A collection of noise related classes and functions.
Specific noises inherit from the abstract class Noise, with each instance having its own RandomStream attribute – which is itself a Traited wrapper of Numpy’s RandomState.
This class provides the ability to create multiple random streams which can be independently seeded or set to an explicit state.
traits on this class:
- init_seed (A random seed)
A random seed used to initialise the state of an instance of numpy’s RandomState.default: 42
Defines a base class for noise. Specific noises are derived from this class for use in stochastic integrations.
[KloedenPlaten_1995] | Kloeden and Platen, Springer 1995, Numerical solution of stochastic differential equations. |
[ManellaPalleschi_1989] | Manella, R. and Palleschi V., Fast and precise algorithm for computer simulation of stochastic differential equations, Physical Review A, Vol. 40, Number 6, 1989. [3381-3385] |
[Mannella_2002] | Mannella, R., Integration of Stochastic Differential Equations on a Computer, Int J. of Modern Physics C 13(9): 1177–1194, 2002. |
[FoxVemuri_1988] | Fox, R., Gatland, I., Rot, R. and Vemuri, G., * Fast , accurate algorithm for simulation of exponentially correlated colored noise*, Physical Review A, Vol. 38, Number 11, 1988. [5938-5940] |
x.__init__(...) initializes x; see help(type(x)) for signature
Generate colored noise. [FoxVemuri_1988]
traits on this class:
- ntau (\(\tau\))
The noise correlation timedefault: 0.0range: low = 0.0 ; high = 20.0- random_stream (Random Stream)
An instance of numpy’s RandomState associated with this specific Noise object.default: None
Additive noise which, assuming the source noise is Gaussian with unit variance, will result in noise with a standard deviation of nsig.
traits on this class:
- nsig (\(D\))
The noise dispersion, it is the standard deviation of the distribution from which the Gaussian random variates are drawn. NOTE: Sensible values are typically ~<< 1% of the dynamic range of a Model’s state variables.default: [ 1.]range: low = 0.0 ; high = 10.0- ntau (\(\tau\))
The noise correlation timedefault: 0.0range: low = 0.0 ; high = 20.0- random_stream (Random Stream)
An instance of numpy’s RandomState associated with this specific Noise object.default: None
With “external” fluctuations the intensity of the noise often depends on the state of the system. This results in the (general) stochastic differential formulation:
for appropriate coefficients \(a(x)\) and \(b(x)\), which might be constants.
From [KloedenPlaten_1995], Equation 1.9, page 104.
traits on this class:
- b (\(b\))
A function evaluated on the state-variables, the result of which enters as the diffusion coefficient.default: Linear(bound=False, value=None)- nsig (\(D\))
The noise dispersion, it is the standard deviation of the distribution from which the Gaussian random variates are drawn. NOTE: Sensible values are typically ~<< 1% of the dynamic range of a Model’s state variables.default: [ 1.]range: low = 0.0 ; high = 10.0- ntau (\(\tau\))
The noise correlation timedefault: 0.0range: low = 0.0 ; high = 20.0- random_stream (Random Stream)
An instance of numpy’s RandomState associated with this specific Noise object.default: None