types.core.DiffusionFunction

types.core.DiffusionFunction

Diffusion function g(x, u) for stochastic systems.

Returns noise gain matrix.

Parameters

Name	Type	Description	Default
x	StateVector	State (nx,)	required
u	Optional[ControlVector]	Control (nu,) or None	required

Returns

Name	Type	Description
	DiffusionMatrix	Diffusion matrix (nx, nw)

Examples

>>> # Additive noise (constant)
>>> def g_additive(x: StateVector, u: ControlVector) -> DiffusionMatrix:
...     return 0.1 * np.eye(nx)
>>> 
>>> # Multiplicative noise (state-dependent)
>>> def g_multiplicative(x: StateVector, u: ControlVector) -> DiffusionMatrix:
...     return np.diag(0.1 * np.abs(x))
>>> 
>>> # Geometric Brownian motion
>>> def g_gbm(x: StateVector, u: ControlVector) -> DiffusionMatrix:
...     return np.array([[sigma * x[0]]])

# types.core.DiffusionFunction { #cdesym.types.core.DiffusionFunction }

`types.core.DiffusionFunction`

Diffusion function g(x, u) for stochastic systems.

Returns noise gain matrix.

## Parameters {.doc-section .doc-section-parameters}

| Name   | Type                      | Description           | Default    |
|--------|---------------------------|-----------------------|------------|
| x      | StateVector               | State (nx,)           | _required_ |
| u      | Optional\[ControlVector\] | Control (nu,) or None | _required_ |

## Returns {.doc-section .doc-section-returns}

| Name   | Type            | Description               |
|--------|-----------------|---------------------------|
|        | DiffusionMatrix | Diffusion matrix (nx, nw) |

## Examples {.doc-section .doc-section-examples}

```python
>>> # Additive noise (constant)
>>> def g_additive(x: StateVector, u: ControlVector) -> DiffusionMatrix:
...     return 0.1 * np.eye(nx)
>>> 
>>> # Multiplicative noise (state-dependent)
>>> def g_multiplicative(x: StateVector, u: ControlVector) -> DiffusionMatrix:
...     return np.diag(0.1 * np.abs(x))
>>> 
>>> # Geometric Brownian motion
>>> def g_gbm(x: StateVector, u: ControlVector) -> DiffusionMatrix:
...     return np.array([[sigma * x[0]]])
```