utils

Utilities to help define hidden Markov models.

NamedFunc

Provides custom repr for functions.

Id_Obs(Nx)

Specify identity observations of entire state.

It is not a function of time.

Parameters:

Name	Type	Description	Default
Nx	int	Length of state vector	required

Returns:

Name	Type	Description
Obs	dict	Observation operator including size of the observation space, observation operator/model and tangent linear observation operator

Id_op()

Id operator (named). Returns first argument.

direct_obs_matrix(Nx, obs_inds)

Generate matrix that "picks" state elements obs_inds out of range(Nx).

Parameters:

Name	Type	Description	Default
Nx	int	Length of state vector	required
obs_inds	ndarray	Indices of elements of the state vector that are (directly) observed.	required

Returns:

Name	Type	Description
H	ndarray	The observation matrix for direct partial observations.

ens_compatible(func)

Decorate to transpose before and after, i.e. func(input.T).T.

This is helpful to make functions compatible with both 1d and 2d ndarrays.

This is not the_way™

Other tricks (ref mods) are sometimes more practical.

Examples:

mods.Lorenz63.dxdt, mods.DoublePendulum.dxdt

See Also

np.atleast_2d, np.squeeze, np.vectorize

linear_model_setup(ModelMatrix, dt0)

Make the Dyn/Obs field of a HMM representing a linear model.

Let M be the model matrix. Then

\[ x(t+dt) = M^{dt/dt0} x(t), \]

i.e.

\[ \frac{dx}{dt} = \frac{\log(M)}{dt0} x(t). \]

In typical use, dt0==dt (where dt is defined by the chronology). Anyways, dt must be an integer multiple of dt0.

Returns:

Type	Description
A `dict` with keys: 'M', 'model', 'linear'.

linspace_int(Nx, Ny, periodic=True)

Provide a range of Ny equispaced integers between 0 and Nx-1.

Parameters:

Name	Type	Description	Default
Nx	int	Range of integers	required
Ny	int	Number of integers	required
periodic	bool	Whether the vector is periodic. Determines if Nx == 0. Default: True	True

Returns:

Name	Type	Description
integers	ndarray	The list of integers.

Examples:

>>> linspace_int(10, 10)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> linspace_int(10, 4)
array([0, 2, 5, 7])
>>> linspace_int(10, 5)
array([0, 2, 4, 6, 8])

name_func(name)

Decorator for creating NamedFunc.

partial_Id_Obs(Nx, obs_inds)

Specify identity observations of a subset of obs. indices.

It is not a function of time.

Parameters:

Name	Type	Description	Default
Nx	int	Length of state vector	required
obs_inds	ndarray	The observed indices.	required

Returns:

Name	Type	Description
Obs	dict	Observation operator including size of the observation space, observation operator/model and tangent linear observation operator