrix([[0.1], [0.2]])
>>> char = NoiseCharacterizer(diffusion, [x1, x2], [u])
>>> results = char.analyze()
>>> print(results.noise_type)
NoiseType.ADDITIVE
>>>
>>> # Multiplicative noise (state-dependent, non-diagonal)
>>> diffusion = sp.Matrix([[0.1 * x1, 0.05 * x2]])
>>> char = NoiseCharacterizer(diffusion, [x1, x2], [u])
>>> results = char.analyze()
>>> print(results.noise_type)
NoiseType.MULTIPLICATIVE
>>> print(results.is_multiplicative)
True

Attributes

Name	Description
characteristics	Get noise characteristics (cached after first analysis).

Methods

Name	Description
analyze	Analyze diffusion expression structure.
from_dict	Create NoiseCharacterizer from configuration dictionary.
get_optimization_hints	Provide optimization hints based on noise structure.
validate_noise_type_claim	Validate that a claimed noise_type matches actual structure.

analyze

systems.base.utils.stochastic.NoiseCharacterizer.analyze()

Analyze diffusion expression structure.

Returns

Name	Type	Description
	NoiseCharacteristics	Complete analysis of noise structure

Examples

>>> char = NoiseCharacterizer(diffusion, states, controls)
>>> results = char.analyze()
>>> if results.is_additive:
...     print("Use specialized additive-noise solver!")

from_dict

systems.base.utils.stochastic.NoiseCharacterizer.from_dict(config)

Create NoiseCharacterizer from configuration dictionary.

This is a convenience factory method for creating characterizers from dictionaries, such as test fixtures or saved configurations.

Parameters

Name	Type	Description	Default
config	Dict	Configuration dictionary with keys: - “diffusion” or “diffusion_expr”: Symbolic diffusion matrix - “state_vars”: List of state symbols - “control_vars”: List of control symbols - “time_var” (optional): Time symbol	required

Returns

Name	Type	Description
	NoiseCharacterizer	Initialized characterizer

Examples

>>> config = {
...     "diffusion": sp.Matrix([[0.1*x]]),
...     "state_vars": [x],
...     "control_vars": [u]
... }
>>> char = NoiseCharacterizer.from_dict(config)
>>> result = char.analyze()

With test fixtures:

>>> @pytest.fixture
... def my_noise():
...     return {"diffusion": ..., "state_vars": ..., "control_vars": ...}
>>>
>>> def test_something(my_noise):
...     char = NoiseCharacterizer.from_dict(my_noise)
...     # or equivalently:
...     char = NoiseCharacterizer(**my_noise)  # Now works!

get_optimization_hints

systems.base.utils.stochastic.NoiseCharacterizer.get_optimization_hints()

Provide optimization hints based on noise structure.

Returns

Name	Type	Description
	Dict[str, any]	Optimization opportunities and recommendations

Examples

>>> hints = char.get_optimization_hints()
>>> if hints['can_precompute']:
...     print("Can precompute constant noise!")

validate_noise_type_claim

systems.base.utils.stochastic.NoiseCharacterizer.validate_noise_type_claim(
    claimed_type,
)

Validate that a claimed noise_type matches actual structure.

Parameters

Name	Type	Description	Default
claimed_type	str	User’s claim about noise type (‘additive’, ‘diagonal’, etc.)	required

Returns

Name	Type	Description
	bool	True if claim matches analysis

Raises

Name	Type	Description
	ValueError	If claimed type contradicts analysis

Examples

>>> char = NoiseCharacterizer(diffusion, states, controls)
>>> char.validate_noise_type_claim('additive')  # Validates